Adaptive graph guided concept factorization on Grassmann manifold

Abstract Motivated by applications in clustering and optimization, there has been significant interest in the variant for which the database models are high-dimensional data (such as imagesets or videos). Matrix factorization approaches, particularly Nonnegative Matrix Factorization (NMF) have achieved favorable results for data clustering tasks. However, these methods suffer from two major drawbacks. First, matrix factorization approaches only partially explore the inter- or intra- relationships between vector-valued data and are unable to handle high-dimensional data. Second, the clustering results largely rely on the predefined similarity matrix, which usually contain large amounts of noise. In this paper, we propose a novel Adaptive Graph Guided Concept Factorization model on Grassmann manifold (A G 3 CF) for imageset clustering in an unsupervised fashion, which imposes concept factorization over the space of linear subspaces. To further explore the structure of data and assign ideal neighbors, an adaptive graph regularization constraint is designed to automatically capture the local relationships of data samples and integrated well into concept factorization framework. An efficient algorithm is also derived to tackle the resulting optimization problem. Experimental results on several public datasets validate that the proposed approach achieves competitive performance in high-dimensional data clustering.