text:
\section{Introduction}

Dimensionality reduction and manifold learning methods are widely useful for feature extraction, manifold unfolding, and data visualization.
The dimensionality reduction methods can be divided into three main categories, i.e., spectral methods, probabilistic methods, and neural network-based methods.
An example for spectral methods is Locally Linear Embedding (LLE) \cite{roweis2000nonlinear,saul2003think,ghojogh2020locally}. Examples for probabilistic methods are factor analysis \cite{fruchter1954introduction,child1990essentials} and probabilistic Principal Component Analysis (PCA) \cite{roweis1997algorithms,tipping1999probabilistic}. An example for neural network-based methods is variational autoencoder \cite{kingma2014auto} which formulates variational inference \cite{bishop2006pattern,blei2017variational,zhang2018advances,ghojogh2021factor} in an autoencoder framework.
In this short paper, we show theoretical connections between the fundamental methods of LLE, factor analysis, and probabilistic PCA. Hence, we connect the spectral and probabilistic approaches of dimensionality reduction.
We also explain why factor analysis and probabilistic PCA are linear and LLE is a nonlinear method.
In Section \ref{section_background}, we review the required background. Section \ref{section_stochastic_LLE} models the linear reconstruction of LLE stochastically. Finally, section \ref{section_conclusion} concludes the paper and discusses the connections of factor analysis, probabilistic PCA, and LLE algorithms.

\section{Technical Background and Preliminaries}\label{section_background}

\subsection{Marginal Multivariate Gaussian Distribution}

Consider two random variables $\ensuremath\boldsymbol{x}_1 \in \mathbb{R}^{d_1}$ and $\ensuremath\boldsymbol{x}_2 \in \mathbb{R}^{d_2}$ and let $\ensuremath\boldsymbol{x}_3 := [\ensuremath\boldsymbol{x}_1^\top, \ensuremath\boldsymbol{x}_2^\top]^\top \in \mathbb{R}^{d_1 + d_2}$. Assume that $\ensuremath\boldsymbol{x}_1$ and $\ensuremath\boldsymbol{x}_2$ are jointly multivariate Gaussian, i.e., $\ensuremath\boldsymbol{x}_3 \sim \mathcal{N}(\ensuremath\boldsymbol{x}_3; \ensuremath\boldsymbol{\mu}_3, \ensuremath\boldsymbol{\Sigma}_3)$.  The mean and covariance can be decomposed as:
\begin{align}
&\ensuremath\boldsymbol{\mu}_3 =  [\ensuremath\boldsymbol{\mu}_1^\top, \ensuremath\boldsymbol{\mu}_2^\top]^\top \in \mathbb{R}^{d_1 + d_2}, \quad \ensuremath\boldsymbol{\Sigma}_3 =
\begin{bmatrix}
\ensuremath\boldsymbol{\Sigma}_{11} & \ensuremath\boldsymbol{\Sigma}_{12} \\
\ensuremath\boldsymbol{\Sigma}_{21} & \ensuremath\boldsymbol{\Sigma}_{22}
\end{bmatrix}
\in \mathbb{R}^{(d_1 + d_2) \times (d_1 + d_2)},
\end{align}
where $\ensuremath\boldsymbol{\mu}_1 \in \mathbb{R}^{d_1}$, $\ensuremath\boldsymbol{\mu}_2 \in \mathbb{R}^{d_2}$, $\ensuremath\boldsymbol{\Sigma}_{11} \in \mathbb{R}^{d_1 \times d_2}$, $\ensuremath\boldsymbol{\Sigma}_{22} \in \mathbb{R}^{d_2 \times d_2}$, $\ensuremath\boldsymbol{\Sigma}_{12} \in \mathbb{R}^{d_1 \times d_2}$, and $\ensuremath\boldsymbol{\Sigma}_{21} = \ensuremath\boldsymbol{\Sigma}_{12}^\top$.

It can be shown that the marginal distributions for $\ensuremath\boldsymbol{x}_1$ and $\ensuremath\boldsymbol{x}_2$ are Gaussian distributions where $\mathbb{E}[\ensuremath\boldsymbol{x}_1] = \ensuremath\boldsymbol{\mu}_1$ and $\mathbb{E}[\ensuremath\boldsymbol{x}_2] = \ensuremath\boldsymbol{\mu}_2$.
The covariance matrix of the joint distribution can be simplified as \cite{ghojogh2021factor}:
\begin{align}\label{equation_covariance_marginal}
&\ensuremath\boldsymbol{\Sigma}_3 \! =\! \mathbb{E}\Bigg[
\begin{bmatrix}
(\ensuremath\boldsymbol{x}_1 - \ensuremath\boldsymbol{\mu}_1)(\ensuremath\boldsymbol{x}_1 - \ensuremath\boldsymbol{\mu}_1)^\top, (\ensuremath\boldsymbol{x}_1 - \ensuremath\boldsymbol{\mu}_1)(\ensuremath\boldsymbol{x}_2 - \ensuremath\boldsymbol{\mu}_2)^\top \\
(\ensuremath\boldsymbol{x}_2 - \ensuremath\boldsymbol{\mu}_2)(\ensuremath\boldsymbol{x}_1 - \ensuremath\boldsymbol{\mu}_1)^\top, (\ensuremath\boldsymbol{x}_2 - \ensuremath\boldsymbol{\mu}_2)(\ensuremath\boldsymbol{x}_2 - \ensuremath\boldsymbol{\mu}_2)^\top
\end{bmatrix}
\Bigg],
\end{align}
where $\mathbb{E}[.]$ is the expectation operator.
According to the definition of the multivariate Gaussian distribution, the conditional distribution is also a Gaussian distribution, i.e., $\ensuremath\boldsymbol{x}_2 | \ensuremath\boldsymbol{x}_1 \sim \mathcal{N}(\ensuremath\boldsymbol{x}_2; \ensuremath\boldsymbol{\mu}_{x_2|x_1}, \ensuremath\boldsymbol{\Sigma}_{x_2|x_1})$ where \cite{ghojogh2021factor}:
\begin{align}
&\mathbb{R}^{d_2} \ni \ensuremath\boldsymbol{\mu}_{x_2|x_1} := \ensuremath\boldsymbol{\mu}_2 + \ensuremath\boldsymbol{\Sigma}_{21}\ensuremath\boldsymbol{\Sigma}_{11}^{-1} (\ensuremath\boldsymbol{x}_1 - \ensuremath\boldsymbol{\mu}_1), \label{equation_mean_conditional_in_joint} \\
&\mathbb{R}^{d_2 \times d_2} \ni \ensuremath\boldsymbol{\Sigma}_{x_2|x_1} := \ensuremath\boldsymbol{\Sigma}_{22} - \ensuremath\boldsymbol{\Sigma}_{21}\ensuremath\boldsymbol{\Sigma}_{11}^{-1} \ensuremath\boldsymbol{\Sigma}_{12}, \label{equation_covariance_conditional_in_joint}
\end{align}
and likewise we have for $\ensuremath\boldsymbol{x}_1 | \ensuremath\boldsymbol{x}_2 \sim \mathcal{N}(\ensuremath\boldsymbol{x}_1; \ensuremath\boldsymbol{\mu}_{x_1|x_2}, \ensuremath\boldsymbol{\Sigma}_{x_1|x_2})$.
Also, note that the probability density function of $d$-dimensional Gaussian distribution is:
\begin{align}\label{equation_multivariate_Gaussian_PDF}
&\mathcal{N}(\ensuremath\boldsymbol{x}; \ensuremath\boldsymbol{\mu}, \ensuremath\boldsymbol{\Sigma})\! =\! \frac{1}{\sqrt{(2\pi)^d |\ensuremath\boldsymbol{\Sigma}|}} \exp\Big(\!\!- \frac{(\ensuremath\boldsymbol{x} - \ensuremath\boldsymbol{\mu})^\top \ensuremath\boldsymbol{\Sigma}^{-1} (\ensuremath\boldsymbol{x} - \ensuremath\boldsymbol{\mu})}{2}\Big),
\end{align}
where $|.|$ denotes the determinant of matrix.

\begin{figure}[!t]
\centering
\includegraphics[width=0.35in]{./images/PGM}
\caption{The probabilistic graphical model for stochastic linear reconstruction in LLE.}
\label{figure_PGM}
\end{figure}

\subsection{Variational Inference}

Assume data $\ensuremath\boldsymbol{x}_i$ is conditioned on a latent factor $\ensuremath\boldsymbol{w}_i$, as shown in Fig. \ref{figure_PGM}. Let the parameters of model be denoted by $\ensuremath\boldsymbol{\theta}$.
In variational inference, the Evidence Lower Bound (ELBO) is a lower bound on the log likelihood of data and is defined as minus Kullback-Leibler (KL) divergence between a distribution $q(.)$ on $\ensuremath\boldsymbol{w}_i$ and the joint distribution of $\ensuremath\boldsymbol{x}_i$ and $\ensuremath\boldsymbol{w}_i$, i.e., $\mathcal{L}(q, \ensuremath\boldsymbol{\theta}) := - \text{KL}\big(q(\ensuremath\boldsymbol{w}_i)\, \|\, \mathbb{P}(\ensuremath\boldsymbol{x}_i, \ensuremath\boldsymbol{w}_i\, |\, \ensuremath\boldsymbol{\theta})\big)$ \cite{ghojogh2021factor,bishop2006pattern,kingma2014auto}.
Maximizing this lower bound results in maximization of likelihood of data \cite{blei2017variational,zhang2018advances}.
Variational inference uses EM for Maximum Likelihood Estimation (MLE) \cite{ghojogh2021factor}:
\begin{align}
& q^{(t)}(\ensuremath\boldsymbol{w}_i) \gets \mathbb{P}(\ensuremath\boldsymbol{w}_i\, |\, \ensuremath\boldsymbol{x}_i, \ensuremath\boldsymbol{\theta}^{(t-1)}), \label{equation_E_step_variationalInference} \\
& \ensuremath\boldsymbol{\theta}^{(t)} \gets \arg \max_{\ensuremath\boldsymbol{\theta}}~ \mathbb{E}_{\sim q^{(t)}(\ensuremath\boldsymbol{w}_i)} \big[\log \mathbb{P}(\ensuremath\boldsymbol{x}_i, \ensuremath\boldsymbol{w}_i\, |\, \ensuremath\boldsymbol{\theta})\big], \label{equation_M_step_variationalInference}
\end{align}
where $\mathbb{E}[.]$ denotes expectation.
Here, we use the EM approach of variational inference for stochastic linear reconstruction in LLE.

