Projective Nonnegative Matrix Factorization with α-Divergence
A new matrix factorization algorithm which combines two recently proposed nonnegative learning techniques is presented. Our new algorithm, α-PNMF, inherits the advantages of Projective Nonnegative Matrix Factorization (PNMF) for learning a highly orthogonal factor matrix. When the Kullback-Leibler (KL) divergence is generalized to α-divergence, it gives our method more flexibility in approximation. We provide multiplicative update rules for α-PNMF and present their convergence proof. The resulting algorithm is empirically verified to give a good solution by using a variety of real-world datasets. For feature extraction, α-PNMF is able to learn highly sparse and localized part-based representations of facial images. For clustering, the new method is also advantageous over Nonnegative Matrix Factorization with α-divergence and ordinary PNMF in terms of higher purity and smaller entropy.
KeywordsFacial Image Nonnegative Matrix Factorization Classical Principal Component Analysis Multiplicative Update Principal Component Analysis Subspace
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- 6.Ding, C., Li, T., Peng, W., Park, H.: Orthogonal nonnegative matrix t-factorizations for clustering. In: Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining, pp. 126–135 (2006)Google Scholar
- 8.Samaria, F., Harter, A.: Parameterisation of a stochastic model for human face identification. In: Proceedings of 2nd IEEE Workshop on Applications of Computer Vision, Sarasota FL, December 1994, pp. 138–142 (1994)Google Scholar