Non-negative Matrix Factorization with Applications to Handwritten Digit Recognition

In the last decade, non-negative matrix factorization (NMF) has become a widely used method for solving problems in data mining and pattern recognition. The NMF in its present state can be traced back to the work of Paatero and Tapper in 1994 at the University of Helsinki under the name, “positive matrix factorization” [1]. This technique was popularized by Lee and Seung in 1999 under its current name, “nonnegative matrix factorization” [2]. In the last decade, Lee and Seung have continued to develop and publish algorithms for the computation of NMF [3]. Since 2005, sparse variants of NMF have become quite popular and have been successfully used in cancer class discovery [4] and microarray data analysis [5]. Recent work has focused on improving existing NMF algorithms by attempting to remove random initialization requirements. In this paper, we discuss dense and sparse algorithms for the computation of NMF, provide their MATLAB implementations, and examine the use of NMF in the context of handwritten digit recognition.