Semi-supervised sparse representation collaborative clustering of incomplete data

Sparse subspace clustering (SSC) focuses on revealing the structure and distribution of high dimensional data from an algebraic perspective. It is a two-phase clustering technique, performing sparse representation of the high dimensional data and subsequently cutting the induced affinity graph, which cannot achieve an optimal or expected clustering result. To address this challenge, this paper proposes an approach to subspace representation collaborative clustering (SRCC) for incomplete high dimensional data. In the proposed model, both phases of sparse subspace representation and clustering are integrated into a unified optimization, in which a fuzzy partition matrix is introduced as a bridge to cluster the extracted sparse representation features of the data. At the same time, the missing entries are adaptively imputed along with the two phases. To generalize SRCC to a semi-supervised case, an adjacency matrix of incomplete data is constructed with the ideas of 'Must-link' and 'Cannot-link'. Meanwhile, a semi-supervised indicator matrix is introduced to promote discriminative capacity of revealing global and local structures of incomplete data and enhance the performance of clustering. The semi-supervised sparse representation collaborative clustering (S3RCC) is modeled. Extensive experiments on lots of real-world benchmark datasets demonstrate the superior performance of the proposed two models on imputation and clustering of incomplete data compared to the state-of-the-art methods.