Convex non-negative matrix factorization for massive datasets

Non-negative matrix factorization (NMF) has become a standard tool in data mining, information retrieval, and signal processing. It is used to factorize a non-negative data matrix into two non-negative matrix factors that contain basis elements and linear coefficients, respectively. Often, the columns of the first resulting factor are interpreted as “cluster centroids” of the input data, and the columns of the second factor are understood to contain cluster membership indicators. When analyzing data such as collections of gene expressions, documents, or images, it is often beneficial to ensure that the resulting cluster centroids are meaningful, for instance, by restricting them to be convex combinations of data points. However, known approaches to convex-NMF suffer from high computational costs and therefore hardly apply to large-scale data analysis problems. This paper presents a new framework for convex-NMF that allows for an efficient factorization of data matrices of millions ...

• Type: Journal
• Year: 2011
• Where: Knowledge and Information Systems
• Authors: C. Thurau, K. Kersting, M. Wahabzada, and C. Bauckhage
• Keywords: Data Mining, Information Retrieval, Large-scale Data Analysis, Low-rank Approximation, Matrix Factorization