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Kernel Alignment-based Multi-view Unsupervised Feature Selection with Sample-level Adaptive Graph Learning

Yalan Tan, Yanyong Huang, Zongxin Shen, Dongjie Wang, Fengmao Lv, Tianrui Li

TL;DR

This work tackles unsupervised feature selection for unlabeled multi-view data by addressing nonlinear feature redundancy and per-sample neighborhood clarity. It introduces KAFUSE, which combines kernel alignment with an orthogonal constraint for redundancy reduction and cross-view consistent graph learning with sample-level adaptive fusion to learn a reliable fused graph Z. An alternating optimization framework jointly updates feature selectors, projections, and graph components, with convergence guarantees and manageable per-iteration complexity. Empirical results on eight real-world datasets show that KAFUSE outperforms state-of-the-art MUFS methods in ACC and NMI, with ablation studies validating the contribution of its kernel-alignment and sample-level fusion components.

Abstract

Although multi-view unsupervised feature selection (MUFS) has demonstrated success in dimensionality reduction for unlabeled multi-view data, most existing methods reduce feature redundancy by focusing on linear correlations among features but often overlook complex nonlinear dependencies. This limits the effectiveness of feature selection. In addition, existing methods fuse similarity graphs from multiple views by employing sample-invariant weights to preserve local structure. However, this process fails to account for differences in local neighborhood clarity among samples within each view, thereby hindering accurate characterization of the intrinsic local structure of the data. In this paper, we propose a Kernel Alignment-based multi-view unsupervised FeatUre selection with Sample-level adaptive graph lEarning method (KAFUSE) to address these issues. Specifically, we first employ kernel alignment with an orthogonal constraint to reduce feature redundancy in both linear and nonlinear relationships. Then, a cross-view consistent similarity graph is learned by applying sample-level fusion to each slice of a tensor formed by stacking similarity graphs from different views, which automatically adjusts the view weights for each sample during fusion. These two steps are integrated into a unified model for feature selection, enabling mutual enhancement between them. Extensive experiments on real multi-view datasets demonstrate the superiority of KAFUSE over state-of-the-art methods.

Kernel Alignment-based Multi-view Unsupervised Feature Selection with Sample-level Adaptive Graph Learning

TL;DR

This work tackles unsupervised feature selection for unlabeled multi-view data by addressing nonlinear feature redundancy and per-sample neighborhood clarity. It introduces KAFUSE, which combines kernel alignment with an orthogonal constraint for redundancy reduction and cross-view consistent graph learning with sample-level adaptive fusion to learn a reliable fused graph Z. An alternating optimization framework jointly updates feature selectors, projections, and graph components, with convergence guarantees and manageable per-iteration complexity. Empirical results on eight real-world datasets show that KAFUSE outperforms state-of-the-art MUFS methods in ACC and NMI, with ablation studies validating the contribution of its kernel-alignment and sample-level fusion components.

Abstract

Although multi-view unsupervised feature selection (MUFS) has demonstrated success in dimensionality reduction for unlabeled multi-view data, most existing methods reduce feature redundancy by focusing on linear correlations among features but often overlook complex nonlinear dependencies. This limits the effectiveness of feature selection. In addition, existing methods fuse similarity graphs from multiple views by employing sample-invariant weights to preserve local structure. However, this process fails to account for differences in local neighborhood clarity among samples within each view, thereby hindering accurate characterization of the intrinsic local structure of the data. In this paper, we propose a Kernel Alignment-based multi-view unsupervised FeatUre selection with Sample-level adaptive graph lEarning method (KAFUSE) to address these issues. Specifically, we first employ kernel alignment with an orthogonal constraint to reduce feature redundancy in both linear and nonlinear relationships. Then, a cross-view consistent similarity graph is learned by applying sample-level fusion to each slice of a tensor formed by stacking similarity graphs from different views, which automatically adjusts the view weights for each sample during fusion. These two steps are integrated into a unified model for feature selection, enabling mutual enhancement between them. Extensive experiments on real multi-view datasets demonstrate the superiority of KAFUSE over state-of-the-art methods.
Paper Structure (25 sections, 35 equations, 7 figures, 4 tables, 1 algorithm)

This paper contains 25 sections, 35 equations, 7 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. The Proposed Method
  4. Notations and Definitions
  5. Kernel Alignment-based Redundancy Reduction for MUFS
  6. Cross-view Consistent Similarity Graph Learning via Auto-weighted Sample-level Fusion
  7. Optimization and Algorithm
  8. Update $\bm{W}^{(v)}$ by Fixing Other Variables
  9. Update $\bm{F}$ by Fixing Other Variables
  10. Update $\bm{Z}$ by Fixing Other Variables
  11. Update $\bm{S}^{(v)}$ by Fixing Other Variables
  12. Update $\bm{q}_{\cdot j}$ by Fixing Other Variables
  13. Update $\bm{\theta}_v$ by Fixing Other Variables
  14. Update $\bm{\omega}_v$ by Fixing Other Variables
  15. Update $\bm{\Lambda^{(v)}}$ by Fixing Other Variables
  16. ...and 10 more sections

Figures (7)

  • Figure 1: The framework of the proposed KAFUSE.
  • Figure 2: ACC of different methods under varying feature selection ratios.
  • Figure 3: NMI of different methods under varying feature selection ratios.
  • Figure 4: Convergence curves of KAFUSE on eight datasets.
  • Figure 5: ACC of KAFUSE with varying parameters $\alpha$, $\beta$ and $r$ and feature selection ratios on COIL20 dataset.
  • ...and 2 more figures