\subsection{Factor Analysis}

Factor analysis \cite{fruchter1954introduction,child1990essentials} assumes that every data point $\ensuremath\boldsymbol{x}_i$ is generated from a latent factor $\ensuremath\boldsymbol{w}_i$. Its probabilistic graphical model is similar to Fig. \ref{figure_PGM} but with a small difference \cite{ghahramani1996algorithm}.
It assumes $\ensuremath\boldsymbol{x}_i$ is obtained by linear projection of $\ensuremath\boldsymbol{w}_i$ onto the space of data by projection matrix $\ensuremath\boldsymbol{\Lambda}$, then applying some linear translation, and finally adding a Gaussian noise $\ensuremath\boldsymbol{\epsilon}$ with covariance matrix $\ensuremath\boldsymbol{\Psi}$. This addition of noise is the main difference from the model depicted in Fig. \ref{figure_PGM}. If $\ensuremath\boldsymbol{\mu}$ denotes the mean of data, factor analysis considers:
\begin{align}
&\ensuremath\boldsymbol{x}_i := \ensuremath\boldsymbol{\Lambda} \ensuremath\boldsymbol{w}_i + \ensuremath\boldsymbol{\mu} + \ensuremath\boldsymbol{\epsilon}, \label{equation_factor_analysis} \\
&\mathbb{P}(\ensuremath\boldsymbol{x}_i\, |\, \ensuremath\boldsymbol{w}_i, \ensuremath\boldsymbol{\Lambda}, \ensuremath\boldsymbol{\mu}, \ensuremath\boldsymbol{\Psi}) = \mathcal{N}(\ensuremath\boldsymbol{x}_i; \ensuremath\boldsymbol{\Lambda} \ensuremath\boldsymbol{w}_i + \ensuremath\boldsymbol{\mu}, \ensuremath\boldsymbol{\Psi}), \label{equation_factor_analysis_likelihood_x_given_z}
\end{align}
where $\mathbb{P}(\ensuremath\boldsymbol{w}_i) = \mathcal{N}(\ensuremath\boldsymbol{w}_i; \ensuremath\boldsymbol{0}, \ensuremath\boldsymbol{I})$ and $\mathbb{P}(\ensuremath\boldsymbol{\epsilon}) = \mathcal{N}(\ensuremath\boldsymbol{\epsilon}; \ensuremath\boldsymbol{0}, \ensuremath\boldsymbol{\Psi})$. Factor analysis uses EM algorithm for finding optimum $\ensuremath\boldsymbol{\Lambda}$ and $\ensuremath\boldsymbol{\Psi}$ (see \cite{ghojogh2021factor} for details of EM in factor analysis).
We will show that the stochastic linear reconstruction in LLE, for modeling the relation between a data point and its latent reconstruction weights, is similar to Eq. (\ref{equation_factor_analysis}).

\subsection{Probabilistic PCA}

Probabilistic PCA \cite{roweis1997algorithms,tipping1999probabilistic} is a special case of factor analysis where the variance of noise is equal in all dimensions of data space with covariance between dimensions, i.e.:
\begin{align}\label{equation_PPCA_Psi}
\ensuremath\boldsymbol{\Psi} = \sigma^2 \ensuremath\boldsymbol{I}.
\end{align}
In other words, probabilistic PCA considers an isotropic noise model.
Similar to factor analysis, it can be solved iteratively using EM \cite{roweis1997algorithms}. However, one can also find a closed-form solution to its EM approach \cite{tipping1999probabilistic}.
Hence, by restricting the noise covariance to be isotropic, its solution becomes simpler and closed-form. See \cite{ghojogh2021factor} for details of derivations and solutions for probabilistic PCA.

\section{Stochastic Modeling of Linear Reconstruction in LLE}\label{section_stochastic_LLE}

\subsection{Notations and Joint and Conditional Distributions}

LLE \cite{roweis2000nonlinear,saul2003think} has two main steps which are linear reconstruction and linear embedding \cite{ghojogh2020locally}.
As Fig. \ref{figure_PGM} depicts, the linear reconstruction step of LLE can be seen stochastically where every point $\ensuremath\boldsymbol{x}_i$ is conditioned on and generated by its reconstruction weights $\ensuremath\boldsymbol{w}_i$ as a latent factor.
Therefore, $\ensuremath\boldsymbol{x}_i$ can be written as a stochastic function of $\ensuremath\boldsymbol{w}_i$ where we assume $\ensuremath\boldsymbol{w}_i$ has a multivariate Gaussian distribution:
\begin{align}
&\ensuremath\boldsymbol{x}_i = \ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{w}_i + \ensuremath\boldsymbol{\mu}, \label{equation_x_X_w} \\
&\mathbb{P}(\ensuremath\boldsymbol{w}_i) = \mathcal{N}(\ensuremath\boldsymbol{w}_i; \ensuremath\boldsymbol{0}, \ensuremath\boldsymbol{\Omega}_i) \implies \mathbb{E}[\ensuremath\boldsymbol{w}_i] = \ensuremath\boldsymbol{0}, ~~\mathbb{E}[\ensuremath\boldsymbol{w}_i \ensuremath\boldsymbol{w}_i^\top] = \ensuremath\boldsymbol{\Omega}_i, \label{equation_prior_w}
\end{align}
where $\ensuremath\boldsymbol{\Omega}_i \in \mathbb{R}^{k \times k}$ is covariance of $\ensuremath\boldsymbol{w}_i$ and $\ensuremath\boldsymbol{\mu} \in \mathbb{R}^d$ is the mean of data because $(1/n) \sum_{i=1}^n \ensuremath\boldsymbol{x}_i = \mathbb{E}[\ensuremath\boldsymbol{x}_i] = \ensuremath\boldsymbol{X}_i \mathbb{E}[\ensuremath\boldsymbol{w}_i] + \ensuremath\boldsymbol{\mu} \overset{(\ref{equation_prior_w})}{=} \ensuremath\boldsymbol{0} + \ensuremath\boldsymbol{\mu} = \ensuremath\boldsymbol{\mu}$.
According to Eq. (\ref{equation_covariance_marginal}), for the joint distribution of $[\ensuremath\boldsymbol{x}_i^\top, \ensuremath\boldsymbol{w}_i^\top]^\top \in \mathbb{R}^{d + k}$,  we have:
\begin{alignat*}{2}
&\ensuremath\boldsymbol{\Sigma}_{11} &&= \mathbb{E}[(\ensuremath\boldsymbol{x}_i - \ensuremath\boldsymbol{\mu}) (\ensuremath\boldsymbol{x}_i - \ensuremath\boldsymbol{\mu})^\top] \overset{(\ref{equation_x_X_w})}{=} \mathbb{E}[(\ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{w}_i) (\ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{w}_i)^\top] = \ensuremath\boldsymbol{X}_i \mathbb{E}[\ensuremath\boldsymbol{w}_i \ensuremath\boldsymbol{w}_i^\top] \ensuremath\boldsymbol{X}_i^\top \overset{(\ref{equation_prior_w})}{=} \ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{\Omega}_i \ensuremath\boldsymbol{X}_i^\top, \\
&\ensuremath\boldsymbol{\Sigma}_{12} &&= \mathbb{E}[(\ensuremath\boldsymbol{x}_i - \ensuremath\boldsymbol{\mu}) (\ensuremath\boldsymbol{w}_i - \ensuremath\boldsymbol{0})^\top] \overset{(\ref{equation_x_X_w})}{=} \ensuremath\boldsymbol{X}_i \mathbb{E}[\ensuremath\boldsymbol{w}_i \ensuremath\boldsymbol{w}_i^\top] \overset{(\ref{equation_prior_w})}{=} \ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{\Omega}_i, \\
&\ensuremath\boldsymbol{\Sigma}_{22} &&= \mathbb{E}[(\ensuremath\boldsymbol{w}_i - \ensuremath\boldsymbol{0}) (\ensuremath\boldsymbol{w}_i - \ensuremath\boldsymbol{0})^\top] = \mathbb{E}[\ensuremath\boldsymbol{w}_i \ensuremath\boldsymbol{w}_i^\top] \overset{(\ref{equation_prior_w})}{=} \ensuremath\boldsymbol{\Omega}_i.
\end{alignat*}
Hence:
\begin{align}\label{equation_joint_distribution_x_w}
\begin{bmatrix}
\ensuremath\boldsymbol{x}_{i} \\
\ensuremath\boldsymbol{w}_{i}
\end{bmatrix}
\sim
\mathcal{N}\Bigg(
\begin{bmatrix}
\ensuremath\boldsymbol{x}_i \\
\ensuremath\boldsymbol{w}_i
\end{bmatrix}
;
\begin{bmatrix}
\ensuremath\boldsymbol{\mu} \\
\ensuremath\boldsymbol{0}
\end{bmatrix}
,
\begin{bmatrix}
\ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{\Omega}_i \ensuremath\boldsymbol{X}_i^\top & \ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{\Omega}_i \\
\ensuremath\boldsymbol{\Omega}_i^\top \ensuremath\boldsymbol{X}_i^\top & \ensuremath\boldsymbol{\Omega}_i
\end{bmatrix}
\Bigg).
\end{align}
We have:
\begin{align}\label{equation_x_given_w}
&\mathbb{P}(\ensuremath\boldsymbol{x}_i\, |\, \ensuremath\boldsymbol{w}_i, \ensuremath\boldsymbol{\Omega}_i) \overset{(a)}{=} \mathcal{N}(\ensuremath\boldsymbol{x}_i; \ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{w}_i + \ensuremath\boldsymbol{\mu}, \ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{\Omega}_i \ensuremath\boldsymbol{X}_i^\top),
\end{align}
where $(a)$ is because of Eqs. (\ref{equation_x_X_w}) and (\ref{equation_joint_distribution_x_w}).
We can use EM for MLE in stochastic linear reconstruction of LLE. In the following, the steps of EM are explained.

\subsection{E-Step in Expectation Maximization}

As we will see later in the M-step of EM, we will have two expectation terms which need to be computed in the E-step. These expectations, which are over the $q(\ensuremath\boldsymbol{w}_i) := \mathbb{P}(\ensuremath\boldsymbol{w}_i\, |\, \ensuremath\boldsymbol{x}_i)$ distribution, are $\mathbb{E}_{\sim q^{(t)}(\ensuremath\boldsymbol{w}_i)}[\ensuremath\boldsymbol{w}_i] \in \mathbb{R}^k$ and $\mathbb{E}_{\sim q^{(t)}(\ensuremath\boldsymbol{w}_i)}[\ensuremath\boldsymbol{w}_i \ensuremath\boldsymbol{w}_i^\top] \in \mathbb{R}^{k \times k}$ where $t$ denotes the iteration index in EM iterations.
According to Eqs. (\ref{equation_mean_conditional_in_joint}), (\ref{equation_covariance_conditional_in_joint}), and (\ref{equation_joint_distribution_x_w}), we have:
\begin{align}
&\mathbb{E}_{\sim q^{(t)}(\ensuremath\boldsymbol{w}_i)}[\ensuremath\boldsymbol{w}_i] = \ensuremath\boldsymbol{\mu}_{w|x} = \ensuremath\boldsymbol{\Omega}_i^\top \ensuremath\boldsymbol{X}_i^\top (\ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{\Omega}_i \ensuremath\boldsymbol{X}_i^\top)^{\dagger} (\ensuremath\boldsymbol{x}_i - \ensuremath\boldsymbol{\mu}), \label{E_step_expectation_w} \\
&\mathbb{E}_{\sim q^{(t)}(\ensuremath\boldsymbol{w}_i)}[\ensuremath\boldsymbol{w}_i \ensuremath\boldsymbol{w}_i^\top] = \ensuremath\boldsymbol{\Sigma}_{w|x} = \ensuremath\boldsymbol{\Omega}_i - \ensuremath\boldsymbol{\Omega}_i^\top \ensuremath\boldsymbol{X}_i^\top (\ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{\Omega}_i \ensuremath\boldsymbol{X}_i^\top)^{\dagger} \ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{\Omega}_i, \label{E_step_expectation_w_w}
\end{align}
where $^\dagger$ denotes either inverse or pseudo-inverse of matrix.

