<p>The authors of your cited paper use the term <em>graph-based semi-supervised learning (G-SSL)</em> to refer to semi-supervised learning techniques which take graph structured data as their input.</p>

<p>Given their main example, the MNIST dataset, is not graph structured, they detail a method for converting the raw Euclidean data <span class="math-container">$X$</span> into said form (represented by its adjacency matrix <span class="math-container">$S$</span>), and then compute the Laplacian <span class="math-container">$L$</span> of this graph:</p>

<blockquote>
  <p>We consider the graph-based semi-supervised learning (G-SSL) problem. The input include labeled data <span class="math-container">$X_{l} ∈ \mathbb{R}^{n_{l}×d}$</span> and unlabeled data <span class="math-container">$X_{u} \in \mathbb{R}^{n_{u}×d}$</span>, we define the whole features <span class="math-container">$X = [X_{l}; X_{u}]$</span>. Denoting the labels of <span class="math-container">$X_{l}$</span> as <span class="math-container">$y_{l}$</span>, our goal is to predict the labels of test data <span class="math-container">$y_{u}$</span>. The learner applies algorithm <span class="math-container">$A$</span> to predict <span class="math-container">$y_{u}$</span> from available data <span class="math-container">$\{X_{l}, y_{l}, X_{u}\}$</span>. Here we restrict <span class="math-container">$A$</span> to label propagation method, where we first generate a graph with adjacency matrix <span class="math-container">$S$</span> from Gaussian kernel:
  <span class="math-container">$S_{ij} = \exp(−γ\lVert x_i − x_j\rVert ^{2})$</span>, where the subscripts <span class="math-container">$x_{i(j)}$</span> represents the <span class="math-container">$i(j)$</span>-th row of <span class="math-container">$X$</span>. Then the graph Laplacian is calculated by <span class="math-container">$L = D − S$</span>, where <span class="math-container">$D = \text{diag}\{\sum_{k=1}^{n} S_{ik}\}$</span> is the degree matrix.</p>
</blockquote>

<ul>
<li><a href="https://arxiv.org/pdf/1910.14147v1.pdf" rel="nofollow noreferrer">A Unified Framework for Data Poisoning Attack to
Graph-based Semi-supervised Learning</a> (2019)</li>
</ul>

<p>This is consistent with the terminology as used in other literature:</p>

<blockquote>
  <p><strong>Semi-supervised learning for node-level classification.</strong>
  Given a single network with partial nodes being labeled and others remaining unlabeled, ConvGNNs can learn a robust model that effectively identifies the class labels for the unlabeled nodes [22]. To this end, an end-to-end framework can be built by stacking a couple of graph convolutional layers followed by a softmax layer for multi-class classification.</p>
</blockquote>

<ul>
<li><a href="https://arxiv.org/pdf/1901.00596.pdf" rel="nofollow noreferrer">A Comprehensive Survey on Graph Neural Networks</a> (2019)</li>
</ul>

CC BY-SA 4.0
2020-04-26T08:58:22.240Z
2020-04-28T01:23:56.603Z
2020-04-28T01:23:56.603Z
brazofuerte
<p>Whenever I look for papers involving semi-supervised learning, I always find some that talk about graph semi-supervised learning (e.g. <a href="https://arxiv.org/pdf/1910.14147v1.pdf" rel="nofollow noreferrer">A Unified Framework for Data Poisoning Attack to Graph-based Semi-supervised Learning</a>). </p>

<p>What is the difference between graph semi-supervised learning and normal semi-supervised learning?</p>

<machine-learning><comparison><geometric-deep-learning><graphs><semi-supervised-learning>
What is the difference between graph semi-supervised learning and normal semi-supervised learning?
boomselector
# What is the difference between graph semi-supervised learning and normal semi-supervised learning?

(Asked by: username_0 on 2020-02-02)

Whenever I look for papers involving semi-supervised learning, I always find some that talk about graph semi-supervised learning (e.g. [A Unified Framework for Data Poisoning Attack to Graph-based Semi-supervised Learning](https://arxiv.org/pdf/1910.14147v1.pdf)).

What is the difference between graph semi-supervised learning and normal semi-supervised learning?

**Tags:** machine-learning, comparison, geometric-deep-learning, graphs, semi-supervised-learning


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## 1 answers

### Answer by username_1 on 2020-04-26. Score: 1

The authors of your cited paper use the term *graph-based semi-supervised learning (G-SSL)* to refer to semi-supervised learning techniques which take graph structured data as their input.

Given their main example, the MNIST dataset, is not graph structured, they detail a method for converting the raw Euclidean data $X$ into said form (represented by its adjacency matrix $S$), and then compute the Laplacian $L$ of this graph:

> We consider the graph-based semi-supervised learning (G-SSL) problem. The input include labeled data $X\_{l} ∈ \mathbb{R}^{n\_{l}×d}$ and unlabeled data $X\_{u} \in \mathbb{R}^{n\_{u}×d}$, we define the whole features $X = [X\_{l}; X\_{u}]$. Denoting the labels of $X\_{l}$ as $y\_{l}$, our goal is to predict the labels of test data $y\_{u}$. The learner applies algorithm $A$ to predict $y\_{u}$ from available data $\{X\_{l}, y\_{l}, X\_{u}\}$. Here we restrict $A$ to label propagation method, where we first generate a graph with adjacency matrix $S$ from Gaussian kernel:
> $S\_{ij} = \exp(−γ\lVert x\_i − x\_j\rVert ^{2})$, where the subscripts $x\_{i(j)}$ represents the $i(j)$-th row of $X$. Then the graph Laplacian is calculated by $L = D − S$, where $D = \text{diag}\{\sum\_{k=1}^{n} S\_{ik}\}$ is the degree matrix.

* [A Unified Framework for Data Poisoning Attack to
  Graph-based Semi-supervised Learning](https://arxiv.org/pdf/1910.14147v1.pdf) (2019)

This is consistent with the terminology as used in other literature:

> **Semi-supervised learning for node-level classification.**
> Given a single network with partial nodes being labeled and others remaining unlabeled, ConvGNNs can learn a robust model that effectively identifies the class labels for the unlabeled nodes [22]. To this end, an end-to-end framework can be built by stacking a couple of graph convolutional layers followed by a softmax layer for multi-class classification.

* [A Comprehensive Survey on Graph Neural Networks](https://arxiv.org/pdf/1901.00596.pdf) (2019)


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