text:
\section{Introduction}
Graph Neural Networks (GNNs) and their variants \cite{abu2019mixhop, kipf2017semi, velivckovic2018graph} have achieved state-of-the-art performance on various tasks such as recommendation system \cite{ying2018graph} and traffic prediction \cite{guo2019attention}. However, as Kipf et al.~\cite{kipf2017semi} point out, deep GCN are prone to over-fitting due to limited labeled data \cite{shorten2019survey} and additional model parameters as the number of parameters increase with model depth. Meanwhile, as a data-based solution of alleviating over-fitting, \emph{data augmentation} has been successfully adopted in many areas, such as computer vision \cite{cubuk2019autoaugment} and natural language processing \cite{fadaee2017data}. Therefore, graph data augmentation has been studied recently. For explicit graph data augmentation, the existing methods can be divided into two categories: either topology-level~\cite{rong2020dropedge, wang2020nodeaug, zhao2021data} or feature-level augmentation~\cite{deng2019batch, feng2019graph, kong2020flag}.

A standard operation on topology-level augmentation is to perturb the adjacency matrix, yielding different graph structures. For instance, DropEdge~\cite{rong2020dropedge} randomly removes a certain percentage of edges of the input graph for each training epoch and can be interpreted as a topology-level augmenter. NodeAug \cite{wang2020nodeaug} adds and removes edges on subgraphs based on their self-defined importance score. Zhao et al.~\cite{zhao2021data} exploit their proposed neural edge predictor to promote intra-class edges and demote inter-class edges in a given graph structure. While feature-level augmentation recovers missing or interrupted vertex features using their context information. Existing feature-level augmentation mainly exploits perturbations guided by adversarial training. Some studies \cite{deng2019batch, feng2019graph, kong2020flag} inject adversarial noise to node attributes and to regularize the training of GNNs. Nevertheless, these feature-level augmentation techniques have three drawbacks. 1) They employ full-batch adversarial training for augmentation, which is unnecessary, and introduce some additional side effects such as over-smoothing~\cite{li2018deeper}. 2) This type of feature-level augmentation is coarse-grained, which focuses on global augmentation and abandons the local information of the neighborhood. 3) Injecting the perturbation into features degrades the quality of the feature representations.
Moreover, to our best knowledge, none of the existing approaches combines both the feature representations and the graph topology, especially the local subgraph structures, for graph-level data augmentation.

In this work, to consider both structure and features, we propose a framework: \textbf{L}ocal \textbf{A}ugmentation for \textbf{G}raph \textbf{N}eural \textbf{N}etworks (LA-GNNs). The term "local augmentation" refers to the generation of neighborhood information by \textbf{conditioning on local structures and node features} via a generative model. Specifically, our proposed framework learns the conditional distribution of the connected neighbors' representations given the representation of the central node, which has an analogy with the Skip-gram of word2vec model~\cite{mikolov2013distributed} that predicts the probability of the context given the central word. The motivation behind this work concludes three-fold. 1) Existing feature-level augmentation works primarily pay attention to global augmentation without considering the informative neighborhood. 2) The distribution of the representations of the neighbors has a close connection to the central node, making ample room for feature augmentation. 3) JKnet~\cite{xu2018representation}, APPNP~\cite{klicpera2019predict} and GCNII~\cite{chen2020simple} preserve the locality of the node representations to avoid the over-smoothing, yielding the demand of local augmentation. And there are several benefits in applying local augmentation for the GNN training. First, local augmentation is essentially a data augmentation technique that can improve the generalization of the GNN models and prevent over-fitting. Second, we can recover some missing or interrupted feature information in an attributed graph via the generative model~\cite{jia2020residual}. Third, our proposed framework is flexible and can be equipped with various popular backbone networks such as GCN~\cite{kipf2017semi}, GAT~\cite{velivckovic2018graph}, GCNII~\cite{chen2020simple}, and GRAND~\cite{feng2020grand} to enhance their performance. Extensive experimental results demonstrate that our proposed framework could improve the performance of GNN variants on benchmark datasets.
\begin{figure}[t]
\centering
\includegraphics[width=13.5cm,height=4.2cm]{images/framework.pdf}
\caption{A schematic depiction of our local augmentation. The purple and yellow circles on the graph correspond to the central node and its augmented neighbors respectively. After augmenting the neighborhood, we concat the initial and the generated feature matrix as input for GNNs.}
\label{framework}
\end{figure}
\section{Local Augmentation}
The local augmentation framework we proposed consists of three modules: the generator, the importance sampling module, and GNN as an auxiliary downstream task, as illustrated in Figure~\ref{framework}. For each node, the pipeline utilizes the generative model to learn the conditional distribution of the feature representations of its connected neighbors. We then exploit importance sampling to determine the optimal generated data to augment the training set, according to the dropout uncertainty of the downstream GNN predictor, which is subsequently trained on the augmented dataset.

\subsection{Notations and Preliminaries}
\paragraph{Notations.}
Let $G=(V, E)$ represent the graph, where $V$ is the set of vertices $\left\{v_{1}, \cdots, v_{N}\right\}$ with $|V|=N$ and $E$ is the set of edges. The adjacency matrix is defined as $\mathbf{A} \in \{0,1\}^{N \times N}$, and $\mathbf{A}_{i j}=1$ if and only if $\left(v_{i}, v_{j}\right) \in E$. Let $\mathbf{\mathcal{N}}_{i}=\{v_j | \mathbf{A}_{ij} = 1\}$ denotes the neighborhood of node $v_i$ and $\mathbf{D}$ denote the diagonal degree matrix, where $\mathbf{D}_{i i}=\sum_{j=1}^{n} \mathbf{A}_{i j}$. The feature matrix is denoted as $\mathbf{X} \in \mathbb{R}^{N \times F}$ where each node $v$ is associated with a $F$-dimensional feature vector $\mathbf{X}_v$. $\mathbf{Y} \in \{0,1\}^{N \times C}$ denote the one-hot label matrix, where $\mathbf{Y}_i \in \{0, 1\}^{C}$ is a one-hot vector and $\sum_{j=1}^{C} \mathbf{Y}_{ij}=1$ for any $v_i \in V$.

\paragraph{GNN.}
Graph Neural Networks (GNNs) are neural network models, such as GCN and GAT~ \cite{kipf2017semi, velivckovic2018graph}, that capture the dependence of graphs via message passing between the nodes of graph as
\begin{equation}
\mathbf{H}^{(\ell)} = f(\mathbf{A}, \mathbf{H}^{(\ell-1)})
\end{equation}
where $f$ denotes the specific  GNN layer for different models, $\mathbf{H}^{(\ell)}$ are the hidden vectors of the $\ell$-th layer and $\mathbf{H}^{(0)} = \mathbf{X}$. For example, $f(\mathbf{A}, \mathbf{H})=\sigma(\hat{\mathbf{A}}\mathbf{H}\mathbf{W})$ for GCN, where $\hat{\mathbf{A}}=\tilde{\mathbf{D}}^{-\frac{1}{2}}\tilde{\mathbf{A}}\tilde{\mathbf{D}}^{-\frac{1}{2}}$, $\tilde{\mathbf{D}}$ is the degree matrix of $\tilde{\mathbf{A}}$, i.e., $\tilde{\mathbf{D}}_{ii}=\sum_j\tilde{\mathbf{A}}_{ij}$, and $\tilde{\mathbf{A}}=\mathbf{A}+\mathbf{I}$.

\subsection{Learning The Conditional Distribution}
\label{Local Augmentation}
We start by reviewing the semi-supervised learning of GNNs. Most existing GNN models~\cite{kipf2017semi, velivckovic2018graph} are viewed as a classification function to predict the class labels of the graph nodes. In this work, we use a GNN classification estimator $P_\theta(\mathbf{Y}|\mathbf{A},\mathbf{X})$ ($\theta$ is the parameter) to model the conditional distribution of label  $\mathbf{Y}$ with respect to the graph structure $\mathbf{A}$ and feature matrix $\mathbf{X}$. Given training samples $\left\{\mathbf{A}, \mathbf{X}, \mathbf{Y}\right\}$, the parameter $\theta$ can be estimated using Maximum Likelihood Estimation (MLE), by optimizing the following likelihood function:

\begin{equation}
\label{likelihood function}
\max \prod_{k \in \mathbf{K}} P_\theta\left(\mathbf{Y}_{k} | \mathbf{A}, \mathbf{X}\right)
\end{equation}

where $\mathbf{K}$ is the set of node indices of the training dataset whose labels are visible during the semi-supervised training. To further boost the performance of GNN, a new model $P_\theta(\mathbf{Y},\mathbf{\overline{X}}|\mathbf{A},\mathbf{X})$ is introduced, where $\mathbf{\overline{X}}$ is generated features by feature-level augmentation~\cite{kong2020flag, zhu2020pre}. For this model, the MLE method needs to optimize a marginalized probability $P_\theta$ over the generated feature matrix $\mathbf{\overline{X}}$:

\begin{equation}
\label{generated x likelihood}
\max \prod_{k \in \mathbf{K}}\int_{\mathbf{\overline{X}}} P_\theta\left(\mathbf{Y}_{k}, \mathbf{\overline{X}}| \mathbf{A}, \mathbf{X}\right)
\end{equation}

