Abstract: Matrix Factorization is an effective and efficient method to solve clustering problems in machine learning. However, for most traditional which factorization based models in clustering, there are two necessary steps to get the final assignments. First, original data can be decomposed to a basis matrix and a coefficient matrix through a certain model. Second, the learned coefficient matrix is fed into K-means to make discretization. This two-step paradigm causes extra computational burden and may have some side effect on the final results due to the sensitivity to initialization of K-means. To this end, a novel model termed fuzzy local coordinate concept factorization with graph regularizer (FLCCF-G) is proposed. Which avoids using K-means by enforcing the sum of each row of the non-negative coefficient matrix to equal to one. Then the final clustering results can obtained directly by checking the maximum value of each row of the coefficient matrix. In addition, through this constraint, our proposed model changes is a fuzzy clustering model rather than hard clustering, indicating that the model has better interpretability to data points in boundaries of different clusters. Extensive experimental results on synthetic and Benchmark data sets indicate the better performance of FLCCF-G on data clustering.

Key words: concept factorization, local coordinate coding, fuzzy clustering, graph regularizer