Discovering structure within a collection of high-dimensional input vectors is a problem that often recurs in the area of machine learning. A very suitable and widely used algorithm for solving such tasks is Non-negative Matrix Factorization (NMF). The high-dimensional vectors are arranged as columns in a data matrix, which is decomposed into two non-negative matrix factors of much lower rank. Here, we adopt the NMF learning scheme proposed by Van hamme (2008) . It involves combining the training data with supervisory data, which imposes the low-dimensional structure known to be present. The reconstruction of such supervisory data on previously unseen inputs then reveals their underlying structure in an explicit way. It has been noted that for many problems, not all features of the training data correlate equally well with the underlying structure. In other words, some features are relevant for detecting patterns in the data, while others are not. In this paper, we propose an algorithm that builds upon the learning scheme of Van hamme (2008) , and automatically weights each input feature according to its relevance. Applications include both data improvement and feature selection. We experimentally show that our algorithm outperforms similar techniques on both counts.
Driesen J., Van hamme H., ''Supervised input space scaling for non-negative matrix factorization'', Signal processing, vol. 92, no. 8, pp. 1864-1874, August 2012, Elsevier Science Pub. Co.