Dual hybrid manifold regularized non-negative matrix factorization with discriminability for image clustering

Matrix factorization techniques are wildly used in computer vision and data mining. Among them, Non-negative Matrix Factorization (NMF) has received considerable attention due to its part-based representation and sparsity. Recent research has shown that not only the data points are sampled from data manifold, but also the features are sampled from feature manifold. To exploit the duality between data space and feature space, researchers have proposed various dual graph regularized matrix. But some shortcomings are shared by the existing methods. 1) Using only one type of graph, k nearest neighbors (KNN) graph, to approximate the complicated manifold in data space and feature space. 2) Most existing methods ignore the discriminative information in image data. In this paper, we propose Dual Hybrid Manifold Regularized Non-negative Matrix Factorization with Discriminability (DHNMFD), a novel nonnegative representation learning algorithm for image clustering. On the one hand, KNN graph and sparse subspace clustering (SSC) based graph are linearly combined to maximally approximate the intrinsic manifold in data space and feature space. On the other hand, discriminative information by approximate orthogonal constraints is exploited to capture the discriminative information of data. We propose an iterative multiplicative updating rule for optimization of DHNMFD. Experiments on two image datasets demonstrated the superiority of DHNMFD compared with other state-of-the-art related methods.