Affine Subspace Clustering with Nearest Subspace Neighbor

In this paper, we consider the problem of affine subspace clustering, which requires to estimate the corresponding subspaces and assign the corresponding labels to data points on or near a union of low-dimensional affine subspaces. To address this problem, we propose a framework based on Nearest Subspace Neighbor (NSN). NSN is originally designed to estimate the geometric structure of clusters that can not be adequately performed by conventional approaches based on a general distance metric such as K-means, and has been applied in solving the linear subspace clustering problem. However, in real-world scenarios, the vast majority of data exist in the affine subspace rather than linear subspaces. To make better use of NSN, we construct an affinity matrix by incrementally picking the points considering affine subspaces in a greedy fashion. Statistical experiments demonstrate that our method outperforms both the original NSN and an affine subspace clustering method.