\subsection{M-Step in Expectation Maximization}

In M-step of EM, we maximize the joint likelihood of data and weights over all $n$ data points where the optimization variable is the covariance of prior distribution of weights:
\begin{align}
& \max_{\{\ensuremath\boldsymbol{\Omega}_i\}_{i=1}^n}~ \sum_{i=1}^n \mathbb{E}_{\sim q^{(t)}(\ensuremath\boldsymbol{w}_i)} \big[\log \mathbb{P}(\ensuremath\boldsymbol{x}_i, \ensuremath\boldsymbol{w}_i\, |\, \ensuremath\boldsymbol{\Omega}_i)\big] \nonumber \\
&\overset{(a)}{=} \max_{\{\ensuremath\boldsymbol{\Omega}_i\}_{i=1}^n}~ \sum_{i=1}^n \Big( \mathbb{E}_{\sim q^{(t)}(\ensuremath\boldsymbol{w}_i)} \big[\log \mathbb{P}(\ensuremath\boldsymbol{x}_i\, |\, \ensuremath\boldsymbol{w}_i, \ensuremath\boldsymbol{\Omega}_i)\big] + \mathbb{E}_{\sim q^{(t)}(\ensuremath\boldsymbol{w}_i)} \big[\log \mathbb{P}(\ensuremath\boldsymbol{w}_i)\big] \Big) \nonumber\\
& \overset{(b)}{=} \max_{\{\ensuremath\boldsymbol{\Omega}_i\}_{i=1}^n} \sum_{i=1}^n \Big( \mathbb{E}_{\sim q^{(t)}(\ensuremath\boldsymbol{w}_i)} \big[\log \mathcal{N}(\ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{w}_i + \ensuremath\boldsymbol{\mu}, \ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{\Omega}_i \ensuremath\boldsymbol{X}_i^\top) \big]   + \mathbb{E}_{\sim q^{(t)}(\ensuremath\boldsymbol{w}_i)} \big[\log \mathcal{N}(\ensuremath\boldsymbol{0}, \ensuremath\boldsymbol{\Omega}_i) )\big] \Big) \nonumber
\end{align}
\begin{align}
&\overset{(\ref{equation_multivariate_Gaussian_PDF})}{=} \max_{\{\ensuremath\boldsymbol{\Omega}_i\}_{i=1}^n}~ \Big( \underbrace{-\frac{d\,n}{2} \log(2\pi)}_\text{constant} - \frac{n}{2} \log |\ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{\Omega}_i \ensuremath\boldsymbol{X}_i^\top| \nonumber \\
&- \frac{1}{2} \sum_{i=1}^n \mathbb{E}_{\sim q^{(t)}(\ensuremath\boldsymbol{w}_i)} \big[ (\ensuremath\boldsymbol{x}_i - \ensuremath\boldsymbol{X}_i\ensuremath\boldsymbol{w}_i - \ensuremath\boldsymbol{\mu})^\top (\ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{\Omega}_i \ensuremath\boldsymbol{X}_i^\top)^{-1}  (\ensuremath\boldsymbol{x}_i - \ensuremath\boldsymbol{X}_i\ensuremath\boldsymbol{w}_i - \ensuremath\boldsymbol{\mu}) \big] \nonumber\\
&-\underbrace{\frac{k\,n}{2} \log(2\pi)}_\text{constant}  - \frac{n}{2} \log |\ensuremath\boldsymbol{\Omega}_i| - \frac{1}{2} \sum_{i=1}^n \mathbb{E}_{\sim q^{(t)}(\ensuremath\boldsymbol{w}_i)} \big[ \ensuremath\boldsymbol{w}_i^\top \ensuremath\boldsymbol{\Omega}_i^{-1} \ensuremath\boldsymbol{w}_i \big] \Big) \nonumber\\
&\overset{(c)}{=} \max_{\{\ensuremath\boldsymbol{\Omega}_i\}_{i=1}^n} \Big(\!\! - \frac{n}{2} \log |\ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{\Omega}_i \ensuremath\boldsymbol{X}_i^\top| - \frac{n}{2} \textbf{tr}\big((\ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{\Omega}_i \ensuremath\boldsymbol{X}_i^\top)^{-1} \ensuremath\boldsymbol{S}_1\big)  - \frac{n}{2} \log |\ensuremath\boldsymbol{\Omega}_i| - \frac{n}{2} \textbf{tr}\big( \ensuremath\boldsymbol{\Omega}_i^{-1} \ensuremath\boldsymbol{S}_2 \big) \Big), \label{equation_joint_likelihood}
\end{align}
where $(a)$ is because of the chain rule $\mathbb{P}(\ensuremath\boldsymbol{x}_i, \ensuremath\boldsymbol{w}_i\, |\, \ensuremath\boldsymbol{\Omega}_i) = \mathbb{P}(\ensuremath\boldsymbol{x}_i\, |\, \ensuremath\boldsymbol{w}_i, \ensuremath\boldsymbol{\Omega}_i)\, \mathbb{P}(\ensuremath\boldsymbol{w}_i)$, and $(b)$ is because of Eqs. (\ref{equation_prior_w}) and (\ref{equation_x_given_w}), and $(c)$ is because we define the scatters $\ensuremath\boldsymbol{S}_1$ and $\ensuremath\boldsymbol{S}_2$ as:
\begin{align}
&\mathbb{R}^{d \times d} \ni \ensuremath\boldsymbol{S}_1 := \frac{1}{n} \sum_{i=1}^n \mathbb{E}_{\sim q^{(t)}(\ensuremath\boldsymbol{w}_i)} \big[ (\ensuremath\boldsymbol{x}_i - \ensuremath\boldsymbol{X}_i\ensuremath\boldsymbol{w}_i - \ensuremath\boldsymbol{\mu})  (\ensuremath\boldsymbol{x}_i - \ensuremath\boldsymbol{X}_i\ensuremath\boldsymbol{w}_i - \ensuremath\boldsymbol{\mu})^\top \big] \quad\quad\quad\quad\quad\quad\quad\quad \nonumber
\end{align}
\begin{align}
&= \frac{1}{n} \sum_{i=1}^n \Big( (\ensuremath\boldsymbol{x}_i - \ensuremath\boldsymbol{\mu}) (\ensuremath\boldsymbol{x}_i - \ensuremath\boldsymbol{\mu})^\top  - 2 \ensuremath\boldsymbol{X}_i \mathbb{E}_{\sim q^{(t)}(\ensuremath\boldsymbol{w}_i)} \big[ \ensuremath\boldsymbol{w}_i \big] (\ensuremath\boldsymbol{x}_i - \ensuremath\boldsymbol{\mu})^\top  + \ensuremath\boldsymbol{X}_i \mathbb{E}_{\sim q^{(t)}(\ensuremath\boldsymbol{w}_i)} \big[ \ensuremath\boldsymbol{w}_i \ensuremath\boldsymbol{w}_i^\top \big] \ensuremath\boldsymbol{X}_i^\top \Big), \label{equation_S1}
\end{align}
\begin{align}
&\mathbb{R}^{k \times k} \ni \ensuremath\boldsymbol{S}_2 := \frac{1}{n} \sum_{i=1}^n \mathbb{E}_{\sim q^{(t)}(\ensuremath\boldsymbol{w}_i)} \big[ \ensuremath\boldsymbol{w}_i \ensuremath\boldsymbol{w}_i^\top \big], \label{equation_S2}
\end{align}
where the expectation terms are found by Eqs. (\ref{E_step_expectation_w}) and (\ref{E_step_expectation_w_w}).
The gradient of the joint likelihood is:
\begin{equation}\label{equation_gradient_joint_likelihood}
\begin{aligned}
\mathbb{R}^{k \times k} \ni \frac{\partial \text{ Eq. } (\ref{equation_joint_likelihood})}{\partial \ensuremath\boldsymbol{\Omega}_i^{-1}} = &\frac{n}{2} \Big[ \textbf{vec}^{-1}_{k \times k} \big[ \ensuremath\boldsymbol{T}_i\, \textbf{vec}_{d^2 \times 1}(\ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{\Omega}_i \ensuremath\boldsymbol{X}_i^\top) \big] \\
&- \textbf{vec}^{-1}_{k \times k} \big[ \ensuremath\boldsymbol{T}_i\, \textbf{vec}_{d^2 \times 1}(\ensuremath\boldsymbol{S}_1) \big] + \ensuremath\boldsymbol{\Omega}_i - \ensuremath\boldsymbol{S}_2 \Big],
\end{aligned}
\end{equation}
where we use the Magnus-Neudecker convention in which matrices are vectorized, $\textbf{vec}(.)$ vectorizes the matrix, $\textbf{vec}^{-1}_{k \times k}(.)$ is de-vectorization to $k \times k$ matrix, $\otimes$ denotes the Kronecker product, and $\mathbb{R}^{k^2 \times d^2} \ni \ensuremath\boldsymbol{T}_i := \ensuremath\boldsymbol{X}_i^\top \otimes \ensuremath\boldsymbol{X}_i^\top$.
In the M-step, one can update the variables $\{\ensuremath\boldsymbol{\Omega}_i\}_{i=1}^n$ using gradient descent with the gradient in Eq. (\ref{equation_gradient_joint_likelihood}). However, we can relax the covariance matrix and simplify the algorithm.

\subsection{Relaxation of Covariance}

Inspired by relaxation of factor analysis for probabilistic PCA (see Eq. (\ref{equation_PPCA_Psi})), we can relax the covariance matrix to be spherical, i.e., diagonal and the variance of weights to be equal in all $k$ dimensions:
\begin{align}\label{equation_diagonal_Omega_covariance}
\ensuremath\boldsymbol{\Omega}_i = \sigma_i \ensuremath\boldsymbol{I} \in \mathbb{R}^{k \times k}.
\end{align}
Substituting this covariance into Eq. (\ref{equation_joint_likelihood}) and noticing the properties of determinant and trace gives:
\begin{align}
&\max_{\{\sigma_i\}_{i=1}^n} \Big(\!\! - \frac{n}{2} \log (\sigma_i^d |\ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{X}_i^\top|) - \frac{n}{2} \sigma_i^{-1} \textbf{tr}\big((\ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{X}_i^\top)^{-1} \ensuremath\boldsymbol{S}_1\big)  - \frac{n}{2} \log \sigma_i^k - \frac{n}{2} \sigma_i^{-1} \textbf{tr}\big( \ensuremath\boldsymbol{S}_2 \big) \Big) \nonumber \\
&\overset{(a)}{=} \max_{\{\sigma_i\}_{i=1}^n} \Big(\!\! - \frac{n}{2} (d + k) \log (\sigma_i)  - \frac{n}{2} \Big[ \textbf{tr}\big((\ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{X}_i^\top)^{-1} \ensuremath\boldsymbol{S}_1\big) - \textbf{tr}\big( \ensuremath\boldsymbol{S}_2 \big) \Big] \sigma_i^{-1} \Big), \label{equation_joint_likelihood_relaxed}
\end{align}
where $(a)$ is because $\log (\sigma_i^d |\ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{X}_i^\top|) = d\log (\sigma_i) + \log (|\ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{X}_i^\top|)$ whose second term is a constant w.r.t. $\sigma_i$.
Setting the gradient of the joint likelihood to zero gives:
\begin{align}
&\mathbb{R} \ni \frac{\partial \text{ Eq. } (\ref{equation_joint_likelihood_relaxed})}{\partial \sigma_i^{-1}} = \frac{n}{2} \Big[ (d + k) \sigma_i  - \Big( \textbf{tr}\big((\ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{X}_i^\top)^{-1} \ensuremath\boldsymbol{S}_1\big) + \textbf{tr}(\ensuremath\boldsymbol{S}_2) \Big) \Big] \overset{\text{set}}{=} 0 \nonumber \\
&\implies \sigma_i = (d + k)^{-1} \Big( \textbf{tr}\big((\ensuremath\boldsymbol{X}_i \ensuremath\boldsymbol{X}_i^\top)^{\dagger} \ensuremath\boldsymbol{S}_1\big) + \textbf{tr}(\ensuremath\boldsymbol{S}_2) \Big), \label{equation_variance_M_step}
\end{align}
where $^\dagger$ denotes either inverse or pseudo-inverse of matrix.
As we also have in probabilistic PCA, the relaxation of covariance matrix results in the closed-form solution of Eq. (\ref{equation_variance_M_step}).
Without this relaxation, the solution of M-step in EM algorithm of LLE is solved iteratively by the gradient in Eq. (\ref{equation_gradient_joint_likelihood}).

