A similarity measure based on subspace distance for spectral clustering

The performance of Spectral Clustering (SC) relies heavily on the choice of similarity matrix used to compute pairwise similarities between data points, especially when handling data distributed across multiple subspaces. Despite the effectiveness of subspace learning methods in identifying clusters within high-dimensional data, their integration into SC is often limited. Specifically, a majority of SC techniques rooted in subspace learning either lack efficient similarity metrics or encounter difficulties in uncovering clusters within datasets that share common subspaces. To address these concerns, this paper introduces a novel similarity metric, termed Similarity Measure based on the Distance of Subspaces (SMDS). The proposed SMDS criterion yields three key advantages. Firstly, SMDS involves identifying the local neighborhood of each sample, which typically exerts a stronger influence than global factors. Secondly, it employs subspace learning, leveraging the fact that estimating small linear subspaces is computationally more tractable than handling larger and more complex ones. Thirdly, it introduces a novel subspace clustering approach by establishing a similarity matrix based on subspace distance. This property effectively addresses the challenges posed by overlapping subspaces and facilitates their merging. Moving forward, this novel SMDS similarity matrix is then utilized within SC, leading to the proposal of SC-SMDS, anew method tailored for clustering tasks. The SC-SMDS method is evaluated through various experiments on a number of real-world benchmark datasets, demonstrating its superior performance over several competing clustering methods.