Compressed subspace clustering: A case study

Subspace clustering possesses a wide range of applications, including network data analysis, image segmentation, and medical image processing, etc. Aimed at reducing the computational complexity of subspace clustering performed on high-dimensional data, we propose a compressed subspace clustering approach by random projection. From the view of subspace principal angles, we analyze the subspace affinity change brought by compression, and provide an estimate of compressed subspace affinity when the embedded subspaces share a certain number of intersected dimensions with all other dimensions orthogonal pairwisely. In such condition, a lower bound on compressed dimensionality is also theoretically proved in this paper. Our results show that the raw data can be compressed to very few measurements yet will remain high subspace separability. Numerical simulations validate the above theoretical results.