Robust jointly sparse 2-dimensional projection fuzzy clustering with local manifold structure preservation

Abstract

Dimensionality reduction clustering methods combine feature reduction and clustering to analyze high-dimensional image data. However, 1D projection subspace clustering vectorizes 2D images into 1D vectors, disrupting spatial correlations and causing information loss. Two-stage models that separate reduction and clustering lack coordination, leading to suboptimal results. We propose a robust sparse two-dimensional projection fuzzy clustering method with local manifold constraints to improve image clustering. Each cluster is represented by a bilinear orthogonal subspace, and F1-norm reconstruction error updates sample memberships. A similarity matrix captures affinities, while a Laplacian matrix preserves manifold geometry during dimensionality reduction. Optimization uses block coordinate descent to alternately refine the projection matrix, cluster centroids, and membership matrix until convergence. This unified, unsupervised model avoids image vectorization, reducing computational complexity and preserving spatial relationships. Experiments on nine benchmark datasets show the RS2DPFC-LMS algorithm improves accuracy by 2.47 % and normalized mutual information by 2 %, demonstrating superior clustering performance, parameter stability, and noise robustness.