Unbiased Sparse Subspace Clustering By Selective Pursuit

TL;DR

This paper investigates the limitations of Sparse Subspace Clustering (SSC) when data points on the same subspace are not well-distributed, revealing failure modes under certain distribution conditions.

Contribution

It analyzes how specific distributions of points within the same subspace affect SSC's ability to correctly cluster, highlighting a previously unexamined failure mode.

Findings

SSC fails when points on the same subspace are split into multiple clusters.

The success of SSC depends on the distribution of points within each subspace.

Certain distributions can cause SSC to incorrectly segment data.

Abstract

Sparse subspace clustering (SSC) is an elegant approach for unsupervised segmentation if the data points of each cluster are located in linear subspaces. This model applies, for instance, in motion segmentation if some restrictions on the camera model hold. SSC requires that problems based on the $l_1$-norm are solved to infer which points belong to the same subspace. If these unknown subspaces are well-separated this algorithm is guaranteed to succeed. The algorithm rests upon the assumption that points on the same subspace are well spread. The question what happens if this condition is violated has not yet been investigated. In this work, the effect of particular distributions on the same subspace will be analyzed. It will be shown that SSC fails to infer correct labels if points on the same subspace fall into more than one cluster.