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Masked Subspace Clustering Methods

Jiebo Song, Huaming Ling

TL;DR

The paper tackles clustering in high-dimensional data by learning pairwise relations through masks and fuse two clustering objectives using a general Bilevel Clustering Optimization (BCO) framework. It introduces three masked subspace clustering variants—BMSC with a hard mask, GMSC with a soft mask, and RMSC with a learnable soft mask and recursive updates—validating them on standard datasets with significant performance gains. The approach leverages a bilevel structure where $M^s=\psi(y)$ guides the outer clustering objective, and the inner clustering informs mask construction, leading to refined affinity matrices. Collectively, the work demonstrates that learnable, recursively updated masks can substantially improve clustering accuracy and stability in high-dimensional settings with minimal supervision.

Abstract

To further utilize the unsupervised features and pairwise information, we propose a general Bilevel Clustering Optimization (BCO) framework to improve the performance of clustering. And then we introduce three special cases on subspace clustering with two different types of masks. At first, we reformulate the original subspace clustering as a Basic Masked Subspace Clustering (BMSC), which reformulate the diagonal constraints to a hard mask. Then, we provide a General Masked Subspace Clustering (GMSC) method to integrate different clustering via a soft mask. Furthermore, based on BCO and GMSC, we induce a learnable soft mask and design a Recursive Masked Subspace Clustering (RMSC) method that can alternately update the affinity matrix and the soft mask. Numerical experiments show that our models obtain significant improvement compared with the baselines on several commonly used datasets, such as MNIST, USPS, ORL, COIL20 and COIL100.

Masked Subspace Clustering Methods

TL;DR

The paper tackles clustering in high-dimensional data by learning pairwise relations through masks and fuse two clustering objectives using a general Bilevel Clustering Optimization (BCO) framework. It introduces three masked subspace clustering variants—BMSC with a hard mask, GMSC with a soft mask, and RMSC with a learnable soft mask and recursive updates—validating them on standard datasets with significant performance gains. The approach leverages a bilevel structure where guides the outer clustering objective, and the inner clustering informs mask construction, leading to refined affinity matrices. Collectively, the work demonstrates that learnable, recursively updated masks can substantially improve clustering accuracy and stability in high-dimensional settings with minimal supervision.

Abstract

To further utilize the unsupervised features and pairwise information, we propose a general Bilevel Clustering Optimization (BCO) framework to improve the performance of clustering. And then we introduce three special cases on subspace clustering with two different types of masks. At first, we reformulate the original subspace clustering as a Basic Masked Subspace Clustering (BMSC), which reformulate the diagonal constraints to a hard mask. Then, we provide a General Masked Subspace Clustering (GMSC) method to integrate different clustering via a soft mask. Furthermore, based on BCO and GMSC, we induce a learnable soft mask and design a Recursive Masked Subspace Clustering (RMSC) method that can alternately update the affinity matrix and the soft mask. Numerical experiments show that our models obtain significant improvement compared with the baselines on several commonly used datasets, such as MNIST, USPS, ORL, COIL20 and COIL100.
Paper Structure (16 sections, 16 equations, 5 figures, 3 tables, 2 algorithms)

This paper contains 16 sections, 16 equations, 5 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Sparse Subspace Clustering
  4. Bilevel Optimization
  5. A Unified Bilevel Clustering Optimization Framework
  6. Masked Subspace Clustering Methods
  7. Basic Masked Subspace Clustering
  8. General Masked Subspace Clustering
  9. Recursive Masked Subspace Clustering
  10. Algorithms for solving RMSC
  11. Experiments
  12. Data description and experimental setting
  13. Compare with the low-rank and sparse-based methods
  14. Comparisons on different methods and datasets.
  15. Comparisons between BMSC, GMSC and RMSC
  16. ...and 1 more sections

Figures (5)

  • Figure 1: Interesting phenomenons: when the number of clusters is greater than 2, it is easier to determine whether two samples belong to the same cluster than to determine which specific cluster a sample belongs to.
  • Figure 2: A unified bilevel optimization framework for clustering with a learnable soft mask.
  • Figure 3: Pairs visualization. Eight pairs of images from MNIST, USPS, ORL, and COIL20 were selected to evaluate the values of the affinity matrices. For each dataset, there have two pairs: one with the same class and the other with different classes.
  • Figure 4: Visualization of the affinity matrix from BMSC, GMSC, and RMSC: RMSC-parts have the highest sparsity and the strongest connections.
  • Figure : for BMSC/GMSC