Non-Negative Matrix Factorization with Auxiliary Information on Overlapping Groups


Matrix factorization is useful to extract the essential low-rank structure from a given matrix and has been paid increasing attention. A typical example is non-negative matrix factorization (NMF), which is one type of unsupervised learning, having been successfully applied to a selection of data as well as documents, pictures and gene expression, where their values are sometimes non-negative. We have a tendency to propose a replacement model of NMF which is trained by using auxiliary information of overlapping groups. This setting is terribly cheap in many applications, a typical example being gene operate estimation where functional gene teams are heavily overlapped with every other. To estimate true groups from given overlapping teams efficiently, our model incorporates latent matrices with the regularization term using a mixed norm. This regularization term permits cluster-wise sparsity on the optimized low-rank structure. The latent matrices and alternative parameters are efficiently estimated by a block coordinate gradient descent method. We tend to empirically evaluated the performance of our proposed model and algorithm from a selection of viewpoints, comparing with four strategies including MMF for auxiliary graph data, by using both artificial and real world document and gene expression information sets.

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