Probabilistic Sparse Subspace Clustering Using Delayed Association

TL;DR

This paper introduces a probabilistic subspace clustering method that delays uncertain point associations to improve accuracy and efficiency, especially in noisy or intersecting subspaces.

Contribution

It proposes a joint optimization approach with delayed association to enhance clustering accuracy and reduce computational costs in high-dimensional data.

Findings

Delayed association improves clustering accuracy in ambiguous subspaces.

The method reduces computational cost via incremental spectral clustering.

Experimental results show superior performance over existing methods.

Abstract

Discovering and clustering subspaces in high-dimensional data is a fundamental problem of machine learning with a wide range of applications in data mining, computer vision, and pattern recognition. Earlier methods divided the problem into two separate stages of finding the similarity matrix and finding clusters. Similar to some recent works, we integrate these two steps using a joint optimization approach. We make the following contributions: (i) we estimate the reliability of the cluster assignment for each point before assigning a point to a subspace. We group the data points into two groups of "certain" and "uncertain", with the assignment of latter group delayed until their subspace association certainty improves. (ii) We demonstrate that delayed association is better suited for clustering subspaces that have ambiguities, i.e. when subspaces intersect or data are contaminated with outliers/noise. (iii) We demonstrate experimentally that such delayed probabilistic association leads to a more accurate self-representation and final clusters. The proposed method has higher accuracy both for points that exclusively lie in one subspace, and those that are on the intersection of subspaces. (iv) We show that delayed association leads to huge reduction of computational cost, since it allows for incremental spectral clustering.