Matrix Factorization as Search ⋆

Abstract. Simplex Volume Maximization (SiVM) exploits distance geometry for e ciently factorizing gigantic matrices. It was proven successful in game, social media, and plant mining. Here, we review the distance geometry approach and argue that it generally suggests to factorize gigantic matrices using search-based instead of optimization techniques. 1 Interpretable Matrix Factorization Many modern data sets are available in form of a real-valued m × n matrix V of rank r ≤ min(m, n). The columns v1,..., vn of such a data matrix encode information about n objects each of which is characterized by m features. Typical examples of objects include text documents, digital images, genomes, stocks, or social groups. Examples of corresponding features are measurements such as term frequency counts, intensity gradient magnitudes, or incidence relations among the nodes of a graph. In most modern settings, the dimensions of the data matrix are large so that it is useful to determine a compressed representation that may be easier to analyze and interpret in light of domain-speci c knowledge