Filtrated Spectral Algebraic Subspace Clustering
This addresses a limitation in subspace clustering for noisy data with varying dimensions, though it appears incremental as it builds on existing ASC methods.
The paper tackles the problem of clustering noisy data from subspaces of arbitrary dimensions by proposing a new Algebraic Subspace Clustering algorithm that constructs a sequence of subspaces and uses distances to build a superior affinity measure. Experiments on the Hopkins 155 dataset show it outperforms sparse and low rank subspace clustering methods.
Algebraic Subspace Clustering (ASC) is a simple and elegant method based on polynomial fitting and differentiation for clustering noiseless data drawn from an arbitrary union of subspaces. In practice, however, ASC is limited to equi-dimensional subspaces because the estimation of the subspace dimension via algebraic methods is sensitive to noise. This paper proposes a new ASC algorithm that can handle noisy data drawn from subspaces of arbitrary dimensions. The key ideas are (1) to construct, at each point, a decreasing sequence of subspaces containing the subspace passing through that point; (2) to use the distances from any other point to each subspace in the sequence to construct a subspace clustering affinity, which is superior to alternative affinities both in theory and in practice. Experiments on the Hopkins 155 dataset demonstrate the superiority of the proposed method with respect to sparse and low rank subspace clustering methods.