Huge volumes of high-dimensional data have been created with the development of information and network technology. So much more computational and storage cost is needed for processing and archiving of high-dimensional data. And increasing dimensionality of data greatly degrades performance of information processing and analysis. Fortunately, the huge volumes of high-dimensional data in our society usually have low-dimensional inner structures. Recovery of those low-dimensional structures of the high-dimensional data can reduce computational complexity and storage requirement of information processing algorithms and improve the performance of machine learning and pattern recognition tasks. Subspace clustering aims to divide high-dimensional data points into multiple subspaces and find a low-dimensional subspace into which each group of data points can fit simultaneously. Subspace clustering as a new and powerful data analysis tool has attracted a great attention due to its promising applications in computer vision and machine learning. However, it is a challenging task to learn low-dimensional subspace structures due to the possible errors (e.g., noise and corruptions) existing in the high-dimensional data. This thesis aims to improve the robustness of subspace clustering algorithms in the presence of large corruptions and outliers. The main work and contributions are as follows: 1） This thesis firstly presents a survey of subspace clustering. The existing subspace clustering methods are classified into four categories. Both strength and weakness of each method are summarized. 2）A novel optimization model based on half-quadratic minimization is introduced to robust subspace clustering. The sparse subspace clustering (SSC) aims to find the sparse representation of the data and apply the spectral clustering to the representation matrix so that the ultimate segmentation results can be obtained. However the original SSC is prone to the presence of noise. Therefore a correntropy loss function is integrated into the sparse representation model to improve the robustness of SSC. Then half-quadratic minimization is provided as an efficient solution of the proposed formulation. Experimental results on two real-world applications, i.e. face clustering and motion segmentation, demonstrate that our method outperforms state-of-the-art subspace clustering methods. 3）A novel subspace clustering method based on correntropy is proposed in the framework of ...
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