For Bayesian tractability, we decompose $P_\theta$ in Eq.(\ref{generated x likelihood}) as a product of two posterior probabilities:

\begin{equation}
\label{two terms of distribution}
P_{\theta, \phi}(\mathbf{Y}_{k}, \mathbf{\overline{X}}|\mathbf{A}, \mathbf{X}) := P_{\theta}(\mathbf{Y}_k|\mathbf{A}, \mathbf{\overline{X}})Q_{\phi}(\mathbf{\overline{X}}|\mathbf{A}, \mathbf{X})
\end{equation}
where $P_{\theta}(\mathbf{Y}_k|\mathbf{A}, \mathbf{\overline{X}})$ and $Q_{\phi}(\mathbf{\overline{X}}|\mathbf{A}, \mathbf{X})$ denote the probabilistic distributions approximated by the downstream GNN and the (feature-level augmentation) generator respectively, parameterized by $\theta$ and $\phi$. \textbf{There are two benefits in the decomposition above.} First, it allows us to decouple the training of the downstream predictor $P_{\theta}$ and the generator $Q_{\phi}$, enabling the generator to easily generalize to other downstream tasks. Moreover, inspired by the successes of data augmentation via deep-learning-based generative modeling \cite{antoniou2017data}, the representation power of Eq.(\ref{two terms of distribution}) is superior than that of a single predictor $P_\theta\left(\mathbf{Y}_{k} | \mathbf{A}, \mathbf{X}\right)$ without data augmentation.

Consequently, once a generator $Q_\phi$ is trained very well, our training procedure can optimize $P_{\theta}(\mathbf{Y}_k|\mathbf{A}, \mathbf{\overline{X}})$ with samples $\mathbf{\overline{X}}$ drawn from the fixed conditional distribution $Q_{\phi}$. Now, we show how to train the generator as follows.
\begin{figure}[t]
\centering
{\scalebox{0.9}[0.9]{
\subfigure[EP-B]{
\begin{minipage}[b]{0.3\textwidth}
\includegraphics[width=1.0\linewidth]{images/EP.pdf}
\end{minipage}}
\subfigure[GraphSAGE]{
\begin{minipage}[b]{0.3\textwidth}
\includegraphics[width=1.0\linewidth]{images/graphsage.pdf}
\end{minipage}}
\subfigure[Local Augmentation]{
\begin{minipage}[b]{0.3\textwidth}
\includegraphics[width=1.0\linewidth]{images/local_augmentation.pdf}
\end{minipage}}
}}
\caption{(a) EP-B exploits the neighbors to reconstruct the central node's embedding. (b) GraphSAGE encourage nearby nodes to have similar embeddings. (c) Given the representation of the central node, our aim is to infer the representations of connected distribution of neighbors.}
\label{fig:compare}
\vspace{-0.2cm}
\end{figure}

\paragraph{Generator}
To learn a feature augmentation generator, a naive solution is to learn one single distribution for all the neighbors using  the MLE method, i.e., solving the following optimization problem
\begin{equation}
\label{conditional likelihood1}
\max _{\psi} \sum_{j \in \mathcal{N}_{i}}\log p_{\psi}\left(\mathbf{X}_{j} |\mathbf{X}_{i}\right) = \max _{\psi} \log \prod_{j \in \mathcal{N}_{i}} p_{\psi}\left(\mathbf{X}_{j} | \mathbf{X}_{i}\right)
\end{equation}
where $\{\mathbf{X}_{j | j \in \mathcal{N}_{i}}, \mathbf{X}_{i}\}$. Then $p_\psi$ can be used to augment features for all the neighbors. However, this method ignores the differences between all the neighbors, which may induce severe noise.

To overcome the limitation, we assume that each neighbor satisfies a different conditional distribution. Specifically, there exists a conditional distribution $p(\cdot|\mathbf{X}_i, \mathbf{z}_j)$ with latent random variable $\mathbf{z}_j$, such that we have $\mathbf{X}_j \sim p(\mathbf{X}|\mathbf{X}_i, \mathbf{z}_j)$ for $\mathbf{X}_{j | j \in \mathcal{N}_{i}}$. Once we obtain $p(\cdot|\mathbf{X}_i, \mathbf{z}_j)$ in some way, we can generate augmented features $\mathbf{\overline{X}}$, and then we can train $P_\theta(\mathbf{Y}_k|\mathbf{A},\mathbf{\overline{X}})$ instead of $P_\theta(\mathbf{Y}_k|\mathbf{A}, \mathbf{X})$ to improve the final performance of $P_\theta$. Below, we will present how to find $p(\cdot|\mathbf{X}_i,\mathbf{z}_j)$, which will produce the generator $Q_\phi$.

To achieve our purpose, a suitable method is the conditional variational auto-encoder (CVAE)~\cite{kingma2013auto, sohn2015learning}, which can help learn the distribution of the latent variable $\mathbf{z}_j$, and the conditional distribution $p(\cdot|\mathbf{X}_i,\mathbf{z}_j)$. So, a CVAE model $Q_{\phi}\left(\mathbf{\overline{X}} | \mathbf{A}, \mathbf{X}\right)$ is adopted as our generator, where $\phi = \{\varphi, \psi \}$, $\varphi$ denotes the variational parameters and $\psi$ represents the generative parameters. To derive the optimization problem for CVAE, $\log p_{\psi}\left(\mathbf{X}_{j} | \mathbf{X}_{i}\right)$ can be written with latent variables $\mathbf{z}$ as follows, following previous work \cite{pandey2017variational, sohn2015learning}:
\begin{equation*}
\begin{split}
\log p_{\psi}\left(\mathbf{X}_{j} | \mathbf{X}_{i}\right) &= \int q_{\varphi}(\mathbf{z} | \mathbf{X}_j, \mathbf{X}_{i}) \log \frac{p_{\psi}(\mathbf{X}_j, \mathbf{z} | \mathbf{X}_{i})}{q_{\varphi}(\mathbf{z} | \mathbf{X}_{j}, \mathbf{X}_i)} \mathrm{d} \mathbf{z}+KL(q_{\varphi}(\mathbf{z} | \mathbf{X}_{j}, \mathbf{X}_i) \| p_{\psi}(\mathbf{z} | \mathbf{X}_{j}, \mathbf{X}_i)) \\ &\geq \int q_{\varphi}(\mathbf{z} | \mathbf{X}_j, \mathbf{X}_{i}) \log \frac{p_{\psi}(\mathbf{X}_j, \mathbf{z} | \mathbf{X}_i)}{q_{\varphi}(\mathbf{z} | \mathbf{X}_{j}, \mathbf{X}_i)} \mathrm{d} \mathbf{z}
\end{split}
\end{equation*}
and the evidence lower bound (ELBO) can be written as:
\begin{equation}
\label{generator elbo}
\mathcal{L}(\mathbf{X}_j, \mathbf{X}_i ; \psi, \varphi) = -K L(q_{\varphi}(\mathbf{z} | \mathbf{X}_j, \mathbf{X}_i) \| p_{\psi}(\mathbf{z} | \mathbf{X}_i))+\int q_{\varphi}(\mathbf{z} | \mathbf{X}_j, \mathbf{X}_i) \log p_{\psi}(\mathbf{X}_j | \mathbf{X}_i, \mathbf{z}) \mathrm{d} \mathbf{z}
\end{equation}

where the encoder $q_{\varphi}(\mathbf{z} | \mathbf{X}_j, \mathbf{X}_i) = \mathcal{N}(f(\mathbf{X}_j, \mathbf{X}_i), g(\mathbf{X}_j, \mathbf{X}_i))$, and the decoder $p_{\psi}(\mathbf{z} | \mathbf{X}_i)=\mathcal{N}(0, I)$, $p_{\psi}(\mathbf{X}_j | \mathbf{X}_i, \mathbf{z}) = \mathcal{N}(f(\mathbf{X}_i, \mathbf{z}), c I)$, and $\{f, g\}$ are approximated by neural networks.
For simplicity and tractability, the implemented generator $Q\left(\mathbf{\overline{X}} | \mathbf{A}, \mathbf{X}\right)$ uses the same parameters across all nodes $v_i \in V$.

