Joint non-negative and fuzzy coding with graph regularization for efficient data clustering

Abstract

Non-negative matrix factorization (NMF) is an effective model in converting data into non-negative coefficient representation whose discriminative ability is usually enhanced to be used for diverse pattern recognition tasks. In NMF-based clustering, we often need to perform K-means on the learned coefficient as postprocessing step to get the final cluster assignments. This breaks the connection between the feature learning and recognition stages. In this paper, we propose to learn the non-negative coefficient matrix based on which we jointly perform fuzzy clustering, by viewing that each column of the dictionary matrix as a concept of each cluster. As a result, we formulate a new fuzzy clustering model, termed Joint Non-negative and Fuzzy Coding with Graph regularization (G-JNFC), and design an effective optimization method to solve it under the alternating direction optimization framework. Besides the convergence and computational complexity analysis on G-JNFC, we conduct extensive experiments on both synthetic and representative benchmark data sets. The results show that the proposed G-JNFC model is effective in data clustering.