[論文レビュー] Align then Fusion: Generalized Large-scale Multi-view Clustering with Anchor Matching Correspondences

Siwei Wang, Xinwang Liu+5 more|arXiv (Cornell University)|May 30, 2022

Remote-Sensing Image Classification被引用数 32

ひとこと要約

FMVACCは、柔軟なアンカーセットを学習し、ビュー間でそれらを整列させるための特徴情報と構造情報の両方を用いて、整列されたアンカーグラフを統合してクラスタリング性能を向上させる、一般化されたスケーラブルな大規模マルチビュークラスタリングのフレームワークを導入します。

ABSTRACT

Multi-view anchor graph clustering selects representative anchors to avoid full pair-wise similarities and therefore reduce the complexity of graph methods. Although widely applied in large-scale applications, existing approaches do not pay sufficient attention to establishing correct correspondences between the anchor sets across views. To be specific, anchor graphs obtained from different views are not aligned column-wisely. Such an extbf{A}nchor- extbf{U}naligned extbf{P}roblem (AUP) would cause inaccurate graph fusion and degrade the clustering performance. Under multi-view scenarios, generating correct correspondences could be extremely difficult since anchors are not consistent in feature dimensions. To solve this challenging issue, we propose the first study of the generalized and flexible anchor graph fusion framework termed extbf{F}ast extbf{M}ulti- extbf{V}iew extbf{A}nchor- extbf{C}orrespondence extbf{C}lustering (FMVACC). Specifically, we show how to find anchor correspondence with both feature and structure information, after which anchor graph fusion is performed column-wisely. Moreover, we theoretically show the connection between FMVACC and existing multi-view late fusion \cite{liu2018late} and partial view-aligned clustering \cite{huang2020partially}, which further demonstrates our generality. Extensive experiments on seven benchmark datasets demonstrate the effectiveness and efficiency of our proposed method. Moreover, the proposed alignment module also shows significant performance improvement applying to existing multi-view anchor graph competitors indicating the importance of anchor alignment. Our code is available at \url{https://github.com/wangsiwei2010/NeurIPS22-FMVACC}.

研究の動機と目的

• Identify and address the Anchor-Unaligned Problem (AUP) in large-scale multi-view clustering.
• Develop a flexible anchor generation and alignment mechanism that works across views with different feature dimensions.
• Enable column-wise fusion of anchor graphs after cross-view anchor matching.
• Theoretically relate FMVACC to existing late fusion and PVC approaches to demonstrate generality.
• Demonstrate efficiency and effectiveness on multiple large-scale datasets and show the alignment module benefits existing methods.

提案手法

• Generate flexible single-view anchors by jointly optimizing Z_i and A_i with A_i A_i^T = I_m to improve anchor discriminativeness.
• Iteratively update Z_i via projection to a simplex with nonnegativity and sum-to-one constraints (row-wise), and update A_i via a truncated SVD given B = Z_i^T X_i.
• Represent each anchor by the corresponding column of Z_i, transforming anchor alignment into a graph matching problem in n-dimensional space.
• Form feature correspondence by maximizing Z_1^T Z_2 under assignment constraints (equivalently, solving a transport/assignment problem).
• Form structure correspondence by aligning inner graph structures using S_1 = Z_1^T Z_1 and S_2 = Z_2^T Z_2, minimizing ||S_1 - P^T S_2 P||_F^2.
• Combine feature and structure cues in a unified quadratic assignment problem to obtain the permutation P that aligns anchors (solved via Projected Fixed-Point Algorithm).
• Fuse the aligned anchor graphs to produce Z_Aligned and obtain clustering via rank-k SVD followed by k-means on the embedding.

実験結果

リサーチクエスチョン

• RQ1 How to effectively align flexible anchor sets across multi-view data with different feature spaces?
• RQ2 Can anchor alignment based on both feature similarity and graph structure improve fusion and clustering performance in large-scale MVC?
• RQ3 What is the theoretical relationship between FMVACC and existing late fusion and PVC approaches?
• RQ4 What are the computational and memory requirements of the proposed FMVACC, and is it scalable to very large datasets?

主な発見

• FMVACC achieves effective anchor alignment by jointly considering first-order (feature) and second-order (structure) correspondences.
• The proposed alignment module significantly improves clustering when applied to existing MVC methods (e.g., LMVSC), reducing noise and improving fusion quality.
• Flexible anchor selection plus alignment outperforms fixed-index approaches (e.g., SFMC) on simulated data and real-world benchmarks.
• FMVACC demonstrates linear time and space complexity in n, making it suitable for large-scale datasets; post-alignment clustering through SVD and k-means remains efficient.
• The alignment component provides notable performance gains across seven real-world multi-view datasets, including large-scale ones like MNIST and YTF variants.