Here, we discuss how our proposed model distinguishes from the classical representation learning models on graphs. Previous methods such as EP-B \cite{garcia2017learning} and GraphSAGE \cite{hamilton2017inductive} rely on reconstruction loss function between the central node and its neighbors' embeddings. EP-B aims to minimize the reconstruction error by optimizing the objective $\operatorname{min} \sum_{u\in V \setminus \{v\} }\left[\gamma+d(\widetilde{h}_{v},h_v)-d(\widetilde{h}_{v},h_u)\right]$ where $h_v$ represents the target node; $h_u$ denotes the neighbor nodes; $\widetilde{h}_{v} = \mathrm{AGG}(h_l | l\in \mathcal{N}(v)$) indicates the reconstruction from neighbors; and $\gamma$ refers to the bias. Besides, GraphSAGE exploits the negative sampling to differentiate the representations of remote node-pairs. GraphSAGE enforce nearby nodes to have similar representations and to enforce disparate nodes to be distinct by minimizing the objective $\operatorname{min}-E_{u \sim \mathcal{N}(v)}\log \left((\sigma(h_{u}^{T} h_{v}))\right)-\lambda E_{v_n \sim P_n(v)}\log \left((\sigma(-h_{v_n}^{T} h_{v}))\right)$ where $h_v$ denotes target node; $h_u$ represents the neighbor node; $h_{v_n}$ is disparate node; and $P_n(v)$ is the negative sampling. These approaches build upon the assumption that adjacent nodes share similar attributes. In contrast, our model does not rely on such assumption and instead generates the neighboring node features from the conditional distribution of central node representations. Given the target node, $\mathbf{X}_v$, our aim is to learn the conditional distribution of the neighbor nodes, $\mathbf{X}_u$. A comparison between the reconstruction-based representation learning on graphs and our proposed framework is illustrated in Figure~\ref{fig:compare}.

\paragraph{Optimization of the MLE}
Now, we present how to optimize the MLE Eq.(\ref{two terms of distribution}) using the feature matrix produced from the generator. Once the augmented feature matrix can be sampled from the generator, we can optimize the parameters of Eq.(\ref{two terms of distribution}) in the following way. Firstly, the parameter $\phi=\{\psi,\varphi\}$ can be optimized by maximizing the ELBO of the generator~(\ref{generator elbo}), i.e., we train the generator. Secondly, the parameter $\theta$ is optimized by maximizing the MLE Eq.(\ref{two terms of distribution}) with $\phi$ fixed, which is the conditional distribution of $\mathbf{Y}_k$ given $\mathbf{A}$ and $\mathbf{\overline{X}}$. In this way, we iteratively and alternately optimize the conditional MLE and ELBO.

In this paper, the MLE is formulated by a GNN model as follows:
\begin{equation}
    P_{\theta}\left(\mathbf{Y}_{k} \mid \mathbf{A}, \overline{\mathbf{X}}\right) \propto-\mathcal{\overline{L}}(\theta | \mathbf{A}, \mathbf{\overline{X}}, \phi)
\end{equation}
where $\mathcal{\overline{L}}(\theta | \mathbf{A}, \mathbf{\overline{X}}, \phi)=-\sum_{k \in \mathbf{T}} \sum_{f=1}^{C} \mathbf{Y}_{k f} \ln\left( \operatorname{softmax}\left(\operatorname{GNN}(\mathbf{A}, \mathbf{\overline{X}})\right)_{kf}\right)$. In addition, a practical trick is introduced which firstly trains GNN parameter $\theta$ with $\mathbf{A}$ and the initial feature matrix $\mathbf{X}$ for some iterations, and then updates it using $\mathbf{A}$ and the augmented feature matrix $\mathbf{\overline{X}}$. Later, section~\ref{Importance Sampling} will further present a close relationship between the inference of the generator and the optimization of the MLE.

\begin{algorithm}[tb]
\small{
\caption{Updating the GNN parameters $\theta$ using the initial feature matrix $\mathbf{X}$ and the generated feature matrix $\mathbf{\mathbf{\overline{X}}}$ selected by the acquisition function}
\hspace*{0.02in} {\bf Input:}
Adjacency matrix $\mathbf{A}$, feature matrix $\mathbf{X}$  \\
\hspace*{0.02in} {\bf Output:}
Generated feature matrix $\mathbf{\overline{X}}_{best}$
\begin{algorithmic}[1]
\State Train GNN $P_{\theta}$ using $\mathbf{A}$ and $\mathbf{X}$ for the number of initial GNN training iterations
\State Initialize $U_{best}$, $\mathbf{\overline{X}}_{best}$
\For{$i=1$ to the number of generator iterations}
    \State Train the generator $Q_{\phi}$ using $\mathbf{A}$ and $\mathbf{X}$
    \State Generate feature matrix $\mathbf{\overline{X}}$ using $Q_{\phi}$
    \State Compute $U(\mathbf{\overline{X}})$ using $P_{\theta}$ and $\mathbf{\overline{X}}$
        \If{$U(\mathbf{\overline{X}})$ > $U_{best}$}
            \State $U_{best}$ = $U(\mathbf{\overline{X}})$
            \If {$i$ > $N_{warmup}$}
                \State Train GNN $P_{\theta}$ using $\mathbf{A}$ and $\mathbf{\overline{X}}$ for the number of continued GNN training iterations
                \State $\mathbf{\overline{X}}_{best}$ = $\mathbf{\overline{X}}$
            \EndIf
        \EndIf
\EndFor
\State \Return Generated feature matrix $\mathbf{\overline{X}}_{best}$
\end{algorithmic}
\label{importance sampling}}
\end{algorithm}

\subsection{Importance Sampling}
\label{Importance Sampling}
After the training of the generator finishes, it is contain an issue of using Eq.(\ref{two terms of distribution}) for inference because $Q$ may generate some rare samples from the side part of the distribution. This critical question makes the inferences Eq.(\ref{two terms of distribution}) inefficient. Inspired by the active learning~\cite{nielsen2019gan}, we introduce importance sampling to capture the suitable generated feature matrix, which improves the inference efficiency and accelerates the optimization of the MLE. During the importance sampling, the probability of each feature is proportional to its uncertainty evaluated by an acquisition function. We adopt the Bayesian Active Learning by Disagreement (BALD) acquisition function~\cite{houlsby2011bayesian} to sample the most important inferences with the approximation from the Monte Carlo (MC) dropout samples as
\begin{equation}
    U(\mathbf{\overline{X}}) \approx H\left[\frac{1}{N} \sum_{n=1}^{N} P_{\theta}\left(\mathbf{Y}_k | \mathbf{\overline{X}}, \boldsymbol{\omega}_{n}\right)\right] -\frac{1}{N} \sum_{n=1}^{N} H\left[P_{\theta}\left(\mathbf{Y}_k | \mathbf{\overline{X}}, \boldsymbol{\omega}_{n}\right)\right]
\end{equation}
where $N$ is the number of MC samples and $\boldsymbol{\omega}_{n}$ are the parameters of the network sampled for the $n$-th MC dropout sample. A high BLAD score indicates a network with high uncertainty about the generated feature matrix. So it tends to be selected to improve the GNN model. Finally, the overall algorithm framework is summarized in Algorithm~\ref{importance sampling}, which assists the optimization of Eq.(\ref{two terms of distribution}) and generates a suitable generated feature matrix for downstream tasks.

\subsection{The Architecture of LA-GNN}
In this section, we discuss the details of how to modify backbone models to exploit the captured augmented feature matrix. We use GCN, GAT, GCNII, and GRAND as the backbone network of the proposed framework and test them on semi-supervised node classification tasks.

When the above steps finish, both the initial data and the generated feature matrix are useful for the training of the backbone networks. Therefore, we mix the initial and generated feature representations using concatenation operation. Then we feed the mixed representation to the next GNN layer to obtain our new model, named LA-GNN, where LA means local augmentation. Specifically, a 2-layer LA-GCN is defined as follows:
\begin{equation}
\mathbf{H}^{(2)}=\sigma\left(\tilde{\mathbf{D}}^{-\frac{1}{2}} \tilde{\mathbf{A}} \tilde{\mathbf{D}}^{-\frac{1}{2}}\left(\sigma\left(\tilde{\mathbf{D}}^{-\frac{1}{2}} \tilde{\mathbf{A}} \tilde{\mathbf{D}}^{-\frac{1}{2}} \mathbf{X} \mathbf{W}_1^{(1)}\right) \bigg{\|} \sigma\left(\tilde{\mathbf{D}}^{-\frac{1}{2}} \tilde{\mathbf{A}} \tilde{\mathbf{D}}^{-\frac{1}{2}} \mathbf{\overline{X}} \mathbf{W}_2^{(1)}\right)\right)\mathbf{W}^{(2)}\right)
\end{equation}
where $\|$ denotes an operator of column-wise concatenation, $\mathbf{W}_1^{(1)}$ and $\mathbf{W}_2^{(1)}$ denote the parameters of the first LA-GCN layer, and $\mathbf{W}^{(2)}$ denotes the parameters of the second LA-GCN layer. Since GCNII~\cite{chen2020simple} applies a fully-connected neural network on $\mathbf{X}$ to obtain a lower-dimensional initial representation $\mathbf{H}^{(0)}$ before the forward propagation, we apply a fully-connected neural network on $\mathbf{X}$ and $\mathbf{\overline{X}}$ to obtain $\mathbf{H}^{(0)}$ for the LA-MLP and LA-GCNII as follows:
\begin{equation}
\mathbf{H}^{(0)}=\sigma\left(\mathbf{X}\mathbf{W}_{1}^{(0)}\big{\|}\mathbf{\overline{X}}\mathbf{W}_{2}^{(0)}\right)
\end{equation}
$\mathbf{H}^{(0)}$ is fed into the next forward propagation layer. LA-GAT has a similar network architecture with LA-GCN, but the graph convolutional layer needs to be replaced by the graph attention layer. The overall architecture of LA-GNN is shown in Figure~\ref{framework}.

