Non-negative matrix factorization with information expansion using item class information

application to association study of genes and functions

Abstract

Non-negative matrix factorization (NMF) is widely used for various problems, such as item recommendation of shopping, image recognition and bioinformatics. However, when the data are sparse, and the row and columns of the items have no association with others, these items tend to be independent resulting poor linking. Here we investigated a method to compensate such too sparse data, by adding information of hierarchical relationships among the items to the matrix analyzed. We show how the additional information helps to make desired new clusters. In addition, too much augmentation of class information makes many items into the same clusters, the situation in which is not desired. Some ideas to avoid excessive compensation are discussed.