Non-negative Matrix Factorization with Pairwise Constraints and Graph Laplacian

Abstract

Non-negative matrix factorization (NMF) is a very effective method for high dimensional data analysis, which has been widely used in information retrieval, computer vision, and pattern recognition. NMF aims to find two non-negative matrices whose product approximates the original matrix well. It can capture the underlying structure of data in the low dimensional data space using its parts-based representations. However, NMF is actually an unsupervised method without making use of prior information of data. In this paper, we propose a novel pairwise constrained non-negative matrix factorization with graph Laplacian method, which not only utilizes the local structure of the data by graph Laplacian, but also incorporates pairwise constraints generated among all labeled data into NMF framework. More specifically, we expect that data points which have the same class label will have very similar representations in the low dimensional space as much as possible, while data points with different class labels will have dissimilar representations as much as possible. Consequently, all data points are represented with more discriminating power in the lower dimensional space. We compare our approach with other typical methods and experimental results for image clustering show that this novel algorithm achieves the state-of-the-art performance.