The EM algorithm for stochastic linear reconstruction in LLE is summarized in Algorithm \ref{algorithm_linear_reconstruction_EM}.
We can sample $\{\ensuremath\boldsymbol{w}_i\}_{i=1}^n$ with the following prior and conditional distributions:
\begin{align}
& \ensuremath\boldsymbol{w}_i \sim \mathcal{N}(\ensuremath\boldsymbol{w}_i; \ensuremath\boldsymbol{0}, \sigma_i \ensuremath\boldsymbol{I}), \\
& \ensuremath\boldsymbol{w}_i\, |\, \ensuremath\boldsymbol{x}_i \sim \mathcal{N}(\ensuremath\boldsymbol{w}_i; \ensuremath\boldsymbol{\mu}_{w | x}, \ensuremath\boldsymbol{\Sigma}_{w | x}), \label{equation_distribution_w_given_x}
\end{align}
where $\ensuremath\boldsymbol{\mu}_{w | x}$ and $\ensuremath\boldsymbol{\Sigma}_{w | x}$ are defined in Eqs. (\ref{E_step_expectation_w}) and (\ref{E_step_expectation_w_w}), respectively.

\SetAlCapSkip{0.5em}
\IncMargin{0.8em}
\begin{algorithm2e}[!t]
\footnotesize
\DontPrintSemicolon
    \textbf{Input: } $\{\ensuremath\boldsymbol{x}_i\}_{i=1}^n$, $k$NN graph or $\{\ensuremath\boldsymbol{X}_i\}_{i=1}^n$ \;
    \textbf{Initialize: } $\{\ensuremath\boldsymbol{\Omega}_i\}_{i=1}^n = \ensuremath\boldsymbol{I}$\;
    \While{not converged}{
        // E-step:\;
        \For{every data point $i$ from $1$ to $n$}{
            Calculate expectations by Eqs. (\ref{E_step_expectation_w}) and (\ref{E_step_expectation_w_w})\;
        }
        // Sampling:\;
        Sample weights $\{\ensuremath\boldsymbol{w}_i\}_{i=1}^n$ using Eq. (\ref{equation_distribution_w_given_x})\;
        // M-step:\;
        Calculate $\ensuremath\boldsymbol{S}_1$ and $\ensuremath\boldsymbol{S}_2$ using Eqs. (\ref{equation_S1}) and (\ref{equation_S2})\;
        \For{every data point $i$ from $1$ to $n$}{
            Calculate $\sigma_i$ by Eq. (\ref{equation_variance_M_step})\;
            Calculate $\ensuremath\boldsymbol{\Omega}_i$ using Eq. (\ref{equation_diagonal_Omega_covariance})\;
        }
    }
    \textbf{Return} weights $\{\ensuremath\boldsymbol{w}_i\}_{i=1}^n$\;
\caption{Stochastic Linear Reconstruction in LLE with EM}\label{algorithm_linear_reconstruction_EM}
\end{algorithm2e}
\DecMargin{0.8em}

\section{Conclusion and Discussion on the Connection of Methods}\label{section_conclusion}

Comparing Eqs. (\ref{equation_factor_analysis}) and (\ref{equation_x_X_w}) shows that data point $\ensuremath\boldsymbol{x}_i$ is conditioned on some latent variable $\ensuremath\boldsymbol{w}_i$, in all methods of factor analysis \cite{fruchter1954introduction,child1990essentials}, probabilistic PCA \cite{roweis1997algorithms,tipping1999probabilistic}, and LLE \cite{roweis2000nonlinear,saul2003think}. In these methods, the latent variable $\ensuremath\boldsymbol{w}_i$ is related to data $\ensuremath\boldsymbol{x}_i$ using a transformation matrix.
In factor analysis and probabilistic PCA (see Eq. (\ref{equation_factor_analysis})), this transformation matrix is a global matrix $\ensuremath\boldsymbol{\Lambda}$ so it is data-independent in the sense that it is the same matrix for all data points. However, the transformation matrix of LLE is $\ensuremath\boldsymbol{X}_i$ (see Eq. (\ref{equation_x_X_w})) which is local and data-dependent in the sense that it is different for every data point. This explains why factor analysis and probabilistic PCA are linear methods and LLE is a nonlinear algorithm.
Moreover, in this framework, if the covariance matrix is relaxed to be spherical (see Eqs. (\ref{equation_PPCA_Psi}) and (\ref{equation_diagonal_Omega_covariance})), the solution becomes closed-form. This relaxation happens in probabilistic PCA and can also be used in LLE to have a closed-form solution (see Eq. (\ref{equation_variance_M_step})).
Finally, the introduced relation of the three algorithms opens the door for more investigation in relation of spectral and probabilistic approaches of machine learning.

\printbibliography[heading=subbibintoc]

\end{document}

redpajama_set_name: RedPajamaArXiv


Production is scheduled to begin in late 2020. Fargo season 4 release date - 2020, to be announced.
The site of the series, based on the film of the Coen brothers, is the border between the US states of North and South Dakota, as well as Minnesota, where all kinds of criminal gangs are bogging down and the often overwhelmed police are struggling with all the bloody chaos And order.
Season 3: The rivalry between the two brothers Emmit and Ray Stussy (both Ewan McGregor) continues to grow and finally crush the two into a criminal world full of murder, violence and unscrupulous gangster bosses.
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What can you learn about the TV series: Fargo season 4?
Fargo is an American Crimean, created and written by Noah Hawley. The series is both a loose adaptation as well as a spin-off of the eponymous film of Ethan and Joel Coen from the year 1996. The Coen brothers are executive producers in the series. In the United States, the series started on 15 April 2014 on FX, Austria, Switzerland and Germany in September 2014 on Netflix. The first broadcast of the second season took place in the USA on 12 October 2015 and in Austria, Switzerland and Germany on 14 October 2015. In November 2015 FX extended the series by a third season, which has been aired since 19 April 2017 in the US.
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Emily Kinney of "The Walking Dead" rocks the red carpet at the "Mad Men" Season 5 Premiere in a SENA Mini Harness Dress. Emily looks beautiful!
Want your own SENA Mini Harness Dress? Just your luck, it's is available here for purchase.
LeToya Luckett celebrated her 30th Birthday in a red SENA Cutout Dress in LA with longtime friends Kelly Rowland and Brandy. Work it!
Love it! Was pleasantly surprised to see that Catt Sadler's Twitter Profile Pic is of her wearing a SENA Slit Maxi Dress in red from when she hosted Cosmo's Fun Fearless Male Awards in New York City! Work it out Catt!
Spotted…Paris Hilton in a red SENA Cutout Dress at Marquee in Vegas!
The gorgeous Catt Sadler wore a red SENA Slit Maxi Dress from our current Spring 2011 Collection while hosting Cosmopolitan's Fun Fearless Male Awards at the Mandarin Oriental in NYC. In attendance were actors Russell Brand, Ian Somerhalder, Mila Kunis, and Penn Badgley. Catt was a knockout in this SENA Dress and she even tweeted about it!


text:
Mexican Artist Enlists Aid Of Illegal Immigrants In Building Wall In New York City "Art" Display
By Susan Wright | 11:30 AM on July 04, 2017
FILE - In this Jan. 4, 2016 photo, a U.S. Border Patrol agent drives near the U.S.-Mexico border fence in Santa Teresa, N.M. Can Donald Trump really make good on his promise to build a wall along the 2,000-mile U.S.-Mexican border to prevent illegal migration? What's more, can he make Mexico pay for it? Sure, he can build it, but it's not nearly as simple as he says. (AP Photo/Russell Contreras)
I loathe political statements-as-art.
Somebody alert ICE. It would serve them right.
According to the Washington Examiner, a Mexican artist is hoping to enlist the aid of other illegal immigrants to help him put on an art exhibit in New York City, meant as a jab against President Trump's border wall.
Bosco Sodi, a painter born in Mexico City, and a team of collaborators will create the six-foot high wall installation in a city park in September and then allow visitors to disassemble the installation and take pieces home, the New York Times reported.
Trump's wall, at this point, is simply the stuff of imagination. There have been reports of prototypes, solar walls, big, beautiful doors, and any amount of rhetoric, but Trump's administration recently decided to keep President Obama's "Dreamers" program in place, and there's no actual date for beginning construction on the wall.
Sodi's artistic protest may be for nothing.
Sodi told the Times that the wall has political significance because the "timbers" were made of clay from Oaxaca, Mexico, and were fired by people who had entered the United States illegally.
"I wanted to create a wall made by Mexicans with Mexican earth," Sodi told the newspaper. "Then the disappearance of the wall will be by the community and all kinds of people who visit the park."
Just for the sake of discussion, what happens if people actually start adding to the wall, rather than taking away?
This has all the significance of the "Fearless Girl" statue that faces down the "Charging Bull" sculpture in New York. The "Charging Bull" was placed in front of the New York Stock Exchange after the market crash of 1987, as a symbol of America's financial resilience.
And by "all the significance of," I mean it's just as stupid and pointless.
Tags: BORDER WALL NEW YORK

