\begin{algorithm}[t]
	\caption{EM-like procedure of the proposed ADGCN}
	\label{algorithm3}
	\footnotesize
	\begin{algorithmic}[1] %Ã¿ÐÐÏÔÊ¾ÐÐºÅ
		\Require
		$\mathcal{G} = \{V, E\} $, $\mathbf{X}$, $A$.
		
		
		
		
		
		\Ensure $\mathbf{H}$: the node disentangled representation matrix of the given graph
		\renewcommand{\algorithmicensure}{\textbf{Hyper-paramters:}}
		\Ensure:  $K$, $\tilde{T}$, $T$, $m$, $\gamma$, $\lambda$, $\eta$
		
		\State Initialization:
		
		$\mathbf{W}=\{\mathbf{W}_k\}_{k=1}^{K}$: projection matrix.
		
		\textcolor{black}{$\alpha$, $\beta$: coefficients of component-specific aggregation.}
		
		$\theta_{D}$: parameters of the discriminator $D$.
		
		
		\For{epoch $t = 1$ to $T$}
		
		\State \textbf{E-step:}
		
		Obtain $\left \{ \mathbf{h}_i^{(t-1)} \right \}_{i=1}^n$ and $\left \{ \mathbf{c}_i ^{(t-1)}\right \}_{i=1}^n$ through \textbf{Alg.}~\ref{algorithm1}.
		
		Obtain $A^{(t)}$ through \textbf{Alg.}~\ref{algorithm2} if performing graph refinement.
		
		\State \textbf{M-step:}
		
		Sample the "real" components from $\left \{ \mathbf{h}_i^{(t-1)} \right \}_{i=1}^n$.
		
		Sample the "fake" components from $\left \{ \mathbf{c}_i^{(t-1)} \right \}_{i=1}^n$.
		
		Update $\mathbf{W}_k$, $k=1,\cdots,K$ by minimizing $\mathcal{L}$ in Eq. (\ref{loss_G}).
		
		Update $\theta_{D}$ by minimizing $\mathcal{L}_{D}$ in Eq. (\ref{loss_G}).
		
		\EndFor
		
	\State \textbf{return} $\mathbf{H}=\left[\mathbf{h}_1^{(T-1)},\cdots,\mathbf{h}_n^{(T-1)}\right]$.
	\end{algorithmic}
\label{EM-like}	
\end{algorithm}

\begin{algorithm}
[t]
\caption{EM-like procedure of the proposed ADGCN}
\footnotesize
\begin{algorithmic}[1]
%Ã¿ÐÐÏÔÊ¾ÐÐºÅ
\Require
$\mathcal{G} = \{V, E\} $, $\mathbf{X}$, $A$.
\Ensure $\mathbf{H}$: the node disentangled representation matrix of the given graph
\renewcommand{\algorithmicensure}{\textbf{Hyper-paramters:}}
\Ensure: $K$, $\tilde{T}$, $T$, $m$, $\gamma$, $\lambda$, $\eta$
\State Initialization:
$\mathbf{W}=\{\mathbf{W}_k\}_{k=1}^{K}$: projection matrix.
\textcolor{black}{$\alpha$, $\beta$: coefficients of component-specific aggregation.}
$\theta_{D}$: parameters of the discriminator $D$.
\For{epoch $t = 1$ to $T$}
\State \textbf{E-step:}
Obtain $\left \{ \mathbf{h}_i^{(t-1)} \right \}_{i=1}^n$ and $\left \{ \mathbf{c}_i ^{(t-1)}\right \}_{i=1}^n$ through \textbf{Alg.}~\ref{algorithm1}.
Obtain $A^{(t)}$ through \textbf{Alg.}~\ref{algorithm2} if performing graph refinement.
\State \textbf{M-step:}
Sample the "real" components from $\left \{ \mathbf{h}_i^{(t-1)} \right \}_{i=1}^n$.
Sample the "fake" components from $\left \{ \mathbf{c}_i^{(t-1)} \right \}_{i=1}^n$.
Update $\mathbf{W}_k$, $k=1,\cdots,K$ by minimizing $\mathcal{L}$ in Eq. (\ref{loss_G}).
Update $\theta_{D}$ by minimizing $\mathcal{L}_{D}$ in Eq. (\ref{loss_G}).
\EndFor
\State \textbf{return} $\mathbf{H}=\left[\mathbf{h}_1^{(T-1)},\cdots,\mathbf{h}_n^{(T-1)}\right]$.
\end{algorithmic}
\end{algorithm}
{
    "title": "adversarial graph disentanglement",
    "id": "2103.07295",
    "abstract": "a real-world graph has a complex topological structure, which is often formed by the interaction of different latent factors. however, most existing methods lack consideration of the intrinsic differences in relations between nodes caused by factor entanglement. in this paper, we propose an \\underline{\\textbf{a}}dversarial \\underline{\\textbf{d}}isentangled \\underline{\\textbf{g}}raph \\underline{\\textbf{c}}onvolutional \\underline{\\textbf{n}}etwork (adgcn) for disentangled graph representation learning. to begin with, we point out two aspects of graph disentanglement that need to be considered, i.e., micro-disentanglement and macro-disentanglement. for them, a component-specific aggregation approach is proposed to achieve micro-disentanglement by inferring latent components that cause the links between nodes. on the basis of micro-disentanglement, we further propose a macro-disentanglement adversarial regularizer to improve the separability among component distributions, thus restricting the interdependence among components. additionally, to reveal the topological graph structure, a diversity-preserving node sampling approach is proposed, by which the graph structure can be progressively refined in a way of local structure awareness. the experimental results on various real-world graph data verify that our adgcn obtains more favorable performance over currently available alternatives. the source codes of adgcn are available at \\textit{\\url{https://github.com/ssgood/adgcn}}.",
    "categories": "cs.lg cs.ai",
    "doi": "",
    "created": "2021-03-12",
    "updated": "2024-01-24",
    "authors": [
        "shuai zheng",
        "zhenfeng zhu",
        "zhizhe liu",
        "jian cheng",
        "yao zhao"
    ],
    "affiliation": [],
    "url": "https://arxiv.org/abs/2103.07295"
}
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