Sparse Representation Based Research On Classification Problems

In the field of pattern classification, sparse representation as a valid and robust feature representation and selection method has been applied to a number of practical applications. Based on its solid theoretical foundation, this dissertation has deeply studied its application on classification problemsAs a special one-class classification problem, foreground-background segmentation has been widely used in video surveillance applications. Based on the study of subspace learning method for background modeling, this dissertation proposes a spatial-temporal sparse representation method for background modeling. By introducing Principal Compo-nent Analysis to extract a low dimensional subspace to represent background, the training stage can be performed without any labeled frame. Adopting eigenvectors as dictionary, the spatial-temporal image patches are represented with all of the eigenvectors rather than only the local subspace so as to prevent the misclassification of foreground and background. The eigenvectors are updated by covariance-free incremental principal component analysis. A new strategy for dictionary updating has been proposed to enhance the model’s capability of recovering from misclassification and representing dynamic background with patterns. In order to speed up our method, random projection emerged from compressive sensing theory is proposed to reduce the dimension of patches. The proposed method is robust to local and global illumination changes, more sensitive to dim foreground than other subspace based approach, able to adapt environmental changes in reality scenes and more robust to dynamic background.Face recognition is a classic multi-class image classification problem. Considering the face recognition problem with very few labeled training samples, ordinary methods tend to fail since there is not enough information for classification. This dissertation proposes a sparse representation-based semi-supervised self-training method for face recognition. With very few labeled training samples as dictionary, the ability of sparse representation based classification cannot be guaranteed. Therefore, we propose to apply semi-supervised di- mensionality reduction in each iteration of self-training by making use of both labeled and unlabeled training data. The unlabeled samples with high confidence of belonging to some class is labeled and added to the labeled set, which strengthens the discriminative ability of the low dimensional subspace. Meanwhile, the labeled samples in the low dimensional sub-space can be naturally used as over-complete dictionary for sparse representation. Moreover, when the data distribution is non-Gaussian, using sparse representation based classification can avoid the bias caused by mean template method. In order to benefit from the classifica-tion ability of sparse representation more adequately, we propose to combine two different l-1-graph into the self-learning algorithm, which improves the consistency of our method and achieves better classification results.Kernel minimum squared error is a classification method based on kernel method and multivariate regression. Based on the summarization of the subset selection methods, this dissertation proposes a sparsity based model to extract features for kernel minimum squared error. By introducing a sparsity shrinkage term, a subset of the original training samples can be selected with least angle regression algorithm. The nodes corresponding to the nonzero coefficients are naturally chosen to be the significant nodes. Due to the small amount of nodes used, the computational burden of feature extraction is alleviated. Meanwhile, in order to deal with classification problems with imbalanced data, we extend our algorithm to a weighted version by imposing a cost sensitive factor to each class.Last of all, the work proposed in this dissertation is summarized. According to the imperfectness of our work, future work has also been discussed and arranged.