Non-negative Matrix Factorization with Auxiliary Information

Abstract:

The most general data format in real world is a table or matrix, where columns are instance and rows are their features, and vice versa. Matrix factorization is useful to extract essential low-rank structures from a given matrix and has been increasing interest in data mining and machine learning. A typical example of matrix factorization is non-negative matrix factorization (NMF), which is one type of unsupervised learning, having been successfully applied to a variety of data including documents, images and gene expression, where their values are usually non-negative.  This talk introduces our new NMF with auxiliary information of overlapping groups, published in [1]. This setting is reasonable in many applications, a typical example being gene function estimation where functional gene groups are heavily overlapped with each other.

To estimate true groups from given overlapping groups efficiently, our model incorporates latent matrices with the regularization term using a mixed norm. This regularization term allows group-wise sparsity on the optimized low-rank structure. The latent matrices and other parameters are efficiently estimated by a block coordinate gradient descent method. We empirically evaluated the performance of our proposed model and algorithm from a variety of viewpoints using both synthetic and real world document datasets.

[1] Motoki Shiga and Hiroshi Mamitsuka, “Non-negative Matrix Factorization with Auxiliary Information on Overlapping Groups”, To appear in IEEE Transactions on Knowledge and Data Engineering.

Biography:

Motoki Shiga is a tenure-track assistant professor of Faculty of Engineering, Gifu University, Japan. He received his B.S. degree (Engineering) in 2001, M.S. degree (Engineering) in 2003, and Ph.D. degree (Engineering) in 2006, from Gifu University. And then he had been a post-doctoral researcher and assistant professor at Professor Hiroshi Mamitsuka’s Lab in Kyoto University. Last year he was appointed his current position, and has been managing his laboratory on data engineering.  His research interest is on data mining, statistical machine learning and its application to Bioinformatics, especially data mining with auxiliary information.