redpajama_set_name: RedPajamaCommonCrawl


text:
Counter Markets
Financial Newsletter for Free Marketeers and Libertarian Entrepreneurs
Counter Markets Newsletter
The Hidden Costs Behind Every Government Program
August 24, 2019 by Counter Markets
By Gor Mkrtchian
When the State constructs a new bike lane, school, or begins a new space mission, the natural inclination of the majority is to cheer this new endeavor as progressive. We possess one new structure or have accomplished one new task than before; society has moved forward, the thinking goes.
The State is responsible for truly technically impressive or beautiful accomplishments like the Apollo missions, the Moscow Metro, the Palace of Versailles, etc. that most would agree clearly produce benefits for society.
Confronted with these concrete and widely celebrated examples of government accomplishments, how can libertarians deny that state action is sometimes a benevolent force in society?
Leaving aside moral considerations and focusing on utilitarian considerations, the answer revolves around opportunity cost and demonstrated preference.
Opportunity cost is the benefits that could have been obtained through the best forgone alternative to an actual employment of resources. If a slice of pizza costs two dollars, and a hamburger costs two dollars, then the opportunity cost of a slice of pizza is a hamburger, and visa-versa.
The resources of any given country are scarce, and the "economic question" that must be solved is, how should the limited resources available be applied to best satisfy people's subjective preferences?
Even if, for example, the State builds a library that is beautiful, the books are neatly organized, the librarian is competent and cordial, the temperature is well-regulated, and the computers are state of the art, we still need to hold our applause.
In order to be able to celebrate the employment of resources by the State in a particular application, it's necessary to consider the alternative uses that could have been possible with those resources. If there exists an alternative option that could have better satisfied subjective preferences, then the actual employment, even if it produced benefits, was a relative failure.
Voluntary Exchange and Demonstrated Preference
Now the question is: by what standard can it be determined which employment of resources is best, relative to the subjective preferences of consumers, in any given case?
In instances of voluntary exchange, every exchange is not only ex-ante mutually beneficial, it's ex-ante the best employment of the resources being exchanged, from the perspectives of the respective property owners. This is called demonstrated preference, which Rothbard explains to mean, "simply this: that actual choice reveals, or demonstrates, a man's preferences; that is, that his preferences are deducible from what he has chosen in action."
For example, if Smith sells Jones a lamp for twenty dollars, we can know that of all of the alternative uses of the lamp Smith had available to him, such as using it to read, using it as a decoration, keeping it in storage, etc., selling it to Jones for twenty dollars was his most highly preferred option, because that is the option that he freely chose.
Likewise, Jones thought buying Smith's lamp was the best of all possible uses available to him of his twenty dollars. Otherwise, he wouldn't have executed that option.
Involuntary Exchange
On the other hand, sometimes exchange, production, and consumption are not conducted as a result of the voluntary decisions of all of the owners of the property involved, but rather under compulsion of physical force. Then, in the absence of demonstrated preference, it can never be known whether the act benefited any of the involved parties or caused them harm, let alone that it was the most beneficial employment of resources for every party involved.
Given that usually countless options are available to actors at any given time, if would be an astronomically unlikely coincidence for the State to happen to dictate what consumers would have voluntarily chosen to do at a particular moment in time anyway. In this way, it's metaphysically possible for State action to be equally ex-ante beneficial to all parties involved as voluntary exchange, but never more.
Fundamentally, acts of taxation and regulation, due to their involuntary nature, sever the link between consumers' subjective preferences and the way in which their resources are deployed.
Behind every million dollar tax-funded high school, for example, there hides a million dollars' worth of other goods and services that these taxpayers never got to purchase, but would have preferred over the high school. Perhaps these goods would have been a million dollars' worth of flowers, food, board games, medical services, books, cutlery, home renovations, farming equipment, computer software, and math tutor services.
There's nothing stopping taxpayers from funding a high school on their own and sparing themselves the deadweight loss of bureaucracy. It really is simply the case that if consumers want a high school, they can pay for one, and as private high schools demonstrate, they often do.
However, the State using taxation to build a particular high school can only divert funds from more highly valued opportunity costs to the lower-ranked high school. Otherwise, no compulsion would have been necessary. Despite this undeniable and simple logic, in the U.S., tax-funded expansions of the government K-12 education system, among other interventions, are widely celebrated.
In terms of public opinion, part of the explanation is that the high school can be seen and cheered because it actually exists, whereas the lost opportunity costs, by their very nature as forgone alternatives, never occurred, as so mourning their loss requires abstract reasoning and imagination on the part of the public.
Frédéric Bastiat described this phenomenon in his classic work "That Which is Seen, and That Which is Not Seen." Conspicuous State projects win the public relations war over quietly letting people spend their money as they actually wish to.
The interstate highway system, the Louvre, and the Sixth Fleet may be impressive, but they're not cause for applause. Relative to the preferences of the taxpayer, no matter how grand and awe-inspiring a project the State completes, it will always and everywhere ex-ante fall short of voluntary exchange.
This article was sourced from Mises.org
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text:
Can you become a Localvore?
Rachel Forrest
"Green" has become the new black. Yes, Green is "in" but more than being the big buzzword, it's a word that represents an ethic of living that supports our planet.
"Green" has become the new black.
Yes, Green is "in" but more than being the big buzzword, it's a word that represents an ethic of living that supports our planet and its inhabitants whether they swim in the ocean and become a fish stew, walk on two legs and sit in an office cube, or grow from the earth to and become our fresh green salad.
One of the ways many people are supporting the environment is by becoming a localvore, at least as much as they can, trying to eat foods grown and produced as close to home as possible. Why? Because not only does this support our local farmers and food producers, it also reduces the "carbon footprint."
Getting your tomatoes from California? That's 3,000 miles of greenhouse gases and carbon dioxide to get here. Getting those tomatoes from the Portsmouth Farmers Market? Did you walk there? You're doing your part for both our local agriculture and the environment. Plus, it tastes better. Produce loses flavor on those long journeys.
Now, more than ever, local is key and there are many groups gathering to help people eat local. Slow Food Seacoast is a year old already, Seacoast Growers' Association is well, growing like arugula with the farmers markets and Seacoast Eat Local is launching a Local Foods Resource Guide to help us make choices close to home.
In September there's an Eat Local Challenge — see how well you do eating foods within our area. Even our restaurants are offering all the seasonal local foods we crave and many localvores are doing everything they can to make it as easy as possible.
Sara Zoe Patterson heads up Seacoast Eat Local, a group dedicated to helping people find their way through the local food chain.
"I started this because I really wanted a method to get out there, to get people an access point. I could find local food and I had access to farmers, but others didn't so putting this information into others' hands was important. I'm personally environmentally motivated. I think, 'What is the kind of area you want to live in?' We can create our environment."
On July 1, Patterson launches the first Local Foods Resource Guide, available in print and via download on the Web site.
"It is the first launch. It's been enormously complicated. We have a committee along with Slow Food and we called farmers, putting it out there. Right now it's incomplete but we'll keep adding more."
Patterson says that one challenge was to figure out how to deal with the inclusion of seafood in the guide. She says they want to support the fishermen but not all fish fit into the sustainability criteria.
"We listed the ten fish and shellfish that met the criteria and not all the favorites are on there. I don't want to put anyone out of business. We just have a category called, 'Better choices for local seafood."
Seacoast Eat Local is also organizing the Eat Local Challenge in September, a monthlong experience where people can attempt to find and consume only those foods grown or produced within 100 miles of the area.
"It originated in the San Francisco Bay area and I personally participated three years ago. ... For me, starting at the end of April and through the end of November I don't enter a grocery store. I might go to Portsmouth Health Food for my toilet paper and Philbrick's Fresh Market has local products as well."
Patterson says that while produce is plentiful, meat is actually the easiest thing on the Seacoast to find locally.
"But you have to be able to cook." She says. "The chicken you're going to get is a whole chicken, and the beef you buy is a large segment. We travel with a cooler in our trunk."
Slow Food Seacoast is another group celebrating local eating in the area. The chapter or convivium of Slow Food, a group founded in 1989 to combat the effect of a "fast food" lifestyle reaches its one year anniversary this summer.
Michelle Moon leads the Seacoast convivium and says she's noticed many changes in the way people think about "eating local."
"The main change we're seeing is that local, sustainable, 'slow' food is no longer a fringe idea — it's becoming part of the mainstream," she says. "Not too long ago, Slow Food was a concept associated with gourmet food and wine lovers; today, it's part of a common vocabulary that we can use to talk about food. There's no one factor that brought this about; I think people who are concerned about the current state of our food system began to talk to one another about what they missed and about what they feared."
Moon says that people miss some of the things we experienced in days gone by.
"They missed being connected to the seasons, enjoying the incredible flavor of the first real summer tomato or a warm pumpkin pie on the fall table. They missed the slower pace of life that encouraged people to simmer stews and make breads. They missed the time spent sitting around the table conversing with family and friends. And they feared the hazards of our industrial system — food safety scares, unfairness to workers, harm to the environment. At every event we attend, we find that people are seeking an alternative to manufactured processed food, convenience meals, and factory farming. These are concerns that people from all walks of life share — not just gourmands and activists, but people who are just seeking a better quality of life."
Slow Food is partnering with other groups to promote the eating local ethic.
"We've just sent out a letter of introduction from Slow Food Seacoast to over 160 retailers, farms, nonprofits, food producers, and restaurants to let them know we're here and ready to partner," Moon says. "There are a number of local chefs and restaurateurs on our mailing list, and we know we're thinking along the same lines when we see that their menu items include products of local farms, listed by origin, and creative versions of regional classics of each season. We want to keep working with the people who make and sell food in our area, so they can educate us and in turn we can continue to bring them an audience eager to taste, explore, and support local flavors."
Eating local not only provides us with good foods and supports area agriculture, it's also better for the environment as a whole. Janice Schenker is co-owner of Portsmouth's popular Caffé Kilim. She's been promoting the localvore ethic for decades.
"We need to concentrate on the food that we eat. When we talk about the food that we consume we also need to be aware that we're consuming safe food. We need to be aware that our food comes from far and away from places like China."
"Al Gore's book comes out and it's 'don't drive this,' 'don't do that,' but it ignores that when you eat beef you're contributing far more to damaging the environment than if you're driving your child to basketball practice. You have to ask where does this beef come from. How much water does it take to raise a cow, how much corn — one of the most sprayed crops? ... What are you going to do? Buy corn from Chile or California? We don't need that."
Finding ways to eat locally is still challenging on the Seacoast, but becoming less so.
Lisa Lane grows organic herbs and vegetables on her Rising Ridge Farm in York and sells at the York farmers market.
"In the last six months or so, I have made it my mission to find out where all of the food my family consumes originates. This not only stems from my interest in healthy foods, which goes back many years to my childhood and the influence of my Dad who grew up poor in rural south Jersey and became skillful at eating off the land, but also from news reports in the last few months that have shined a light on China's increasingly unsafe treatment of foods destined for the U.S."
Lane says she will point out to produce workers in our local supermarkets issues surrounding the produce they carry, often from California. She also laments not being able to find potatoes from Maine, a state famous for its potatoes.
Despite the challenges, becoming a localvore is getting easier on the Seacoast, thanks to the many groups working to make it so. Moon says that supporting small-scale farm funding through the Farm Bill is a start as is asking our markets to carry local foods.
As Schenker says, it's all up to us.
"We all have the responsibility to cut back and put up food, dry it, can it, freeze it for the winter. People with the means need to set an example. Everyone can do more."
© Copyright 2006-2019 GateHouse Media, LLC. All rights reserved • GateHouse Entertain


text:
Craving Filipino food, COVID-19 front-line nurses open restaurant in NYC
The three hard-working friends didn't let the pandemic crush their restaurateur dreams.
Nurses open Filipino restaurant near hospital during pandemic
Dec. 2, 202003:23
Dec. 2, 2020, 2:09 PM UTC / Source: TODAY
By Yi-Jin Yu
Taking care of sick COVID-19 patients is undeniably grueling work. Opening and running a restaurant is, too, especially during a worldwide pandemic. But for nurses Joan Calanog, Jude Canela and Maricris Dinopol, it's all in a (very) long day's work and, more importantly, it's a dream come true.
The three Filipino health care workers and close friends teamed up to bring Bilao to life in August, all without giving up their full-time jobs. The restaurant, located in New York City's Upper East Side neighborhood, specializes in Filipino cuisine and brings the flavors of home-cooked meals to the area's residents, visitors and even to other health care workers. In fact, Bilao is strategically situated just blocks from several of the Big Apple's major hospitals, including the one all three work in — Mount Sinai Hospital.
Maricris Dinopol, Jude Canela and Joan Calanog decided to open up a Filipino restaurant in New York City, despite the challenges posed by the global coronavirus pandemic.Courtesy of Joan Calanog, Jude Canela and Maricris Dinopol
On the 3rd Hour of TODAY, Calanog said that she and her friends work nights at the hospital between 7 p.m. and 7 a.m. Canela added, "We work three 12's. So we're all night shifters and we work sometimes three nights or four nights in a week."
So why would three young and busy nurses want to break into the restaurant industry? Canela explained to Sheinelle Jones, "It was actually a random joke one day. Maybe we should start a restaurant because we were like, really craving for Filipino food getting off from work."
This Ethiopian-Jewish restaurateur is nourishing bodies and minds with food, art and music
Sept. 30, 202009:31
After the idea took hold, Canela recalled, "We started conceptualizing, planning it day by day. We were supposed to open early this year and then COVID happens."
Calanog, Canela and Dinopol had to press pause on their Filipino restaurant dream temporarily to respond to the growing public health crisis.
"It was pretty much overwhelming. I would say nerve-racking at first," Canela recollected. "We were all stressed out. We're afraid of going home with our family. Our anxiety from that alone is pretty much overwhelming."
The idea for Bilao began as a simple joke.Courtesy of Joan Calanog, Jude Canela and Maricris Dinopol.
But as restaurants throughout the city and the country started winding down operations or shutting down completely, the three friends never gave up their goal. Dinopol said one of the main reasons they didn't abandon their plan was because of their fellow front-line colleagues.
"I think it's because our target customers are frontliner," she explained. "So regardless of the pandemic, our jobs really don't stop." Plus, she added, "There's a lot of Filipino nurses."
Canela agreed: "It's based on experience because we're nurses. As soon as we get off from our shift, we know that we're hungry."
Bilao opened in New York City's Upper East Side neighborhood in August.Courtesy of Joan Calanog, Jude Canela and Maricris Dinopol.
Bilao currently offers about 40 dishes all day long, including a five-item savory breakfast menu. The best-selling dishes at the restaurant, whose name refers to a woven tool used to winnow rice and grains, include kare-kare (stewed oxtail with peanut sauce), lechon kawali (deep fried pork belly), crispy pata (deep fried pork knuckles) and sizzling sisig (pork hash).
https://www.instagram.com/p/CHvdzp1jFHI/
Now that their restaurant dream has been realized, Dinopol said, "It's very fulfilling for me to serve my own countrymen. You know, I take so much pride for bringing Filipino food in this country."
Calanog added, "New Yorkers, they support our food, our culture, and it's very heartwarming."
Canela echoed their sentiments: "I'm very proud. And for us to cater our own authentic dishes to the world, it's already an achievement."
https://www.instagram.com/p/CIPev-fjOop/
And it's not just locals who have been singing Bilao's praises: The restaurant has since been reviewed by the New York Times' Pete Wells and named as a critic's pick; Eater NY's Robert Sietsema called Bilao "one of the best overviews of the collective national cuisine that NYC has yet seen"; and Gothamist described the restaurant as "fantastic" and a "win for the Upper East Side."
Yi-Jin Yu
Yi-Jin Yu is an editor and reporter for TODAY Digital and leads digital coverage for Weekend TODAY on Saturday mornings. She is based in New York City.
Robert Ciridon contributed.


