Affiliations: [a] School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou, China
| [b] MoE Key Laboratory of Advanced Perception and Intelligent Control of High-end Equipment, Anhui Polytechnic Universtiy, Wuhu, China
| [c] Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin, China
| [d] Key Laboratory of Brain Machine Collaborative Intelligence of Zhejiang Province, Hangzhou, China
Correspondence:
[*]
Corresponding author. Yong Peng, School of Computer Science and Technology, Hangzhou Dianzi University,
Hangzhou 310018, China. E-mail: [email protected].
Abstract: 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 some related models.
Keywords: Concept factorization, auto-weighting, feature map, data representation, clustering