\subsection{Discussion}\label{discussion}
In this section, we discuss the motivation of this work and provide some analysis.
\paragraph{Local Augmentation vs. General Augmentation} General image augmentation algorithms include geometric transformations, feature space augmentation, adversarial training, and generative adversarial networks~\cite{shorten2019survey}. It is impossible to apply geometric transformations directly to graph data augmentation since graphs are sensitive to node permutation. General adversarial training, feature space augmentation, and generative adversarial networks don't take the graph structure into account. Graphs consist of a set of identities with certain pairs of these identities connected by edges. We need to consider node features and the graph structure when designing the graph data augmentation framework. Our proposed method of local augmentation fully considers these two points. By extracting the neighbors' feature vectors, we have enough data points to learn the distribution. There are two benefits to designing local augmentation. First, by taking the sub-graph structure and feature representation associated with this sub-graph structure as input for the generative model, we can learn the information of the sub-graph structure. Second, the number of data points to learn the distribution depends on the node degree. This assures that we have enough data points compared with the general feature augmentation and we can learn a better distribution.

\paragraph{Complementing missing Information} Jia et al.~\cite{jia2020residual} points out that some attribute information might be missing on a subset of vertices. By learning the distribution of node representations from the observed data, we can utilize the produced node representations from the generative model to Complement the information missing in the nodes' attributes, which boosts the robustness of downstream tasks. And we show that our model still works in the scenario that nodes lose a certain percentage of attributes.

\section{Related Work}
\paragraph{Graph Neural Networks} In general, convolution in the graph domain involves non-spectral (spatial) and spectral approaches. Non-spectral methods generalize convolutions operating on spatially close neighbors to the graph domain. Duvenaud et al.~\cite{duvenaud2015convolutional} define the convolutional operation with a specific weight matrix for each node degree. Diffusion-convolution neural networks (DCNNs) \cite{atwood2016diffusion} employs the transition matrix power series to propagate features. Niepert et al.~\cite{niepert2016learning} extract local features with a fixed number of neighbors. Monet \cite{monti2017geometric} proposes a unified framework to generalize CNN architectures on non-Euclidean domains. Spectral approaches define the convolution operations based on the spectral formulation. Bruna et al.~\cite{bruna2014spectral} specify the convolution operator with the spectrum of the graph Laplacian. Defferrard et al.~\cite{defferrard2016convolutional} approximate the filters by computing the Chebyshev polynomial recurrently, yielding fast and localized spectral ones. Graph Convolutional Network (GCN) \cite{kipf2017semi}, one of the most influential techniques, applies the first-order approximation of localized spectral filters to operate the connected neighbors. Recently, several methods \cite{abu2019mixhop, liao2019lanczosnet} based on GCN have been proposed to obtain the higher-order filters. Besides, GAT \cite{velivckovic2018graph}, Graph U-Nets \cite{gao2019graph} combine attention networks and pooling operation with GNN separately, which achieve state-of-the-art performance on node and link classification tasks. In this work, local augmentation can be embedded in various popular backbone models to improve performance.

\paragraph{Graph Generative Models} Generative models \cite{goodfellow2014generative, kingma2013auto} are powerful tools of learning data distribution through unsupervised learning,
 and they have achieved tremendous success in various applications. Recently, researchers have proposed several interesting generative models for graph data generation. Variational graph auto-encoder (VGAE) \cite{kipf2016variational} makes use of latent variables and learns interpretable latent representations for undirected graphs. Salha et al.~\cite{salha2019keep} replace the GCN encoder in VGAE with a simple linear model and emphasize the effectiveness of a simple node encoding scheme. Xu et al.~\cite{xu2019generative} propose a generative model framework to learn node representations, by sampling graph generation sequences constructed from observed graph data. ConDgen \cite{yang2019conditional} exploits the GCN encoder to handle the inherent challenges of flexible context-structure conditioning and permutation-invariant generation. Besides, some methods have been proposed to apply the graph generative models in various application such as graph matching \cite{simonovsky2018graphvae}, molecule design\cite{liu2018constrained}, retrosynthesis prediction \cite{shi2020graph} and chemical design\cite{samanta2018designing}. Compared with these approaches mainly focusing on structure generation, our model takes full use of the power of the generative model for feature representation generation, which can serve as an enhanced technique for the downstream backbone models.

\paragraph{Topology-level Augmentation.} Topology-level augmentation usually perturbs $\mathbf{A}$ to generate different graph structures,  which can be formulated as $\mathbf{A'} = \mathcal{F}(\mathbf{A}, \mathbf{X})$, where $\mathcal{F}(\cdot)$ is a structure perturbation function. For example, DropEdge~\cite{rong2020dropedge} considers $\mathcal{F}(\mathbf{A}, \mathbf{X}) = \mathbf{A} - \mathbf{A_s}$ which is independent of $\mathbf{X}$, where $\mathbf{A_s}$ is a sparse matrix consists of a subset of the original edges $E$. \textsc{Gaug-O}~\cite{zhao2021data} employs a non-close-form formulation of the function and leverages their proposed neural edge predictors to produce a different structure $\mathbf{A'}$ where $\mathbf{A}_{i j}^{\prime}=\left\lfloor\frac{1}{1+e^{-\left(\log \mathbf{P}_{i j}+G\right) / \tau}}+\frac{1}{2}\right\rfloor$, $\mathbf{P}_{i j}=\alpha \mathbf{M}_{i j}+(1-\alpha) \mathbf{A}_{i j}$, $\mathbf{M}=\sigma\left(\mathbf{Z} \mathbf{Z}^{T}\right)$, $\mathbf{Z}=f\left(\mathbf{A}, f(\mathbf{A}, \mathbf{X})\right)$, $\tau$ is the temperature of Gumbel-Softmax distribution, $G \sim \operatorname{Gumbel}(0,1)$ is a Gumbel random variate, and $\alpha$ is a hyperparameter mediating the influence of edge predictor on the original graph.

\paragraph{Feature-level Augmentation.}
\label{Feature-level Augmentation}
\begin{wraptable}{7}{0.62\textwidth}
    \vspace*{-\baselineskip}
	\centering
	\vspace{-1mm}
	\caption{Comparison of existing graph data augmentation.}
    {\scriptsize
	\begin{tabular} { | l || c ||  c ||  c | }
    \hline
    \multicolumn{4} { | c | }{Graph Data Augmentation}\\
    \hline
    Method & Considered Part & Type & Perturbed Part \\
    \hline
    DropEdge & $\mathbf{A}$ & Sampling& $\mathbf{A}$ \\
    \textsc{Gaug-O}& $\mathbf{A} \& \mathbf{X}$ & Reconstruction& $\mathbf{A}$ \\
    FLAG & $\mathbf{X}$ & Noise Injection &$\mathbf{X}$ \\
    G-GCN & $\mathbf{A} \& \mathbf{X}$ & Reconstruction & $\mathbf{X}$ \\
    Local Augmentation & $\mathbf{A} \& \mathbf{X}$ & Generation & $\mathbf{X}$ \\
    \hline
    \end{tabular}
	}

	\label{Comparison of data augmentation}
\end{wraptable}
Besides, feature-level augmentation function can be defines as $\mathbf{X'} = \mathcal{H}(\mathbf{A}, \mathbf{X})$, where $\mathcal{H}(\cdot)$ is a feature perturbation function. FLAG~\cite{kong2020flag} defines the perturbation function as $\mathcal{H}(\mathbf{A}, \mathbf{X}) = \mathbf{X} + \boldsymbol{\delta}$ where perturbation $\boldsymbol{\delta}$ is updated iteratively during the adversarial training phase. G-GCN (plain) ~\cite{zhu2020pre} obtains the global attribute feature matrix $\mathbf{X}^{(a)} \in \mathbb{R}^{N \times d_{a}} $ through minimizing the objective $\prod_{v \in V} \prod_{a \in C A(v)} \frac{\exp \left(\mathbf{X}_{v}^{(a)} \cdot \mathbf{V}_{a}\right)}{\sum_{k \in U} \exp \left(\mathbf{X}_{v}^{(a)} \cdot \mathbf{V}_{k}\right)}$ where $U$ is the set of all attributes, $CA(v)$ is the sampled context attributes of $v$, and $\mathbf{V} \in \mathbb{R}^{d_{a} \times F}$ denotes the parameters. Obviously, the perturbation function of G-GCN has no close-form solution.
In this work, we propose a novel feature perturbation function, named local augmentation, whose differences with existing methods are presented. And the comparison of the details of various graph data augmentation techniques can be found in Table~\ref{Comparison of data augmentation}.

\begin{table}[tb]
    \caption{Classification results on random split (\%)}
    \label{random split}

