The schemes based on matrix factorization have been applied in many fields, such as recommender system, image classification, data clustering, face recognition and so on. Among them, non negative matrix factorization (NMF) and concept factorization (CF) are the two most commonly used matrix decomposition techniques. NMF decomposes a matrix into the product of two non negative matrices and CF divides a matrix into the product of three matrices. CF is considered as one variant of NMF. The biggest difference between them is that CF can be executed in a kernel space. The development of supervised learning methods show that label information is critical to enhance the model’s ability. In this paper, NMF and CF based on label consistent constraint methods are presented respectively for data clustering. The corresponding multiplicative update solutions, parameters selection and convergence verification are given. Clustering results on three data sets reveal that our methods outperform the state-of-the-art algorithms in terms of accuracy and normalized mutual information.
As one kind of popular clustering techniques, Concept Factorization (CF) has been widely employed in computer vision and pattern recognition fields. However, existing clustering algorithms based on CF do not consider the complementarity between multiple features. In order to solve this problem, many joint learning methods have been proposed in recent years, such as Joint Non-negative Matrix Factorization (JNMF), Laplacian Regularized Joint Non-negative Matrix Factorization (LJ-NMF). Inspired by these, Joint Concept Factorization (JCF) and Joint Locally Consistent Concept Factorization (JLCCF) schemes are proposed in this paper. Experimental results on image clustering show that the proposed schemes outperform some existing algorithms in terms of accuracy and normalized mutual information.
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