Research Of Image Clustering Based On Local Structure Constraints

A lot of image data have been produced in our daily life with the fast development of information science and technology. The problem of how to effectively and correctly cluster these data into corresponding subspace has been an important research area in machine learning. The purpose of image clustering is to classify images automatically according to the content or the spatial structure.Researchers have proposed different clustering methods according to different principles in the field of computer vision. However, most of the existing subspace clustering algorithms are global and the discriminative local structures are discarded. In this thesis, we propose two novel and robust clustering methods based on local information constraints.Firstly, we summarise several state-of-the-art clustering algorithms. Sparse methods use local structure of image, but ignores the coherence between data. The low rank representation methods can pursue the global structure of data space by low-rank regularisation, however, there are a large amount of sparse noise in the affinity graph. Furthermore, the mechanism of low rank representation that make use of the noisy data itself as the dictionary instead of the clean data is not quite reasonable.Low rank clustering is one of the state-of-the-art subspace clustering algorithms,but it suffers from dense adjacency map and noise. In the third chapter, we propose a robust low rank clustering algorithm according to the local graphLaplace constraint,which enhance the sparsity of the adjacency matrix while maintain the clustering characteristic. An efficient solution based on linearized alternating direction method is built for our method, and the theoretical analysis for existence of solution is discussed.In the fourth chapter, we present a locality-constrained nonnegative robust shape interaction subspace clustering method. This method integrates the local manifold structure of data into the robust shape interaction in a unified formulation, which guarantees the locality and the low-rank property of the optimal affinity graph.Comparing with traditional low rank representation learning method, this method can not only pursuit the global structure of data space by low-rank regularization, but alsokeep the locality manifold, which lead to a sparse and low-rank affinity graph. The theoretic analysis of the clustering effect is discussed, and we prove that the optimal affinity matrix obtained by our algorithm will be block-diagonal. An efficient solution based on linearized alternating direction method with adaptive penalty is built for our method.In this thesis, two novel robust subspace clustering models are proposed.Comparing with existing methods, the proposed models are robust and discriminative by use of the local structure constraints. The representation matrix obtained by our methods guarantee both the low-rank block and the sparse characteristics. Finally,experimental results show that our algorithms outperform several state-of-the-art algorithms.