Subspace Clustering And Its Applications

In modern society, many real-world problems deal with collections of high-dimensional data, such as images, videos, text and web documents, DNA micro-array data, and so on. Traditional clustering methods commonly adopt Euclidean distance among the datasets as the similarity measure. However it is difficult to use this similarity measure in high-dimensional linear space. In this dissertation, we study several effective subspace clustering algorithms based on the sparse and low rank representation.First of all, it introduces preliminaries on subspace clustering algorithms, including graph theory, matrix norm and spectral clustering.We mainly present the connected graph, the graph adjacency matrix and the graph Laplacian matrix in graph theory. In addition, we provide the detailed process of subspace clustering algorithm and spectral clustering algorithm.Secondly, this dissertation reviews eight popular subspace clustering algorithms,including sparse subspace clustering algorithm, low rank representation algorithm, low rank subspace clustering algorithm and least squares regression clustering algorithms. It gives the detailed implementation of each algorithm, and compares their models and constraint conditions.Then, this dissertation applies the existing mainstream subspace clustering algorithms to the fields of high-dimensional data clustering, synthetic data clustering,face clustering and motion segmentation. We have the following observations from extensive experiments. In the high-dimensional data clustering, the normalization processing has significant effect on enhancing the clustering performance. For low rank synthetic data, the subspace representation matrix of uncorrupted data has obvious blockdiagonal structure, and low-rank representation with a symmetric constraint algorithm is more robust to noise than other algorithms. In face clustering, low-rank representation with a symmetric constraint algorithm is still robust to sparse large noise. In motion segmentation, least quadratic regression algorithm has achieved the best clustering results.Finally, we analyze the deficiency of the existing algorithms and point out the direction of further research.