Structure constrained nonnegative matrix factorization for pattern clustering and classification

Decomposing data into a small number of essential components is usually an efficient strategy for data exploration, analysis and interpretation. Various workhorse methods such as principal component analysis (PCA) and nonnegative matrix factorization (NMF) have been developed along this line of ideas. These methods impose different constraints (e.g., orthogonality for PCA) to obtain compact or physically meaningful bases. However, it is more natural to learn the constraints directly from data and use them to guide the decomposition procedure. Also, existing methods mainly focus on inter-sample information and the intra-sample structure information has rarely been explored. We propose a novel method, called structure constraint nonnegative matrix factorization (SCNMF), which makes use of the intra-sample structures to facilitate the decomposition process. SCNMF mimics the recognition mechanism of the human brain to extract structure information, and has several attractive properties like always generating orthogonal bases. For concept proof and illustration purpose, human face images are the primary data used in our experiment studies, and the results suggest a superior performance of SCNMF over other representative decomposition algorithms. To illustrate the generality of the proposed method, we also show one example of the application of SCNMF in supervised learning of electrocorticography data.