Non-negative matrix factorization with fixed row and column sums

Non-negative matrix factorization with fixed row and column sums

In this short note, we focus on the use of the generalized Kullback–Leibler (KL) divergence in the problem of non-negative matrix factorization (NMF). We will show that when using the generalized KL divergence as cost function for NMF, the row sums and the column sums of the original matrix are preserved in the approximation. We will use this special characteristic in several approximation prob...

Matrices with Prescribed Row and Column Sums

This is a survey of the recent progress and open questions on the structure of the sets of 0-1 and non-negative integer matrices with prescribed row and column sums. We discuss cardinality estimates, the structure of a random matrix from the set, discrete versions of the Brunn-Minkowski inequality and the statistical dependence between row and column sums.

Non-negative matrix factorization

Non-negative Matrix Factorization with Sparseness Constraints

Non-negative matrix factorization (NMF) is a recently developed technique for finding parts-based, linear representations of non-negative data. Although it has successfully been applied in several applications, it does not always result in parts-based representations. In this paper, we show how explicitly incorporating the notion of ‘sparseness’ improves the found decompositions. Additionally, ...

Non-Negative Matrix Factorization with Sinkhorn Distance

Non-negative Matrix Factorization (NMF) has received considerable attentions in various areas for its psychological and physiological interpretation of naturally occurring data whose representation may be parts-based in the human brain. Despite its good practical performance, one shortcoming of original NMF is that it ignores intrinsic structure of data set. On one hand, samples might be on a m...