Groupwise Constrained Reconstruction for Subspace Clustering
This addresses a limitation in subspace clustering for applications with many subspaces, though it appears incremental as it builds on existing reconstruction-based methods.
The paper tackles the problem of subspace clustering when the assumption of independent subspaces fails, proposing a model that directly builds the affinity matrix from latent cluster indicators. Experimental results show the model outperforms state-of-the-art methods on synthetic and real-world datasets.
Reconstruction based subspace clustering methods compute a self reconstruction matrix over the samples and use it for spectral clustering to obtain the final clustering result. Their success largely relies on the assumption that the underlying subspaces are independent, which, however, does not always hold in the applications with increasing number of subspaces. In this paper, we propose a novel reconstruction based subspace clustering model without making the subspace independence assumption. In our model, certain properties of the reconstruction matrix are explicitly characterized using the latent cluster indicators, and the affinity matrix used for spectral clustering can be directly built from the posterior of the latent cluster indicators instead of the reconstruction matrix. Experimental results on both synthetic and real-world datasets show that the proposed model can outperform the state-of-the-art methods.