    \vspace*{-\baselineskip}
    \centering
    \vskip 0.10in

    {\scalebox{0.82}[0.82]{
    \begin{tabular}{lccccccccc}
    \toprule
    \textbf{Dataset} &APPNP & S$^{2}$GC & GCN & DropEdge-GCN & LA-GCN & GAT & LA-GAT & GCNII & LA-GCNII \\
     \midrule
\textbf{Squirrel}  &21.6 &21.3  &22.5  &21.9  &23.2  &24.2  &28.2 &25.3 &\textbf{28.6}  \\
\textbf{Actor}     &32.1 &27.8  &26.2  &26.5  &27.0  &27.2  &27.4 &31.9 &\textbf{32.7}   \\
\textbf{Chameleon} &33.0 &30.2  &25.1  &25.0  &28.9  &34.8  &\textbf{38.6} &30.2 &32.5   \\
\textbf{Cornell}   &\textbf{58.7} &57.2  &55.7  &53.6  &56.1  &55.8  &56.5 &57.3 &56.6   \\
    \bottomrule
    \end{tabular}
    }}

    \vskip -0.15in
  \end{table}

\vspace*{-\baselineskip}
\section{Experiments}

\begin{wraptable}[15]{r}{0.48\textwidth}
    \vspace{-6ex}
	\centering
	\caption{Classification results on fixed split (\%)}
	\label{fixed split}
    {\scriptsize
	\begin{tabular}{lccc}
		\toprule
		\textbf{Method} & \textbf{Cora} & \textbf{Citeseer} & \textbf{Pubmed} \\
		\midrule
        Chebyshev~\cite{defferrard2016convolutional}         &81.2  &69.8  &74.4   \\
        APPNP~\cite{klicpera2019predict}     &83.8  &71.6  &79.7   \\
        MixHop~\cite{abu2019mixhop}      &81.9  &71.4  &80.8   \\
        Graph U-net~\cite{gao2019graph}     &84.4  &73.2  &79.6   \\
        GSNN-M~\cite{wang2020graph}        &83.9  &72.2  &79.1   \\
        S$^{2}$GC~\cite{zhu2021simple}         &83.5  &73.6  &80.2   \\
        \midrule
        GCN~\cite{kipf2017semi}         &81.6  &70.3  &78.9   \\
        GAT~\cite{velivckovic2018graph}         &83.0  &70.4  &OOM   \\
        GCNII~\cite{chen2020simple}      &85.2  &73.1  &80.0   \\
        \textsc{GRAND~\cite{feng2020grand}}      &85.4  &75.4  &82.7   \\
        \midrule
        G-GCN\cite{zhu2020pre}    &83.7  &71.3  &80.9\\
        DropEdge-GCN\cite{rong2020dropedge}    &82.8  &72.3  &79.6\\
        \textsc{Gaug-O}-GCN\cite{zhao2021data}    &83.6  &73.3  &79.3\\
        LA-GCN    &84.1  &72.5  &81.3\\
        LA-GAT      &83.9  & 72.3 &OOM \\
        LA-GCNII    &85.2  &73.7  &81.6\\
        \textsc{LA-GRAND}      &\textbf{85.8}  &\textbf{75.8}  &\textbf{83.3}   \\
        \bottomrule
        \vspace*{-\baselineskip}
	\end{tabular}
	}
\vspace*{-\baselineskip}
\end{wraptable}
In this section, we evaluate the performance of our proposed model on semi-supervised node classification tasks on a  variety of public graph datasets and compare our model with the state-of-the-art graph neural networks. We also carry out additional experiments to showcase the necessity of our design and its robustness to missing information.

\subsection{Datasets}
\begin{wrapfigure}{r}{.45\textwidth}
 \centering
\vspace*{-\baselineskip}
\adjincludegraphics[trim={{.03\width} {.02\height} {.05\width} {.05\height}}, clip,width=.45\columnwidth]{images/attributes.pdf}
\vspace*{-\baselineskip}
\caption{The inferred distribution of the attributes of the neighbors vs. the original distribution, with KL divergence = 0.0026}
\label{figure:attention_weights}
\end{wrapfigure}
We utilize seven public graph datasets (Cora, Citeseer, Pubmed, Squirrel, Actor, Chameleon, and Cornell) for semi-supervised node classification tasks. The details of these datasets can be found in the appendix.

\subsection{Semi-supervised Node Classification}
\paragraph{Baselines and Experimental Setup.} We apply the standard fixed splits~\cite{yang2016revisiting} on three datasets Cora, Citeseer, and Pubmed, with 20 nodes per class for training, 500 nodes for validation, and 1,000 nodes for testing. And we consider four backbones: GCN~\cite{kipf2017semi}, GAT~\cite{velivckovic2018graph}, GCNII~\cite{chen2020simple}, and GRAND~\cite{feng2020grand} to evaluate our proposed framework and compare our model against state-of-the-art models including 1) backbone models: Chebyshev~\cite{defferrard2016convolutional}, GCN, GAT, APPNP~\cite{klicpera2019predict}, Graph U-net~\cite{gao2019graph}, MixHop~\cite{abu2019mixhop}, GCNII, GSNN-M~\cite{wang2020graph}, S$^{2}$GC~\cite{zhu2021simple}, and GRAND and 2) feature-level and topology-level augmentation models: G-GNNs~\cite{zhu2020pre}, DropEdge~\cite{rong2020dropedge} and \textsc{Gaug-O}~\cite{zhao2021data}. For four datasets Squirrel, Actor, Chameleon, and Cornell, we randomly split nodes of each class into 10\%, 30\%, and 60\% for training, validation, testing; measure the performance of GCN, GAT, GCNII and corresponding modified models.

\paragraph{Results}
For three citation network datasets Cora, Citeseer, and Pubmed, we report the mean classification accuracy on the test nodes of all our models after 100 runs and report the values after running the experiments of their models with our own server under their setting hyperparameters in their original papers. We implement GAT with code published at $\footnote{\url{https://github.com/Diego999/pyGAT}}$. The results of the evaluation experiments are summarized in Tables~\ref{random split} and \ref{fixed split}, which demonstrate that the backbone models equipped with our method achieve the best performance across all the datasets except the Cornell dataset. More specifically, we are able to improve upon GCN by a margin of 2.5\%, 2.2\%, and 2.4\% on Cora, Citeseer, and Pubmed respectively. Moreover, LA-GNN outperforms other backbone models including GAT and GCNII as well as data augmentation models~\cite{zhu2020pre, rong2020dropedge, zhao2021data} on these citation network datasets. Figure~\ref{figure:attention_weights} shows the distribution of the attributes of the original and inference neighbors, which can demonstrate our inference feature matrix follow the distribution of the initial feature matrix.

\subsection{Ablation Study}\label{Ablation Study}

\begin{wraptable}[14]{r}{0.5\textwidth}
    \vspace*{-\baselineskip}
	\centering
	\vspace{-2ex}
	\caption{Effects of different components of our framework evaluated on the standard split of the Cora, Citeseer and Pubmed dataset.}
    \label{ablation results}
    {\scriptsize
	\begin{tabular}{lccc}
		\toprule
		\textbf{Method} & \textbf{Cora} & \textbf{Citeseer} & \textbf{Pubmed} \\
		\midrule
        GCN        &81.6  &70.3  &78.9   \\
        GCNII      &85.2  &73.1  &80.0   \\
        \midrule
        GCN\ +\ width    &82.0  &71.4  &79.5\\
        GCN\ +\ concatenation   &81.8  &71.6  &78.8\\
        GCN\ +\ plain neighborhood      &80.9  &68.8  &75.0 \\
        \midrule
        GCNII\ +\ width    &85.1 &73.1  &80.2\\
        GCNII\ +\ concatenation   &85.2  &73.3  &80.2\\
        GCNII\ +\ plain neighborhood      &83.3 &71.9  &78.1 \\
        \midrule
        LA-GCN      &84.1    &72.5  &81.3\\
        LA-GCNII    &85.2    &73.7  &81.6\\
        \bottomrule
	\end{tabular}
	}
	\vspace{0.cm}
\end{wraptable}

In this section, to demonstrate the effectiveness of our proposed generative framework, we conduct experiments that compare LA-GNN to several of its ablated variants without generative modeling.
The results are shown in Table~\ref{ablation results}. "GCN + width" only increases the first network layer width for GCN and GCNII to match LA-GNN without giving generated samples as input. "+ concatenation" only replaces the generated feature matrix of LA-GNN with the original feature matrix of the central node.
 "+ plain neighborhood" replaces the generated feature matrix of LA-GNN with a neighborhood feature matrix where each row corresponds to the feature vector of the randomly sampled neighbor. The results show that the first two variants provide no notable improvement for the backbone models, and the third variant even results in degradation. By eliminating the possibility that these confounding factors irrelevant to our core approach may contribute to the final performance, it's evident that the performance gain in Table \ref{random split} and \ref{fixed split} are due to our proposed generative local augmentation framework.

