Tensor Laplacian Regularized Low-Rank Representation for Non-uniformly Distributed Data Subspace Clustering

TL;DR

This paper introduces a tensor Laplacian regularized low-rank representation method that improves subspace clustering accuracy for non-uniformly distributed data by incorporating locality and structure information through a hypergraph model.

Contribution

It proposes a novel hypergraph-based tensor Laplacian regularization approach for low-rank representation, addressing limitations of existing methods in handling non-uniform data distributions.

Findings

Higher clustering accuracy and precision demonstrated on artificial and real datasets.

Significant improvement over state-of-the-art methods in complex data structures.

Enhanced robustness to nonlinearity, geometrical overlap, and outliers.

Abstract

Low-Rank Representation (LRR) highly suffers from discarding the locality information of data points in subspace clustering, as it may not incorporate the data structure nonlinearity and the non-uniform distribution of observations over the ambient space. Thus, the information of the observational density is lost by the state-of-art LRR models, as they take a constant number of adjacent neighbors into account. This, as a result, degrades the subspace clustering accuracy in such situations. To cope with deficiency, in this paper, we propose to consider a hypergraph model to facilitate having a variable number of adjacent nodes and incorporating the locality information of the data. The sparsity of the number of subspaces is also taken into account. To do so, an optimization problem is defined based on a set of regularization terms and is solved by developing a tensor Laplacian-based algorithm. Extensive experiments on artificial and real datasets demonstrate the higher accuracy and precision of the proposed method in subspace clustering compared to the state-of-the-art methods. The outperformance of this method is more revealed in presence of inherent structure of the data such as nonlinearity, geometrical overlapping, and outliers.