Locality-constrained concept factorization

Abstract

Matrix factorization based techniques, such as non-negative matrix factorization (NMF) and concept factorization (CF), have attracted great attention in dimension reduction and data clustering. Both of them are linear learning problems and lead to a sparse representation of the data. However, the sparsity obtained by these methods does not always satisfy locality conditions, thus the obtained data representation is not the best. This paper introduces a locality-constrained concept factorization method which imposes a locality constraint onto the traditional concept factorization. By requiring the concepts (basis vectors) to be as close to the original data points as possible, each data can be represented by a linear combination of only a few basis concepts. Thus our method is able to achieve sparsity and locality at the same time. We demonstrate the effectiveness of this novel algorithm through a set of evaluations on real world applications.