Unbiased Sparse Subspace Clustering By Selective Pursuit
This addresses a limitation in unsupervised segmentation for applications like motion segmentation, but it is incremental as it analyzes a specific condition rather than proposing a new solution.
The paper investigates the failure of Sparse Subspace Clustering (SSC) when data points within the same subspace are not well-spread but form multiple clusters, showing that SSC incorrectly infers labels under such distributions.
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.