text:
Mazoon Dairy Expands into GCC Market
In its first achievement alongside its participation in Gulfood Exhibition 2022, Mazoon Dairy announced its...
Mazoon Dairy Announces Participation in the 2022 Edition of Gulfood
The flagship dairy company of the Sultanate of Oman, Mazoon Dairy, recently announced its participation...
MAZOON DAIRY HIGHLIGHTS MILESTONES AND 5-YEAR PROSPECTS ON OMAN INDUSTRY DAY
Mazoon Dairy, the flagship dairy company of the Sultanate, commemorated Oman's annual Industry Day on...
Mazoon Dairy Business Forum to start on March 30
Mazoon Dairy has announced that it will organize the Mazoon Business Forum in the Al Buraimi Governorate on Wednesday, March 30, under the auspices of Sayyid Dr Hamad bin Ahmed al Busaidy, Governor of Al Buraimi, and with the participation of a large number of regulatory, legislative and financial authorities, as well as entrepreneurs, university and college students and the residents of the province.
The list of participating parties includes the Ministry of Commerce, Industry and Investment Promotion, Oman Chamber of Commerce and Industry in the Al Buraimi Governorate, the Small and Medium Enterprises Development Authority (Riyada), the Industrial Innovation Academy (Madayn), Oman Development Bank, National Bank of Oman, Bank Muscat, Oman Fund Technology, Small and Medium Enterprises Development Fund (Inmaa), and the Youth Enterprise Development Fund (Sharaka).
The forum falls within the framework of the company's social responsibility and its support for entrepreneurship in the Al Buraimi
In its first achievement alongside its participation in Gulfood Exhibition 2022, Mazoon Dairy announced its signing of an exclusive distribution agreement with Ghassan Aboud Trading Group for the distribution of all Mazoon products within the UAE market....
The flagship dairy company of the Sultanate of Oman, Mazoon Dairy, recently announced its participation at the 27th edition of Gulfood, the largest food and beverage processing and packaging exhibition in the Middle East, Asia, and Africa. The event brings together a wide range of participants from the food and beverage sourcing ecosystem from around the world....
Mazoon Dairy, the flagship dairy company of the Sultanate, commemorated Oman's annual Industry Day on Wednesday by highlighting its various milestones cemented since operation in 2019. In addition, the company also shed light on its noteworthy development plans for the next 5 years....


Are you the type of traveler who like to plan your holiday choosing the places to visit and the various excursions? Or are you the type who likes to set off on an adventure? In both cases, here are the routes for you to discover our Maremma... From hidden coves behind Monte Argentario to walks in the Nature Park of Maremma to boat rides to the islands of Giglio and Giannutri and trips to the small towns of Pitigliano, Sovana and Magliano.


text:
Q: textfield with scala play form helper Scala form helper is not as consistent as I would expect
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  <fieldset>
    @textarea(field = articleForm("text"), args = 'rows -> 3, 'cols -> 50)
    @input(articleForm("author"), "author")
  </fieldset>
}

The input fields look really nice and have labels on the left with fields on the right. But the textarea is just weird, it's not wrapped in a
 with a label, but it's in a
 tag and at the bottom there's a 'Required' sign that I don't know how to remove.
Here's the image of how it looks:

Any tips on how I can get the form to look consistent?
Thanks.

A: You have a few options.
First, you can override the helper to just put in your own hand-rolled HTML for the textarea control.  This is described in the documentation under "Using the form template helpers" under the section "Handling HTML input creation yourself", and common pitfalls are described here. If you want a div containing a label, you'd do something like this:
@helper.input(field = articleForm("text")) { (id, name, value, args) =>

        text
        <textarea name="@name" id="@id" rows='3' cols='50'>@value</textarea>

}

You can also use CSS to style the default HTML produced by the textarea helper.  The
 tag is simply a definition list and can by styled much like any html list.  For reference, you can find the default field constructor code in github, which shows you what the generated html looks like.
I assume that the "Required" sign you're talking about is the error
 tag you can see in that generated HTML.  If you aren't going the hand-rolled HTML route, then to get rid of it you'll need to define your own field constructor.  That is also described in the Play help page I linked to above.  But if all you care about is getting rid of the error, it should be pretty easy, just make a copy of the default field constructor code (also linked above), and alter or just remove the parts that read @if(elements.hasErrors) {error} and the three lines starting with @elements.errors(elements.lang).map. The "Required" error itself is from @elements.infos....
Or is the problem that this field is not supposed to be required?  That is an issue with the form definition, not the helper.  Make the "text" field in your form optional, as shown on the Scala Forms help page under "Optional values". For example, if your task definition is in Application.scala:
   val taskForm = Form (
     "text" -> optional(text) // changed from 'nonEmptyText'
   )

This will also make the "text" field map to an Option[String] instead of a plain String. If your form is backed by a case class (or other mapping logic), you'll have to change it accordingly.

redpajama_set_name: RedPajamaStackExchange


text:
Blog/ International Children & Nature Conference Brings Thought Leaders to Austin
International Children & Nature Conference Brings Thought Leaders to Austin
AUSTIN — This year has been a momentous year for the children and nature movement. Ten years after publication of Richard Louv's Last Child in the Woods: Saving our Children from Nature-Deficit Disorder, and five years after the establishment of the Texas Children in Nature collaborative, there is new and growing urgency around connecting children and families to nature.
The Children & Nature Network 2015 Conference at the Hyatt Lost Pines Resort on April 7-9 has attracted more than 500 leaders from around the world representing the conservation, health, education, technology and built- environment communities. Attendees will explore innovative ways to encourage families, schools, churches, non-profits and businesses to support getting kids active and into nature.
"Texas is honored to host this outstanding conference in our state," says Jennifer Bristol, Coordinator for Texas Children in Nature. "Research shows that children and families who spend time in nature are healthier, happier and smarter. We want this conference to inspire action to get more Texans enjoying the outdoors."
One initiative highlighted this year is the groundbreaking national effort "Every Kid in a Park." In February the National Park Service in partnership with the White House announced this new program to give every fourth grader a National Parks Pass to get kids out enjoying their public lands. National Park Service Director, Jonathon Jarvis will be at the conference to promote the initiative alongside Christy Goldfuss, Managing Director of the White House Council on Environmental Quality.
"As the world becomes more urban and more plugged-in, we need nature more than ever," says Sarah Milligan-Toffler, Executive Director of the Children & Nature Network. "Parents, teachers and city leaders are seeing the need to reverse Nature-Deficit disorder."
Louv says the children and nature movement has been growing steadily for a decade, but he believes 2015 is a tipping point. In Texas and around the world, at the grassroots and at the national level, there has been a surge in action and progress.
The first day of the conference focuses on the intersection of technology and nature and will explore both the limitations of technology and how it can be used as a tool to help children and families explore outside.
"After years of condemning technology for driving our children away from the wonder and joy of nature and outdoor play, the children and nature movement is looking at positive ways in which technology can be used to encourage and engage children in nature play and learning," says Molly Stevens, Executive Director of the Westcave Outdoor Discovery Center.
The Technology and Nature Summit taking place on the first day of the conference showcases some of the latest apps and gear used to help families explore in nature. Tuesday afternoon, a drone used by the Boy Scouts in Bastrop will be featured to show the growth and density of the tree canopy.
Highlights from the April 8conference day include presentations on promoting access to nature in cities with internationally renowned speaker Gil Penelosa; Dr. Joe Frost and Rusty Keeler will explore the value of nature play; and Nick Clemons from the National Park Service and Catlin Cox of Disney will talk about engaging Millennials with nature-smart jobs.
Other sessions will address the importance of nature connections for the healthy development of children with experts such as Catherine Jordan, Ph.D. from the University of Minnesota, Jeannette Ickovics, Ph.D. from Yale University, and Autumn Saxton-Ross, Ph.D. of the National Collaborative for Health Equity.
The final day of the conference is designed to put inspiration into action and will feature a session on how to Engage Diversity in Careers in the Outdoor Industry hosted by Texas Children in Nature and Audubon Texas. There will be a field trip to some of Austin's most notable natural play areas, such as the one at the Lady Bird Johnson Wildflower Center and a service project to give back to the community at Bastrop State Park.
The Children & Nature Conference is a collaborative effort between the Children & Nature Network, Texas Children in Nature and Westcave Outdoor Discovery Center. Major sponsors of the Conference include; Playcore, Canadian Wildlife Federation, The Meadows Foundation, Disney World Wildlife Fund, Applied Materials, Texas Parks and Wildlife Department, Audubon Texas, Conserve School, Landscape Structures, Toyota, St. David's Foundation, Bienenstock Natural Playgrounds and many others.
Photo by: Jennifer Bristol
Original: http://texaschildreninnature.org/blog-notes/international-children-nature-conference-brings-thought-leaders-to-austin
Explore Nature Rocks Texas in other cities
Copyright 2022 Texas Children in Nature


