Locality-Constrained Concept Factorization

Haifeng Liu, Zheng Yang, Zhaohui Wu

Matrix factorization based techniques, such as nonnegative 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.