Auto-weighted concept factorization for joint feature map and data representation learning

Concept factorization (CF) is an effective matrix factorization model which has been widely used in many applications. In CF, the linear combination of data points serves as the dictionary based on which CF can be performed in both the original feature space as well as the reproducible kernel Hilbert space (RKHS). The conventional CF treats each dimension of the feature vector equally during the data reconstruction process, which might violate the common sense that different features have different discriminative abilities and therefore contribute differently in pattern recognition. In this paper, we introduce an auto-weighting variable into the conventional CF objective function to adaptively learn the corresponding contributions of different features and propose a new model termed Auto-Weighted Concept Factorization (AWCF). In AWCF, on one hand, the feature importance can be quantitatively measured by the auto-weighting variable in which the features with better discriminative abilities are assigned larger weights; on the other hand, we can obtain more efficient data representation to depict its semantic information. The detailed optimization procedure to AWCF objective function is derived whose complexity and convergence are also analyzed. Experiments are conducted on both synthetic and representative benchmark data sets and the clustering results demonstrate the effectiveness of AWCF in comparison with the related models.