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Multi-view clustering integrating anchor attribute and structural information

Xuetong Li, Xiao-Dong Zhang

TL;DR

A novel multi-view clustering algorithm, AAS, that utilizes a two-step proximity approach via anchors in each view, integrating attribute and directed structural information, which enhances the clarity of category characteristics in the similarity matrices.

Abstract

Multisource data has spurred the development of advanced clustering algorithms, such as multi-view clustering, which critically relies on constructing similarity matrices. Traditional algorithms typically generate these matrices from sample attributes alone. However, real-world networks often include pairwise directed topological structures critical for clustering. This paper introduces a novel multi-view clustering algorithm, AAS. It utilizes a two-step proximity approach via anchors in each view, integrating attribute and directed structural information. This approach enhances the clarity of category characteristics in the similarity matrices. The anchor structural similarity matrix leverages strongly connected components of directed graphs. The entire process-from similarity matrices construction to clustering - is consolidated into a unified optimization framework. Comparative experiments on the modified Attribute SBM dataset against eight algorithms affirm the effectiveness and superiority of AAS.

Multi-view clustering integrating anchor attribute and structural information

TL;DR

A novel multi-view clustering algorithm, AAS, that utilizes a two-step proximity approach via anchors in each view, integrating attribute and directed structural information, which enhances the clarity of category characteristics in the similarity matrices.

Abstract

Multisource data has spurred the development of advanced clustering algorithms, such as multi-view clustering, which critically relies on constructing similarity matrices. Traditional algorithms typically generate these matrices from sample attributes alone. However, real-world networks often include pairwise directed topological structures critical for clustering. This paper introduces a novel multi-view clustering algorithm, AAS. It utilizes a two-step proximity approach via anchors in each view, integrating attribute and directed structural information. This approach enhances the clarity of category characteristics in the similarity matrices. The anchor structural similarity matrix leverages strongly connected components of directed graphs. The entire process-from similarity matrices construction to clustering - is consolidated into a unified optimization framework. Comparative experiments on the modified Attribute SBM dataset against eight algorithms affirm the effectiveness and superiority of AAS.

Paper Structure

This paper contains 27 sections, 6 theorems, 31 equations, 6 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notations
  4. Multi-view subspace clustering based on anchors
  5. Multi-view spectral clustering via integrating nonnegative embedding and spectral embedding(NESE)
  6. Proposed Method
  7. Structural Similarity of Anchors
  8. Anchor selection
  9. Structural Similarity of Anchors
  10. Fusion Framework
  11. Optimization of proposed method
  12. Optimization Algorithm
  13. Computation of $\overline{S}^{i}$
  14. Computation of H
  15. Computation complexity and convergence analysis
  16. ...and 12 more sections

Key Result

Theorem 1

For the directed graph $G$ with its adjacency matrix denoted by $A$ and the out-degree matrix by $D^{+}$, assume all out-degrees are nonzero. Let $P = \left(D^{+}\right)^{-1}A$ represent the probability transition matrix of a Markov process on the directed graph. The vector $\phi$ is defined as the

Figures (6)

  • Figure 1: Overview of the AAS framework. The principle of the AAS and its matrix-based framework are shown on a green background. Green and blue matrices illustrate the computation of similarity matrices using attribute and structural information, respectively, which are then integrated for multi-view clustering. Anchor selection and the two-step proximity approach in the $\overline{S}^{i}\Tilde{S}^{i}$ process are visualized with nodes on a grey background. The first step reduces the distance between nodes and nearby anchors based on attribute information. The second step brings anchors within the same strongly connected components closer together based on structural information. "Proximity" is indicated by increased matrix values, aiming to produce a similarity matrix with clearer implicit cluster features.
  • Figure 2: Network visualization of 3 views on Attribute SBM_50 and Attribute SBM_5000
  • Figure 3: Attributes visualization of 3 views on Attribute SBM_50 and Attribute SBM_5000
  • Figure 4: Visualization of anchor similarity matrices on 3 views
  • Figure 5: Running time and convergence curve of AAS
  • ...and 1 more figures

Theorems & Definitions (10)

  • Theorem 1
  • Lemma 1
  • Theorem 2
  • Theorem 3
  • proof
  • Theorem 4
  • proof
  • Theorem 5
  • proof
  • proof