Ideas for art start as tiny notions, as little specks of gold amongst the sand.
When you see an amazing artwork do you think the idea came to the artist like a hurricane in the night? Or was it just a little hint? A tiny notion? Sometimes an idea comes almost complete but often that amazing idea started off pretty small.
An artist can work from an idea that is just a tickle, a whisper. You have to listen pretty carefully to your own ideas to hear them.
Maybe it's as small as this: an attempt to capture something dynamic in a line, using width and weight.
A first sketch after an idea: the energy created with nothing other than lines of varying widths.
Or a combination of colours seen in a certain light.
Or light falling on a bright yellow curtain.
Maybe the light falling on the curtain and the light coming in from behind trigger something off. An initial idea can be a tiny notion.
But is that really an artwork you ask? No not yet, its just the hint, the trigger.
A thought you had during the day, something you noticed on the way to work, a piece of rusty metal wire looped into a funny shape.
Any small thought can be the germ of a good idea. Just let your mind float along with the idea, taking twists and turns, letting it go where it wants.
You start by opening up, letting ideas in. You don't limit yourself. Don't censor your thoughts or judge their quality as you have them. Use these germ ideas, these seeds to build up ideas that will become your artworks.
Tap into your creativity and let yourself think crazy thoughts.
I found a little section of an animal skull on the footpath at the base of a tree. When I pushed around the dirt with my foot I found a section of jaw. I took them home and kept looking at them. [Yes I am disgusting and do this kind of thing fairly often.] I washed the mud off and when they dried they were fairly clean and bleached. Old. Maybe they were from a cat? They looked about that size.
After a couple of days I made a little stack of round pebbles and placed the jaw bone on top. Now it looked like a little offering. I have a bit of a thing for creepy movies, voodoo etc and I also love ancient artefacts. So although I wasn't sure where it was heading I was finding this little pile of objects quite a potent trigger. I'm not sure where this artwork is leading; at the moment I am just listening to my thoughts and jotting down snippets. It's that simple.
I also took a photo with my favourite sketchy app, left and painted them, right.
Next I cast them in wax, by pressing them into clay and pouring in wax.
Above left, the teeth on the left in pink and white wax and in the right image cast in only white which is more effective I think. Act and re-act. This is how you make art. Continue going in the direction of the more successful pieces.
After casting the teeth I started casting other bones I had collected.
Just play with your idea. Even if it never turns into a major artwork, you'll have a fun.
Making art is like an adventure or an experiment. I often play when I am in between big projects. I experiment in an open ended fashion, with new mediums, and try out different ideas. These projects, these experiments, sometimes don't work. And that is ok. Because quite often there is an element I really like, just a tiny element that I can re-use. And if there is something I really don't like going on, for example if I think a drawing looks really stiff, then I react against it, and try to bring some looseness into my work. Acting and reacting is what art making is.
Take an Art Quest: kickstart your art making.
All content copyright Making Art 2016.


Patrons dance to music at the Eatonic Music Festival over Labor Day weekend at the Preble County Fairgrounds. Despite headliner Buddy Guy being rained out on Friday, Sept 4, the festival continued on Saturday, Sept 5 and Sunday, Sept 6, as music fans from all over enjoyed rock and bluegrass music.
Concert host Manfred Schreyer throws t-shirts to people at the Eatonic Music Festival on Sunday, Sept 6. The festival had a slow start when weather prevented headliner Buddy Guy's performance, but rocked through the weekend as music fans came from around the area to celebrate their love of rock-n-roll and bluegrass.
Rumpke Mountain Boys play at the Eatonic Music Festival on Sunday, Sept 6. The festival had a rough start when it was rained out on Friday, Sept 4, but that didn't stop people from enjoying a weekend full of bluegrass and rock-n-roll music.
Despite the absence of headliner Buddy Guy and most of the performers slated for the Friday evening, Sept. 4, blues night at the Eatonic Music Festival, other performers played when sunny weather returned Saturday and Sunday.
EATON — The combination of rain and lighting was too much for much of anything to happen on Friday, Sept. 4, and that included six-time Grammy Award-winning Buddy Guy taking the stage in Eaton.
Guy was scheduled to headline and help kick-off the first-ever Eatonic Music Festival last weekend but was unable to do so because of fear for safety of both the crowd and the 79-year-old blues legend.
Manfred Schreyer, who orchestrated the Eatonic event said the decision was made by Guy and his people around 10 p.m.
Schreyer was sympathetic to those who missed out on the legend.
Schreyer said the following days of the festival were full of good music.
Schreyer said they will "learn and advance" from putting on the first music festival within the county, and hopes to be able to put the concert on next year.
Schreyer saying Friday night's storms were "an act of God not falling under rain or shine" was important for those who only bought tickets for Friday. Those tickets were originally non-refundable, but Schreyer allowed those who had tickets to come to the rest of the weekend on the Friday night tickets. He said they will also be eligible for weekend passes to next year's concert.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_Eatonic-6-.jpgPatrons dance to music at the Eatonic Music Festival over Labor Day weekend at the Preble County Fairgrounds. Despite headliner Buddy Guy being rained out on Friday, Sept 4, the festival continued on Saturday, Sept 5 and Sunday, Sept 6, as music fans from all over enjoyed rock and bluegrass music.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_Eatonic-11-.jpgPatrons dance to music at the Eatonic Music Festival over Labor Day weekend at the Preble County Fairgrounds. Despite headliner Buddy Guy being rained out on Friday, Sept 4, the festival continued on Saturday, Sept 5 and Sunday, Sept 6, as music fans from all over enjoyed rock and bluegrass music.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_Eatonic-9-.jpgPatrons dance to music at the Eatonic Music Festival over Labor Day weekend at the Preble County Fairgrounds. Despite headliner Buddy Guy being rained out on Friday, Sept 4, the festival continued on Saturday, Sept 5 and Sunday, Sept 6, as music fans from all over enjoyed rock and bluegrass music.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_Eatonic-12-.jpgConcert host Manfred Schreyer throws t-shirts to people at the Eatonic Music Festival on Sunday, Sept 6. The festival had a slow start when weather prevented headliner Buddy Guy's performance, but rocked through the weekend as music fans came from around the area to celebrate their love of rock-n-roll and bluegrass.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_Eatonic-4-.jpgRumpke Mountain Boys play at the Eatonic Music Festival on Sunday, Sept 6. The festival had a rough start when it was rained out on Friday, Sept 4, but that didn't stop people from enjoying a weekend full of bluegrass and rock-n-roll music.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_Eatonic-10-.jpgPatrons dance to music at the Eatonic Music Festival over Labor Day weekend at the Preble County Fairgrounds. Despite headliner Buddy Guy being rained out on Friday, Sept 4, the festival continued on Saturday, Sept 5 and Sunday, Sept 6, as music fans from all over enjoyed rock and bluegrass music.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_eatonic1.jpgDespite the absence of headliner Buddy Guy and most of the performers slated for the Friday evening, Sept. 4, blues night at the Eatonic Music Festival, other performers played when sunny weather returned Saturday and Sunday.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_eatonic2.jpgDespite the absence of headliner Buddy Guy and most of the performers slated for the Friday evening, Sept. 4, blues night at the Eatonic Music Festival, other performers played when sunny weather returned Saturday and Sunday.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_eatonic3.jpgDespite the absence of headliner Buddy Guy and most of the performers slated for the Friday evening, Sept. 4, blues night at the Eatonic Music Festival, other performers played when sunny weather returned Saturday and Sunday.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_eatonic4.jpgDespite the absence of headliner Buddy Guy and most of the performers slated for the Friday evening, Sept. 4, blues night at the Eatonic Music Festival, other performers played when sunny weather returned Saturday and Sunday.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_eatonic5.jpgDespite the absence of headliner Buddy Guy and most of the performers slated for the Friday evening, Sept. 4, blues night at the Eatonic Music Festival, other performers played when sunny weather returned Saturday and Sunday.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_eatonic6.jpgDespite the absence of headliner Buddy Guy and most of the performers slated for the Friday evening, Sept. 4, blues night at the Eatonic Music Festival, other performers played when sunny weather returned Saturday and Sunday.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_eatonic7.jpgDespite the absence of headliner Buddy Guy and most of the performers slated for the Friday evening, Sept. 4, blues night at the Eatonic Music Festival, other performers played when sunny weather returned Saturday and Sunday.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_eatonic8.jpgDespite the absence of headliner Buddy Guy and most of the performers slated for the Friday evening, Sept. 4, blues night at the Eatonic Music Festival, other performers played when sunny weather returned Saturday and Sunday.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_eatonic9.jpgDespite the absence of headliner Buddy Guy and most of the performers slated for the Friday evening, Sept. 4, blues night at the Eatonic Music Festival, other performers played when sunny weather returned Saturday and Sunday.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_eatonic10.jpgDespite the absence of headliner Buddy Guy and most of the performers slated for the Friday evening, Sept. 4, blues night at the Eatonic Music Festival, other performers played when sunny weather returned Saturday and Sunday.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_eatonic11.jpgDespite the absence of headliner Buddy Guy and most of the performers slated for the Friday evening, Sept. 4, blues night at the Eatonic Music Festival, other performers played when sunny weather returned Saturday and Sunday.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_eatonic_j1.jpgDespite the absence of headliner Buddy Guy and most of the performers slated for the Friday evening, Sept. 4, blues night at the Eatonic Music Festival, other performers played when sunny weather returned Saturday and Sunday.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_eatonic_j2.jpgDespite the absence of headliner Buddy Guy and most of the performers slated for the Friday evening, Sept. 4, blues night at the Eatonic Music Festival, other performers played when sunny weather returned Saturday and Sunday.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_eatonic_j3.jpgDespite the absence of headliner Buddy Guy and most of the performers slated for the Friday evening, Sept. 4, blues night at the Eatonic Music Festival, other performers played when sunny weather returned Saturday and Sunday.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_eatonic_j4.jpgDespite the absence of headliner Buddy Guy and most of the performers slated for the Friday evening, Sept. 4, blues night at the Eatonic Music Festival, other performers played when sunny weather returned Saturday and Sunday.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_eatonic_j5.jpgDespite the absence of headliner Buddy Guy and most of the performers slated for the Friday evening, Sept. 4, blues night at the Eatonic Music Festival, other performers played when sunny weather returned Saturday and Sunday.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_eatonic_j6.jpgDespite the absence of headliner Buddy Guy and most of the performers slated for the Friday evening, Sept. 4, blues night at the Eatonic Music Festival, other performers played when sunny weather returned Saturday and Sunday.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_eatonic_j7.jpgDespite the absence of headliner Buddy Guy and most of the performers slated for the Friday evening, Sept. 4, blues night at the Eatonic Music Festival, other performers played when sunny weather returned Saturday and Sunday.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_eatonic_j8.jpgDespite the absence of headliner Buddy Guy and most of the performers slated for the Friday evening, Sept. 4, blues night at the Eatonic Music Festival, other performers played when sunny weather returned Saturday and Sunday.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_eatonic_j9.jpgDespite the absence of headliner Buddy Guy and most of the performers slated for the Friday evening, Sept. 4, blues night at the Eatonic Music Festival, other performers played when sunny weather returned Saturday and Sunday.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_eatonic_j10.jpgDespite the absence of headliner Buddy Guy and most of the performers slated for the Friday evening, Sept. 4, blues night at the Eatonic Music Festival, other performers played when sunny weather returned Saturday and Sunday.
http://aimmedianetwork.com/wp-content/uploads/sites/41/2015/09/web1_eatonic_j11.jpgDespite the absence of headliner Buddy Guy and most of the performers slated for the Friday evening, Sept. 4, blues night at the Eatonic Music Festival, other performers played when sunny weather returned Saturday and Sunday.


text:
export class ErrorResponse implements Error {

    constructor(message?: string){
        this.message = message
    }

    response: Response;
    message: string;
    name: string;
    stack: string;
}

redpajama_set_name: RedPajamaGithub


Looking for 5 volunteers to aid in duties helping cat director. This is mostly evening work with some day duties. Duties include delivering supplies to fosters, transporting animals between adoption centers, and taking animals to scheduled vet appointments..


