Component-based nearest neighbour subspace clustering

In this paper, the problem of clustering data points that lie near or on a union of independent low-dimensional subspaces is addressed. To this end, the popular spectral clustering-based algorithms usually follow a two-stage strategy that initially builds an affinity matrix and then applies spectral clustering. However, an inappropriate affinity matrix that does not sufficiently connect data points lying on the same subspace will easily lead to the issue of over-segmentation. To alleviate this issue, building the affinity matrix based on subspace hypotheses generated by an iterative sampling operation according to the Random Cluster Model under the framework of energy minimisation is proposed. Specifically, each hypothesis is generated from a large number of data points by sampling a component in a K-nearest neighbour graph. Extensive experiments on synthetic data and real-world datasets show that the proposed method can improve the connectivity of the affinity matrix and provide competitive results against state-of-the-art methods.