\subsection{Robustness to Missing Information}
In this section, we conduct experiments to verify that our proposed framework can robustify downstream tasks against missing information in the feature attributes. Specifically, we mask a certain percentage of the attributes of each feature vector and use the same pipeline to do augmentation for the masked feature matrix. As shown in Table~\ref{recover study results}, one can see that as the mask ratio increases, the gap of the performance between the GCN and LA-GCN enlarges in most cases in Cora and Citeseer, which corroborates our insight discussed in Section \ref{discussion}. Since there exists large redundancy in the features of the Pubmed dataset, the performance of GCN and LA-GCN decrease little as the mask ratio increases. And so the gap of the performance between the GCN and LA-GCN does not enlarge in the Pubmed dataset.

\begin{table}[tbh]
\normalsize
\centering
\caption{Summary of results on recovering study in terms of classification accuracy (\%)}
\setlength{\tabcolsep}{1.5mm}
\label{recover study results}
\begin{adjustbox}{width=\textwidth}
\begin{tabular}{ccccccccccccc}
\toprule
\multicolumn{1}{c}{Dataset}& \multicolumn{4}{c}{Cora} & \multicolumn{4}{c}{Citeseer} & \multicolumn{4}{c}{Pubmed}  \\
\cmidrule(r){1-1} \cmidrule(r){2-5} \cmidrule(r){6-9} \cmidrule(r){10-13}
Mask Ratio&  0.1     &  0.2  &   0.4 & 0.8
&  0.1     &  0.2  &   0.4 & 0.8 &  0.1     &  0.2  &   0.4 & 0.8\\
\midrule
GCN         &81.0 ($\downarrow$0.6)  &80.6 ($\downarrow$1.0)   &80.1 ($\downarrow$1.5)    &76.0 ($\downarrow$5.6)   &70.1 ($\downarrow$0.2)   &69.3 ($\downarrow$1.0)   &67.2 ($\downarrow$3.1)   &61.0 ($\downarrow$9.3)   &78.5 ($\downarrow$0.4)   &78.5 ($\downarrow$0.4)   &77.5 ($\downarrow$1.4)   &76.9 ($\downarrow$2.0)  \\
LA-GCN      &83.5 ($\downarrow$0.6)   &83.1 ($\downarrow$1.0)   &81.6 ($\downarrow$2.5)    &81.1 ($\downarrow$3.0)   &72.2 ($\downarrow$0.3)   &71.7 ($\downarrow$0.8)   &69.3 ($\downarrow$3.2)   &65.9 ($\downarrow$6.6)  &81.4 ($\downarrow$0.1)   &80.9 ($\downarrow$0.6)   &80.5 ($\downarrow$1.0)   &79.4 ($\downarrow$2.1) \\
\bottomrule
\end{tabular}
\end{adjustbox}
\end{table}

\section{Conclusion}
We propose local augmentation, a brand-new technique that exploits the generative model to learn the conditional distribution of the central node's neighbors' feature representations given its own representation. We can feed the generated feature matrix from a well-trained generative model to some modified backbone GNN models to enhance model performance. Experiments show that our model can improve performance across various GNN architectures and benchmark datasets. Besides, our model achieves new state-of-the-art results on various semi-supervised node classification tasks.

One limitation of our proposed framework is that we do not exploit the 2-hop neighbors or use the random walk to find more related neighbors for the central node. And one future work is that we can extract more 2/3-hop neighbors if the central node's degree is small and learn the conditional distribution for random sampling nodes if the graph is large.
\newpage

redpajama_set_name: RedPajamaArXiv


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A Florida sheriff said Friday that his department will not arrest a White man who shot and killed a Black man after the two confronted one another over a handicap parking space, citing the state's "stand your ground" law, the Tampa Bay Times reports.
The law protects those who use deadly force to defend themselves if they are in fear of their lives, and according to the sheriff's office, this incident falls under the law, according to the Tampa Bay Times.
Michael Drejka, 47, shot and killed Markeis McGlockton, 28, on Thursday at a Circle A Food Store parking lot in Clearwater.
Law enforcement officials said Drejka confronted Britany Jacobs, McGlockton's girlfriend, because she reportedly parked in a handicap parking spot, according to reports.
Pinellas County Sheriff Bob Gualtieri said that McGlockton "slammed [Drejka] to the ground," and that is when Drejka pulled out his handgun and shot McGlockton in the chest.
The incident "is within the bookends of 'stand your ground' and within the bookends of force being justified," the sheriff said. "I'm not saying I agree with it, but I don't make that call," Gualtieri said, according to the Tampa Bay Times.
Drejka told police that he feared that he would be attacked again. He reportedly owned the gun legally and had a concealed carry permit.
McGlockton and Jacobs have a 4-month-old, a 3-year-old, who were in the car, and a 5-year-old son, who saw Jacobs try to save his father by applying pressure to the wound, she told the Tampa Bay Times.
"He's not too good. It comes and goes, but he knows he (his father) is dead," she said.
A customer of the convenience store told the newspaper that he got into an altercation with Drejka months ago when he was questioned about parking in a handicap spot. He said that Drejka threatened to shoot him.


text:
Now is the time to expedite hybrid propulsion development
18 Apr 2019by Jamey Bergman
Research demonstrated significant operating cost and maintenance savings for tugboat owners while capex in energy storage systems is decreasing
Although marine hybrid propulsion was in its infancy just a decade ago, today's hybrid propulsion trains are proving to offer lower operating expenditures than traditional tug propulsion systems.
Nevertheless, hybrid propulsion systems still make up only a small percentage of propulsion systems in the market. So, what is holding owners back from ordering hybrid systems?
In a report titled, Hybrid power workboats: a holistic approach for better capex, MAN Energy Solutions' Mark Watson – sales manager in the tug and workboat division of MAN's four-stroke marine engines business – said there are two big hurdles: higher up-front capital expenditure and perceived risks around certification, installation and operation of hybrid technology.
Tug Technology & Business caught up with Mr Watson to discuss how he and his co-authors* sought to battle misconceptions regarding cost differentials and push forward the uptake and development of hybrid technologies.
First, the group defined the fundamental approach: working with known partners to achieve cost efficiencies and build expertise that could lead to further innovation.
Secondly, Mr Watson says he felt the project needed an external benchmark against which to compare development of hybrid technologies within maritime. To his mind, the answer was clear.
"I took a broader-based view and said let's look at other industries and this is why we looked at the automotive industry," Mr Watson explains.
"The technology is clearly more advanced than it is in other sectors because they have just been doing it for longer, so that was a good place to say ok, here is a starting point, look where they have gotten in 30 years of development [and] using that as a benchmark, as a target" he says.
With a benchmark defined, the next challenge to overcome was developing a viable system on a vessel type that made sense.
Mr Watson leveraged MAN's partnership with Aspin Kemp and Associates to design the hybrid propulsion system and arranged to use hybrid thrusters that Schottel had developed independently. In terms of the vessel, focusing on tugboats made sense in that both firms had experience in the sector.
On this basis, the group managed to show that they could pare back the increases in initial capital expenditures while retaining – and in some areas improving on – expected operational expenditure savings and safety considerations.
For the propulsion plant itself, the project found an increase in investment of less than 10% was needed for their hybrid concept, rising to 12.5% with the use of an energy storage system (ESS).
Overall, that added up to somewhere between 2.5-4% extra initial capital expenditure to install a hybrid system, without including an estimate for shipyard costs including foundations, wiring, installation and component tests.
Typical cost increases and cost savings
As the report notes, although the overall percentage increase in spend on their hybrid propulsion solution ran between 10-12.5%, significant changes in cost distribution and structure bear mentioning. Depending on use of an ESS, the larger gensets needed for a hybrid propulsion train are 10-20% more expensive than their traditional counterparts.
"As power provision is shifted from the main engines to the electrical system, the size of the generators needs to be increased accordingly and consideration of IMO Tier III compliance also has to be factored in here," the report said.
Further equipment costs involve PTI/PTO electric motors to convert the electric battery power into mechanical power, which "should not be underestimated" in spite of a general downward trend in the cost of electrical components.
In terms of savings, the report cites the largest potential cost savings coming from the main engine selection.
"The reduction from 16 to 12 cylinders decreases initial expenditure of the drivetrain by more than 10 per cent," the findings revealed.
"The reduction from 16 to 12 cylinders decreases initial expenditure of the drivetrain by more than 10 per cent"
Owners can find other cost reductions in the exhaust gas after-treatment selective catalytic reduction (SCR) system. "The application of a modular after-treatment system allows for a 12V engine, the usage of an optimised, scaled-down system, with an overall reduction of the number of components utilised," the report said.
The other major cost reduction factor relates to the rudder propellers, their auxiliary equipment and the shaft line. "Even though most components remain the same, as the total torque on the shaft does not change significantly, there are savings of about 7%. This is predominantly due to the substitution of the slipping clutch by the secondary power input and a conventional disengaging clutch where additional costs are overcompensated," the report detailed.
The report's authors also made note of the relevance of savings over the lifetime of the vessel, including reduction of operational expenditures, better amortisation and value preservation of the investment.
"As experience shows, a realistic share of full electric operation can achieve 50%, as long as loitering and transit can be covered in such a way that operational procedures are not affected," the report said. Using an average annual operation time of 3,000 hours for the propulsion plant a savings of 50% (1,500 hours per year) could add 10 years between main engine overhaul works.
Ultimately, although he would not be drawn on a prediction for exactly when due to the complexities involved with the price of battery technology, Mr Watson said it was only a matter of time before the difference in capex outlay between traditional propulsion and hybrid was non-existent.
"All these things over time will come down so our view is, 'Ok, if there is a 10-12% higher capex today, maybe in 10 years' time or 5 years' time that is going to be virtually zero in any case.'
"If there is a 10-12% higher capex today, maybe in 10 years' time or 5 years' time that is going to be virtually zero in any case"
"So, longer term the view is we will get there with a hybrid system that can completely replace a conventional system for no additional capital expenditure. That is obviously the goal and is what needs to be achieved to make it competitive and most interesting to operators and shipyards."
For the time being, Mr Watson says, the kind of holistic cost savings investigated in his project were an obvious choice for many operators facing a race to reduce emissions and fuel consumption.
"Of course, there is going to be a strong push to reduce emissions, particularly in this case you think about the harbour tug, it is operating close to shore, it is very visible and to see a harbour tug belching out black smoke … is not a pretty sight for anybody," he says.
"I think the environmental factor is one thing that will drive hybrid propulsion and I think operators generally accept that is the way it is going to go … This is why we focused on the capex, because they want to see something competitive that they can use."
[Footnote]
*Co-authors of Hybrid power workboats: a holistic approach for better capex included representatives from Germany's University of Applied Science in Munich and the University of Augsburg and industry partners, such as Canadian engineering firm Aspin Kemp and Associates and German propulsion specialists Schottel.
Marine Propulsion & Auxiliary Machinery Propellers Propulsion Thrusters Tug Technology & Business
Two tugs delivered for growing Chinese port

