Yes we can: simplex volume maximization for descriptive web-scale matrix factorization

Matrix factorization methods are among the most common techniques for detecting latent components in data. Popular examples include the Singular Value Decomposition or Nonnegative Matrix Factorization. Unfortunately, most methods suffer from high computational complexity and therefore do not scale to massive data. In this paper, we present a linear time algorithm for the factorization of gigantic matrices that iteratively yields latent components. We consider a constrained matrix factorization s.t. the latent components form a simplex that encloses most of the remaining data. The algorithm maximizes the volume of that simplex and thereby reduces the displacement of data from the space spanned by the latent components. Hence, it also lowers the Frobenius norm, a common criterion for matrix factorization quality. Our algorithm is efficient, well-grounded in distance geometry, and easily applicable to matrices with billions of entries. In addition, the resulting factors allow for an int...

• Type: Journal
• Year: 2010
• Where: CIKM
• Authors: Christian Thurau, Kristian Kersting, Christian Bauckhage
• Keywords: CIKM 2010, Information Technology, Latent Components, Matrix Factorization, Matrix Factorization Methods