AnchorGAE: General Data Clustering via $O(n)$ Bipartite Graph Convolution

• URL: http://arxiv.org/abs/2111.06586v1
• Date: Fri, 12 Nov 2021 07:08:13 GMT
• Title: AnchorGAE: General Data Clustering via $O(n)$ Bipartite Graph Convolution
• Authors: Hongyuan Zhang, Jiankun Shi, Rui Zhang, Xuelong Li
• Abstract summary: We show how to convert a non-graph dataset into a graph by introducing the generative graph model, which is used to build graph convolution networks (GCNs) A bipartite graph constructed by anchors is updated dynamically to exploit the high-level information behind data. We theoretically prove that the simple update will lead to degeneration and a specific strategy is accordingly designed.
• Score: 79.44066256794187
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Graph-based clustering plays an important role in clustering tasks. As graph convolution network (GCN), a variant of neural networks on graph-type data, has achieved impressive performance, it is attractive to find whether GCNs can be used to augment the graph-based clustering methods on non-graph data, i.e., general data. However, given $n$ samples, the graph-based clustering methods usually need at least $O(n^2)$ time to build graphs and the graph convolution requires nearly $O(n^2)$ for a dense graph and $O(|\mathcal{E}|)$ for a sparse one with $|\mathcal{E}|$ edges. In other words, both graph-based clustering and GCNs suffer from severe inefficiency problems. To tackle this problem and further employ GCN to promote the capacity of graph-based clustering, we propose a novel clustering method, AnchorGAE. As the graph structure is not provided in general clustering scenarios, we first show how to convert a non-graph dataset into a graph by introducing the generative graph model, which is used to build GCNs. Anchors are generated from the original data to construct a bipartite graph such that the computational complexity of graph convolution is reduced from $O(n^2)$ and $O(|\mathcal{E}|)$ to $O(n)$. The succeeding steps for clustering can be easily designed as $O(n)$ operations. Interestingly, the anchors naturally lead to a siamese GCN architecture. The bipartite graph constructed by anchors is updated dynamically to exploit the high-level information behind data. Eventually, we theoretically prove that the simple update will lead to degeneration and a specific strategy is accordingly designed.

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