redpajama_set_name: RedPajamaCommonCrawl


text:
Oceanic Encounters: Exchange, Desire, Violence
Jolly, Margaret
Tcherkézoff, Serge
Tyron, Darrell
This volume, the result of ongoing collaborations between Australian and French anthropologists, historians and linguists, explores encounters between Pacific peoples and foreigners during the longue durée of European exploration, colonisation and settlement from the sixteenth century to the twentieth century. It deploys the concept of 'encounter' rather than the more common idea of 'first contact' for several reasons. Encounters with Europeans occurred in the context of extensive prior encounters and exchanges between Pacific peoples, manifest in the distribution of languages and objects and in patterns of human settlement and movement. The concept of encounter highlights the mutuality in such meetings of bodies and minds, whereby preconceptions from both sides were brought into confrontation, dialogue, mutual influence and ultimately mutual transformation. It stresses not so much prior visions of 'strangers' or 'others' but the contingencies in events of encounter and how senses other than vision were crucial in shaping reciprocal appraisals. But a stress on mutual meanings and interdependent agencies in such cross-cultural encounters should not occlude the tumultuous misunderstandings, political contests and extreme violence which also characterised Indigenous-European interactions over this period.
linquistics; history; south pacific; anthropology; Ankave language; Ethnic groups in Europe; James Cook; New Guinea
Relevant Wikipedia pages: Ankave language - https://en.wikipedia.org/wiki/Ankave_language; Ethnic groups in Europe - https://en.wikipedia.org/wiki/Ethnic_groups_in_Europe; James Cook - https://en.wikipedia.org/wiki/James_Cook; New Guinea - https://en.wikipedia.org/wiki/New_Guinea


text:
Book of the Month: A Court of Contempt by Rebekah Lee Jenkins
April's Book of the Month is A Court of Contempt by Rebekah Lee Jenkins. In a perfect blend of history and story, romance and tension Jenkins delivers a frank examination of the stark inequalities of the Canadian legal system at the turn of the century. She reminds us that not so long ago a woman could not open her own bank account, all her property legally belonged to her husband, and if she left an abusive relationship she could be obligated by law to return to him to "render conjugal rights."
Jenkin's account of historical facts is precise and she holds them together with warm characters and smaller storylines that keep you wanting more. This is a story of courage in the face of overwhelming odds and a must read for lovers of Canadian historical fiction.
Fiery and determined Cora Rood, the main character of A Court of Contempt, is based on historical accounts of Clara Brett Martin, the first woman to be called to the bar as a lawyer in Canada. Martin's work as a lawyer was one of the first steps taken towards women's equality in Canadian history. Like many historical figures, Martin held problematic views (she expressed strong anti-Semitic opinions in some of her surviving letters). Examining this kind of history is an opportunity for us to remember that true equality is a nuanced and continuing journey and that we have much more work to do to achieve equality for all women.
Why We Love This Book
We love historical fiction and this novel is no exception. Rebekah dives right into the history of the women's rights movement and we love it even more because most of the action takes place in our very own Manitoba. Jenkins reminds us with vivid and shocking examples that not so long ago women in Canadian courts had no rights at all. Her story is a reminder of how far we have come. And the women in her story who support one another and hold each other up, remind us of exactly what we need to carry on until courts (and the world) are a truly equal place. We thoroughly enjoyed this glimpse into the lives and hearts of some of the women who took the first steps toward change.
Rebekah Lee Jenkins lives and works as a writer and hairstylist in Souris, Manitoba. She wrote A Court of Contempt while she was the writer in residence at the Margaret Lawrence House in 2018.
You can find out more about Rebekah and her writing at her website: rebekahleejenkins.com
Dimensions: 6 inches x 9 inches
Buy it here: Buy Rebekah's Books
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Laurie is an editor, writer, and researcher. Her deep love of stories led to an Honours degree and a Master's degree in English Language and Literature from the University of Windsor. Originally from Southern Ontario, Laurie has lived in Manitoba for more than ten years, exploring the stories, landscape, plants, and people of some of the most remote parts of the province including three years in Churchill and two years in God's Lake Narrows First Nation. Laurie and her family now live on an acreage outside of Carberry.
Announcing our 2021 International Book Excellence Award
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Are you passionate about sport? The Ambrose Lions could be the right fit for you.
Our athletic culture supports you as an individual and encourages you to grow as a whole person. As you grow as a person and as an athlete, you'll be surrounded by a great community that's built upon teamwork. The Lions Athletics program not only helps you develop your athletic skills, it also equips you for leadership, discipleship, and service in all areas of your life.
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China's e-commerce leader Alibaba Group Holding is pushing further into bricks-and-mortar retail as it joins forces with Bailian Group to create a strategic partnership.
The deal will integrate Alibaba's almost 500 million active users with Bailian Group's 4,700 supermarkets, convenience stores and pharmacies across China.
Alibaba has also spent $4.6bn on a minority stake in appliances retailer Suning Commerce Group and is leading a $2.6bn bid to make department store and shopping mall operator Intime Retail Group private. It also bought a stake in grocery chain Sanjiang Shopping Club last November.
A financial investment has not been included in the deal but the retail firms will share big data and logistics to integrate online and offline shopping.
Alibaba referred to the partnership as 'new retail' to describe its aim to make the distinction between online and offline commerce obsolete, as internet users continue to migrate to mobile devices from desktop computers.
China's traditional retail market has seen three years of continuous decline, most recently, the country's top 50 retailers reported a 0.5% in 2016.
"Traditional commerce needs to embrace innovation and change to thrive if they are to ride atop this new consumption trend," said Ye Yongming, Chairman of Bailian Group.


Arch Auto Parts customer-first web design and OE-brand partnerships elevate NY online and retail parts sale. Most orders ready for pick-up in 30 minutes; all 50,000+ OE-quality, low-cost auto parts available within 3 hours, the fastest availability in New York.
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The site features an online parts catalog, including part fitment information, so users can easily find parts that fit their specific vehicle. To extend Arch's experienced counterman expertise to online shoppers, Arch has staffed a new Arch Online Team of experienced parts experts, to help customers in English and Spanish. The team is available by phone and online chat, to help customers determine which parts will work best for their vehicle and get the "Right Parts, Right Now™".
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The SEO-enhanced site is mobile-friendly to help parts shoppers near our stores in Brooklyn, Queens, and Long Island, as well as shoppers in the Bronx, Manhattan, and Staten Island find the same-day parts they need. In addition, the site features a quick-search store finder, to map and give directions to the closest Arch Auto Parts store.
Founded in 1979, Arch Auto Parts' ten locally owned and operated stores in Brooklyn, Queens and Long Island, NY, serve professional service and repair shops as well as DIY mechanics and auto enthusiasts. Arch Auto Parts delivers unsurpassed customer service and discount prices on a wide selection of OE-quality auto parts from AC Delco, Aisin, Akebono, Anchor Doan, AP Exhaust, Arc, Auto 7, BCA / NTN, Bosch, Centric, Continental, Denso, FCS, Fram, Gabriel, GMB, Mahle, MAS, Motorcraft, MPA, NGK, Pex, Sachs, Standard, Stant, Sylvania, Timken, TRW, TYC, VDO and other trusted brands.
Arch Auto Parts stocks more than 50,000 OEM and high-quality aftermarket auto parts for domestic and foreign vehicles, including brake pads, drums and rotors; wheel hubs and bearings; motor mounts, chassis and control arms; steering and suspension parts; cabin filters, oil filters, fuel and emission filters and manifolds; sensors and switches; timing belts and water pumps; ignition, batteries, starters, alternators and distributors; heating and air conditioning; and hard-to-find car parts such as window regulators and wiper motors. Arch Auto Parts is open seven days a week with experienced counter staff dedicated to helping New York customers find exactly the parts they need. For more information, visit us at http://www.ArchAutoParts.com or call 718-425-ARCH (718-425-2724).