text:
Polarization-Based Histopathology Classification of Ex Vivo Colon Samples Supported by Machine Learning
Deyan Ivanov*, Viktor Dremin, Tsanislava Genova, Alexander Bykov, Tatiana Novikova, Razvigor Ossikovski, Igor Meglinski
Aston Institute of Photonics Technology (AIPT)
Mechanical, Biomedical & Design Engineering
In biophotonics, novel techniques and approaches are being constantly sought to assist medical doctors and to increase both sensitivity and specificity of the existing diagnostic methods. In such context, tissue polarimetry holds promise to become a valuable optical diagnostic technique as it is sensitive to tissue alterations caused by different benign and malignant formations. In our studies, multiple Mueller matrices were recorded for formalin-fixed, human, ex vivo colon specimens containing healthy and tumor zones. The available data were pre-processed to filter noise and experimental errors, and then all Mueller matrices were decomposed to derive polarimetric quantities sensitive to malignant formations in tissues. In addition, the Poincaré sphere representation of the experimental results was implemented. We also used the canonical and natural indices of polarimetric purity depolarization spaces for plotting our experimental data. A feature selection was used to perform a statistical analysis and normalization procedure on the available data, in order to create a polarimetric model for colon cancer assessment with strong predictors. Both unsupervised (principal component analysis) and supervised (logistic regression, random forest, and support vector machines) machine learning algorithms were used to extract particular features from the model and for classification purposes. The results from logistic regression allowed to evaluate the best polarimetric quantities for tumor detection, while the use of random forest yielded the highest accuracy values. Attention was paid to the correlation between the predictors in the model as well as both losses and relative risk of misclassification. Apart from the mathematical interpretation of the polarimetric quantities, the presented polarimetric model was able to support the physical interpretation of the results from previous studies and relate the latter to the samples' health condition, respectively.
Frontiers in Physics
https://doi.org/10.3389/fphy.2021.814787
Published - 24 Jan 2022
© 2022 Ivanov, Dremin, Genova, Bykov, Novikova, Ossikovski and Meglinski. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
Funding: The experimental investigations were supported by the Bulgarian National Science Fund under grant #KP06-N38/13/2019. The current research was supported by the Academy of Finland (Grants 314639 and 325097) and INFOTECH strategic funding. Prof. Igor Meglinski also acknowledges the support from the Ministry of Science and Higher Education of the Russian Federation within the framework of state support for the creation and development of world-class research centres "Digital Biodesign and Personalized Healthcare" No. 075-15-2020-926. VD kindly acknowledges for personal support from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant, agreement No. 839888.
tissue polarimetry
Mueller matrices
physical realizability
symmetric decomposition
depolarization spaces
Ex vivo colon samples
10.3389/fphy.2021.814787
Final published version, 2.2 MBLicence: CC BY 3.0
https://www.frontiersin.org/articles/10.3389/fphy.2021.814787/full
Dive into the research topics of 'Polarization-Based Histopathology Classification of Ex Vivo Colon Samples Supported by Machine Learning'. Together they form a unique fingerprint.
Polarimetry Chemistry 100%
machine learning Physics & Astronomy 89%
Polarization Mathematics 79%
Depolarization Chemistry 79%
Mueller Matrix Mathematics 63%
Sphere Chemistry 59%
Ivanov, D., Dremin, V., Genova, T., Bykov, A., Novikova, T., Ossikovski, R., & Meglinski, I. (2022). Polarization-Based Histopathology Classification of Ex Vivo Colon Samples Supported by Machine Learning. Frontiers in Physics, 9, [814787]. https://doi.org/10.3389/fphy.2021.814787
Ivanov, Deyan ; Dremin, Viktor ; Genova, Tsanislava et al. / Polarization-Based Histopathology Classification of Ex Vivo Colon Samples Supported by Machine Learning. In: Frontiers in Physics. 2022 ; Vol. 9.
@article{d2391208bdf647a8837c2682861a9635,
title = "Polarization-Based Histopathology Classification of Ex Vivo Colon Samples Supported by Machine Learning",
abstract = "In biophotonics, novel techniques and approaches are being constantly sought to assist medical doctors and to increase both sensitivity and specificity of the existing diagnostic methods. In such context, tissue polarimetry holds promise to become a valuable optical diagnostic technique as it is sensitive to tissue alterations caused by different benign and malignant formations. In our studies, multiple Mueller matrices were recorded for formalin-fixed, human, ex vivo colon specimens containing healthy and tumor zones. The available data were pre-processed to filter noise and experimental errors, and then all Mueller matrices were decomposed to derive polarimetric quantities sensitive to malignant formations in tissues. In addition, the Poincar{\'e} sphere representation of the experimental results was implemented. We also used the canonical and natural indices of polarimetric purity depolarization spaces for plotting our experimental data. A feature selection was used to perform a statistical analysis and normalization procedure on the available data, in order to create a polarimetric model for colon cancer assessment with strong predictors. Both unsupervised (principal component analysis) and supervised (logistic regression, random forest, and support vector machines) machine learning algorithms were used to extract particular features from the model and for classification purposes. The results from logistic regression allowed to evaluate the best polarimetric quantities for tumor detection, while the use of random forest yielded the highest accuracy values. Attention was paid to the correlation between the predictors in the model as well as both losses and relative risk of misclassification. Apart from the mathematical interpretation of the polarimetric quantities, the presented polarimetric model was able to support the physical interpretation of the results from previous studies and relate the latter to the samples{\textquoteright} health condition, respectively.",
keywords = "Physics, tissue polarimetry, Mueller matrices, physical realizability, symmetric decomposition, depolarization spaces, Ex vivo colon samples, classification, machine learning",
author = "Deyan Ivanov and Viktor Dremin and Tsanislava Genova and Alexander Bykov and Tatiana Novikova and Razvigor Ossikovski and Igor Meglinski",
note = "{\textcopyright} 2022 Ivanov, Dremin, Genova, Bykov, Novikova, Ossikovski and Meglinski. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. Funding: The experimental investigations were supported by the Bulgarian National Science Fund under grant #KP06-N38/13/2019. The current research was supported by the Academy of Finland (Grants 314639 and 325097) and INFOTECH strategic funding. Prof. Igor Meglinski also acknowledges the support from the Ministry of Science and Higher Education of the Russian Federation within the framework of state support for the creation and development of world-class research centres "Digital Biodesign and Personalized Healthcare" No. 075-15-2020-926. VD kindly acknowledges for personal support from the European Union{\textquoteright}s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant, agreement No. 839888.",
doi = "10.3389/fphy.2021.814787",
Ivanov, D, Dremin, V, Genova, T, Bykov, A, Novikova, T, Ossikovski, R & Meglinski, I 2022, 'Polarization-Based Histopathology Classification of Ex Vivo Colon Samples Supported by Machine Learning', Frontiers in Physics, vol. 9, 814787. https://doi.org/10.3389/fphy.2021.814787
Polarization-Based Histopathology Classification of Ex Vivo Colon Samples Supported by Machine Learning. / Ivanov, Deyan; Dremin, Viktor; Genova, Tsanislava et al.
In: Frontiers in Physics, Vol. 9, 814787, 24.01.2022.
T1 - Polarization-Based Histopathology Classification of Ex Vivo Colon Samples Supported by Machine Learning
AU - Ivanov, Deyan
AU - Dremin, Viktor
AU - Genova, Tsanislava
AU - Bykov, Alexander
AU - Novikova, Tatiana
AU - Ossikovski, Razvigor
AU - Meglinski, Igor
N1 - © 2022 Ivanov, Dremin, Genova, Bykov, Novikova, Ossikovski and Meglinski. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. Funding: The experimental investigations were supported by the Bulgarian National Science Fund under grant #KP06-N38/13/2019. The current research was supported by the Academy of Finland (Grants 314639 and 325097) and INFOTECH strategic funding. Prof. Igor Meglinski also acknowledges the support from the Ministry of Science and Higher Education of the Russian Federation within the framework of state support for the creation and development of world-class research centres "Digital Biodesign and Personalized Healthcare" No. 075-15-2020-926. VD kindly acknowledges for personal support from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant, agreement No. 839888.
N2 - In biophotonics, novel techniques and approaches are being constantly sought to assist medical doctors and to increase both sensitivity and specificity of the existing diagnostic methods. In such context, tissue polarimetry holds promise to become a valuable optical diagnostic technique as it is sensitive to tissue alterations caused by different benign and malignant formations. In our studies, multiple Mueller matrices were recorded for formalin-fixed, human, ex vivo colon specimens containing healthy and tumor zones. The available data were pre-processed to filter noise and experimental errors, and then all Mueller matrices were decomposed to derive polarimetric quantities sensitive to malignant formations in tissues. In addition, the Poincaré sphere representation of the experimental results was implemented. We also used the canonical and natural indices of polarimetric purity depolarization spaces for plotting our experimental data. A feature selection was used to perform a statistical analysis and normalization procedure on the available data, in order to create a polarimetric model for colon cancer assessment with strong predictors. Both unsupervised (principal component analysis) and supervised (logistic regression, random forest, and support vector machines) machine learning algorithms were used to extract particular features from the model and for classification purposes. The results from logistic regression allowed to evaluate the best polarimetric quantities for tumor detection, while the use of random forest yielded the highest accuracy values. Attention was paid to the correlation between the predictors in the model as well as both losses and relative risk of misclassification. Apart from the mathematical interpretation of the polarimetric quantities, the presented polarimetric model was able to support the physical interpretation of the results from previous studies and relate the latter to the samples' health condition, respectively.
AB - In biophotonics, novel techniques and approaches are being constantly sought to assist medical doctors and to increase both sensitivity and specificity of the existing diagnostic methods. In such context, tissue polarimetry holds promise to become a valuable optical diagnostic technique as it is sensitive to tissue alterations caused by different benign and malignant formations. In our studies, multiple Mueller matrices were recorded for formalin-fixed, human, ex vivo colon specimens containing healthy and tumor zones. The available data were pre-processed to filter noise and experimental errors, and then all Mueller matrices were decomposed to derive polarimetric quantities sensitive to malignant formations in tissues. In addition, the Poincaré sphere representation of the experimental results was implemented. We also used the canonical and natural indices of polarimetric purity depolarization spaces for plotting our experimental data. A feature selection was used to perform a statistical analysis and normalization procedure on the available data, in order to create a polarimetric model for colon cancer assessment with strong predictors. Both unsupervised (principal component analysis) and supervised (logistic regression, random forest, and support vector machines) machine learning algorithms were used to extract particular features from the model and for classification purposes. The results from logistic regression allowed to evaluate the best polarimetric quantities for tumor detection, while the use of random forest yielded the highest accuracy values. Attention was paid to the correlation between the predictors in the model as well as both losses and relative risk of misclassification. Apart from the mathematical interpretation of the polarimetric quantities, the presented polarimetric model was able to support the physical interpretation of the results from previous studies and relate the latter to the samples' health condition, respectively.
KW - Physics
KW - tissue polarimetry
KW - Mueller matrices
KW - physical realizability
KW - symmetric decomposition
KW - depolarization spaces
KW - Ex vivo colon samples
KW - classification
KW - machine learning
UR - https://www.frontiersin.org/articles/10.3389/fphy.2021.814787/full
U2 - 10.3389/fphy.2021.814787
DO - 10.3389/fphy.2021.814787
Ivanov D, Dremin V, Genova T, Bykov A, Novikova T, Ossikovski R et al. Polarization-Based Histopathology Classification of Ex Vivo Colon Samples Supported by Machine Learning. Frontiers in Physics. 2022 Jan 24;9:814787. doi: 10.3389/fphy.2021.814787