Achieving stable subspace clustering by post-processing generic clustering results

TL;DR

This paper introduces a post-processing method for sparse subspace clustering that enhances clustering stability and accuracy by identifying and reassigning misclustered points through stable subspace computation and a dominant nearest subspace classification scheme.

Contribution

It presents a novel post-processing scheme that improves sparse subspace clustering results by stable subspace selection and reclassification, outperforming PCA-based methods.

Findings

Reduces clustering errors significantly on motion segmentation and face clustering datasets.

Demonstrates convergence and robustness of the proposed algorithm.

Introduces negligible disturbance to correctly clustered data points.

Abstract

We propose an effective subspace selection scheme as a post-processing step to improve results obtained by sparse subspace clustering (SSC). Our method starts by the computation of stable subspaces using a novel random sampling scheme. Thus constructed preliminary subspaces are used to identify the initially incorrectly clustered data points and then to reassign them to more suitable clusters based on their goodness-of-fit to the preliminary model. To improve the robustness of the algorithm, we use a dominant nearest subspace classification scheme that controls the level of sensitivity against reassignment. We demonstrate that our algorithm is convergent and superior to the direct application of a generic alternative such as principal component analysis. On several popular datasets for motion segmentation and face clustering pervasively used in the sparse subspace clustering literature the proposed method is shown to reduce greatly the incidence of clustering errors while introducing negligible disturbance to the data points already correctly clustered.