Affinity learning via a diffusion process for subspace clustering

Subspace clustering refers to the problem of finding low-dimensional subspaces (clusters) for high-dimensional data. Current state-of-the-art subspace clustering methods are usually based on spectral clustering, where an affinity matrix is learned by the self-expressive model, i.e., reconstructing every data point by a linear combination of all other points while regularizing the coefficients using the ℓ1 norm. The sparsity nature of ℓ1 norm guarantees the subspace-preserving property (i.e., no connection between clusters) of affinity matrix under certain condition, but the connectedness property (i.e., fully connected within clusters) is less considered. In this paper, we propose a novel affinity learning method by incorporating the sparse representation and diffusion process. Instead of using sparse coefficients directly as the affinity values, we apply the ℓ1 norm as a neighborhood selection criterion, which could capture the local manifold structure. An effective diffusion process is then deployed to spread such local information along with the global geometry of data manifold. Each pairwise affinity is augmented and re-evaluated by the context of data point pair, yielding significant enhancements of within-cluster connectivity. Extensive experiments on synthetic data and real-world data have demonstrated the effectiveness of the proposed method in comparison to other state-of-the-art methods.