This post was originally posted on November 20, 2015 and has since been updated.
I absolutely adore having keepsakes that are pictures of my children, especially around the holidays. Hanging up ornaments with pictures of my kids (like these puzzle piece frame Christmas ornaments) always bring back such special memories, and the kids always feel so proud when they see them on the tree.
This silhouette Christmas ornament is super easy to make and is one I know I'll cherish every year. It would also make a special gift to give grandparents and other family members. This post contains affiliate links.
Shrink film- We used this matte shrink film.
1. Find or take a picture of your child's profile. I snapped a quick picture on my phone and printed it out on white paper using our printer.
3. Cut out your profile drawing from the shrink film. Punch a hole in the top of the film.
5. Once it shrinks completely, press it down flat with a spatula before it completely hardens.
7. Tie some red ribbon through the hole for hanging. That's it!
Want to make some more ornament keepsakes with your leftover shrink film? Try these kid-made ornaments!
Love this idea for my 2nd grade students! What was the original size you did before they shrunk to make an ornament?
Thanks, Erin! Each sheet of shrink film was 8.5 x 11 inches, and I used a half sheet of shrink film for each ornament.
Oops, just saw this. You can ignore my question. Thank you.
Can I get 2 kid's ornaments made from one sheet of shrink film? Thinking of trying this for school, but it's cost prohibitive if it's one sheet per student.
Where can I buy the shrink film?
Hello, I bought clear matte and it did not turn white. where did you find white matte? I clicked the link but only see white, not white matte. Just want to make sure I get the right thing.
I ordered the matte that you linked to and it turned white like in your picture. 🙂 Any suggestions for keeping it from curling up on itself?
To keep the shrink film from curling , you need to leave it in the oven a lot longer than it says. It says 3 minutes and I left it in for 11 minutes and it it perfect.
What color shrink film did you use, clear or white?
Hi Pat- It definitely looks better on white. The one I linked to in the post is called "matte". It appears clear in the beginning and turns white when you shrink it.


text:
En bioquímica i farmacologia, un antagonista (del llatí antagonista i aquest del grec , qui lluita en contra) és aquella molècula que no té cap resposta biològica a l'unir-se a un receptor però bloquegen la resposta dels agonistes sobre el teixit, òrgan o animal complet. Hi ha dos tipus d'antagonistes:
 Antagonistes competitius: Els antagonistes lluiten contra l'agonista per a unir-se al receptor pel mateix lloc.
 Antagonistes no competitius: Els antagonistes bloquegen al receptor amb la unió d'aquest a un lloc accessori del receptor. Amb aquesta unió, la zona d'unió amb l'agonista canvia de conformació i no deixa que s'unesca al receptor.

Per a mesurar l'efecte dels antagonistes en corbes dosi-resposta, cada corba dosi-resposta representa la concentració d'agonista que cal per a arribar al màxim de resposta biològica que anteriorment se li ha afegit una determinada concentració d'antagonista. Quan més a l'esquerra de la gràfica, cada corba té una concentració d'antagonista més alta.

Ciències farmacèutiques
Fisiologia
Metabolisme

redpajama_set_name: RedPajamaWikipedia


text:
Printed from https://ideas.repec.org/a/oup/wbrobs/v19y2004i1p1-39.html
Community-Based and -Driven Development: A Critical Review
Ghazala Mansuri
Community-based and -driven development projects have become an important form of development assistance, with the World Bank's portfolio alone approximating $7 billion. A review of their conceptual foundations and evidence on their effectiveness shows that projects that rely on community participation have not been particularly effective at targeting the poor. There is some evidence that such projects create effective community infrastructure, but not a single study establishes a causal relationship between any outcome and participatory elements of a community-based development project. Most such projects are dominated by elites, and both targeting and project quality tend to be markedly worse in more unequal communities. A distinction between potentially "benevolent" forms of elite domination and more pernicious types of capture is likely to be important for understanding project dynamics and outcomes. Several qualitative studies indicate that the sustainability of community-based initiatives depends crucially on an enabling institutional environment, which requires government commitment, and on accountability of leaders to their community to avoid "supply-driven demand-driven" development. External agents strongly influence project success, but facilitators are often poorly trained, particularly in rapidly scaled-up programs. The naive application of complex contextual concepts like participation, social capital, and empowerment is endemic among project implementers and contributes to poor design and implementation. The evidence suggests that community-based and -driven development projects are best undertaken in a context-specific manner, with a long time horizon and with careful and well-designed monitoring and evaluation systems. Copyright 2004, Oxford University Press.
Ghazala Mansuri, 2004. "Community-Based and -Driven Development: A Critical Review," The World Bank Research Observer, World Bank Group, vol. 19(1), pages 1-39.
Handle: RePEc:oup:wbrobs:v:19:y:2004:i:1:p:1-39
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text:
Felicia Day Cast as New MST3K Villain
By Ryan Schwartz / November 24 2015, 7:48 AM PST
Felicia Day knows a thing or two about mad scientists — and now she'll get to play one.
The Dr. Horrible alum has joined the upcoming revival of Mystery Science Theater 3000 as Kinga, daughter of Dr. Clayton Forrester. (As you'll remember, it was Forrester who sent Janitor Joel Robinson to Space in the original 1988-'99 program.)
Joining the Whedonverse alum are comedians Hampton Yount and Baron Vaughn (Grace and Frankie) as the new voices behind Crow and Servo; Nerdist comedian Jonah Ray is also being eyed as new host.
Since its Nov. 10 launch, MST3K creator Joel Hodgson's Kickstarter to revive the series has reached its goal of $2 million to produce three full-length episodes. The campaign, which still has 17 days to go, is looking to raise as much as $5.5 million to complete a full 12-episode season.
Are you geeking out over Day's latest role? Sound off below.
TAGS: Felicia Day, Mystery Science Theater 3000
GET MORE: Casting News, Revivals and Reboots


Spooky Empire's Ultimate Horror Weekend!
I just returned from Orlando, where I was an author guest at Spooky Empire's Ultimate Horror Weekend. With media guests, authors and artists, the convention was full of horror goodness. Owl Goingback did an amazing job organizing the author side of the event, with signings and panels.
On Friday I moderated the Evolution of the Vampire panel with fellow authors Jeff Strand, Lynne Hansen, and Vince Courtney. We discussed early works such as Varney the Vampire and Stoker's Dracula and how they compare to vampires in current books and films like Twilight, Buffy the Vampire Slayer, and 30 Days of Night. Vince regaled the audience with hilarious stories about how being a vampire cop might be a disadvantage when one is confronted with an upturned truck full of garlic pizzas.
After that I signed some books, and the vampire panelists rejoined for dinner, talking of writing, stories, and monsters.
On Saturday I was on the Women in Horror panel, and discussed the work of women writers and directors in the horror genre. I signed more books afterward. I met actor Chris Sarandon and we talked briefly about vampires and their association with religious iconography, and how that figured into his film Fright Night.
Later that day I met actor and writer William Forsythe, whose work I very much enjoy. He's got a dynamic range of portraying really dastardly villains and heroic good guys. He was incredibly nice.
Afterward, my third panel, Regional Horror, went very well. Fellow panelists included author and astronomer Mike Brotherton, Owl Goingback and Vince Courtney. We discussed researching specific settings for novels and how to be true to a region while still creating your own story set there. Owl talked about mysterious legends of Florida. I talked about setting my novel Voracious in Glacier National Park.
Saturday night was another fantastic dinner with writers. Mike Brotherton and Owl Goingback and I discussed cryptozoology and tales of creature sightings.
On the last day of the con I met John Landis (director of one of my favorite films, American Werewolf in London), who was very kind.
I also met Ricou Browning (The Creature From The Black Lagoon), which was fantastic.
Next I was on a panel I'd been looking forward to all weekend -- The Cryptid Panel, with Mike Brotherton, Owl Goingback, and Scott Marlowe, a cryptozoologist and skunk ape expert. I talked about my master's thesis research into sightings of Bigfoot, lake monsters and El Chupacabra. Owl Goingback told stories of mysterious tall people found buried in Florida. Mike talked of hearing eerie cries in the darkness while searching for Bigfoot. Scott Marlowe thrilled us with tales of skunk ape sightings. The audience asked great questions and we just had a blast talking about one of our favorite subjects -- creatures!
My last panel of the con was Choosing Your Monsters. Fellow panelists included writers Mary SanGiovanni and Jeff Strand, who were a delight to chat with. We talked about how we pick monsters for our novels. Vampires, zombies, succubi, werewolves and more made appearances in our talk. The audience was very participatory, asking some great questions. Even more obscure creatures from mythology got touched on. It was a very well attended panel, especially for being late in the day on the last day of the con.
I was delighted to be a part of the programming at the con and to meet so many fellow people in the industry. Thanks to all who attended!