Multi-View Clustering Via Multi-Manifold Regularized Nonnegative Matrix Factorization

Clustering, which aims to partition a dataset into groups according to data points’ similarities, is a fundamental topic in machine learning and data mining. Many real-world datasets are comprised of different views, and the views often provide compatible and complementary information. Thus it is natural to integrate information from multiple views to gain better clustering performance than relying on a single view. Multi-view clustering has become a hot topic in the past decade and many algorithms have been proposed.Multi-view clustering integrates complementary information from multiple views to gain better clustering performance rather than relying on a single view. NMF based multi-view clustering algorithms have shown their competitiveness among different multi-view clustering algorithms. However, NMF fails to preserve the locally geometrical structure of the data space.In this paper, we propose a multi-manifold regularized nonnegative matrix factorization framework (MMNMF) which can preserve the locally geometrical structure of the views for multi-view clustering. Intuitively, for multi-view clustering, each view can be regarded as one manifold and the intrinsic manifold of the dataset can be treated as a mixture of the manifolds naturally. Suppose that the intrinsic manifold is embedded in a convex hull of all the views’ manifolds, the key idea of our framework is to find such an intrinsic manifold and an intrinsic (consistent) coefficient matrix, and then incorporate them with a multi-manifold regularizer to preserve the locally geometrical structure of the multi-view data space.That is to say, MMNMF regards that the intrinsic manifold of the dataset is embedded in a convex hull of all the views’manifolds, and incorporates such an intrinsic manifold and an intrinsic (consistent) coefficient matrix with a multi-manifold regularizer to preserve the locally geometrical structure of the multi-view data space. We use linear combination to construct the intrinsic manifold, and propose two strategies to find the intrinsic coefficient matrix, which lead to two instances of the framework. Experimental results show that the proposed algorithms outperform existing NMF based algorithms for multi-view clustering.