During the last decades, we have witnessed a surge of interests of learning a low-dimensional space with discriminative information from one single view. Even though most of them can achieve satisfactory performance in some certain situations, they fail to fully consider the information from multiple views which are highly relevant but sometimes look different from each other. Besides, correlations between features from multiple views always vary greatly, which challenges multi-view subspace learning. Therefore, how to learn an appropriate subspace which can maintain valuable information from multi-view features is of vital importance but challenging. To tackle this problem, this paper proposes a novel multi-view dimension reduction method named Multi-view Locality Low-rank Embedding for Dimension Reduction (MvL2E). MvL2E makes full use of correlations between multi-view features by adopting low-rank representations. Meanwhile, it aims to maintain the correlations and construct a suitable manifold space to capture the low-dimensional embedding for multi-view features. A centroid based scheme is designed to force multiple views to learn from each other. And an iterative alternating strategy is developed to obtain the optimal solution of MvL2E. The proposed method is evaluated on 5 benchmark datasets. Comprehensive experiments show that our proposed MvL2E can achieve comparable performance with previous approaches proposed in recent literatures.
Despite many empirical successes of spectral clustering methods— algorithms that cluster points using eigenvectors of matrices derived from the data—there are several unresolved issues. First. there are a wide variety of algorithms that use the eigenvectors in slightly different ways. Second, many of these algorithms have no proof that they will actually compute a reasonable clustering. In this paper, we present a simple spectral clustering algorithm that can be implemented using a few lines of Matlab. Using tools from matrix perturbation theory, we analyze the algorithm, and give conditions under which it can be expected to do well. We also show surprisingly good experimental results on a number of challenging clustering problems.