Feature selection is an important technique in machine learning research. An effective and robust feature selection method is desired to simultaneously identify the informative features and eliminate the noisy ones of data. In this paper, we consider the unsupervised feature selection problem which is particularly difficult as there is not any class labels that would guide the search for relevant features. To solve this, we propose a novel algorithmic framework which performs unsupervised feature selection. Firstly, the proposed framework implements structure learning, where the data structures (including intrinsic distribution structure and the data segment) are found via a combination of the alternative optimization and clustering. Then, both the intrinsic data structure and data segmentation are formulated as regularization terms for discriminant feature selection. The results of the feature selection also affect the structure learning step in the following iterations. By leveraging the interactions between structure learning and feature selection, we are able to capture more accurate structure of data and select more informative features. Clustering and classification experiments on real world image data sets demonstrate the effectiveness of our method.

While recent techniques for discriminative dictionary learning have attained promising results on the classification tasks, their performance is highly dependent on the number of labeled samples available for training. However, labeling samples is expensive and time consuming due to the significant human effort involved. In this paper, we present a novel semi- supervised dictionary learning method which utilizes the structural sparse relationships between the labeled and unlabeled samples. Specifically, by connecting the sparse reconstruction coefficients on both the original samples and dictionary, the unlabeled samples can be automatically grouped to the different labeled samples, and the grouped samples share a small number of atoms in the dictionary via mixed l2p- norm regularization. This makes the learned dictionary more representative and discriminative since the shared atoms are learned by using the labeled and unlabeled samples potentially from the same class. Minimizing the derived objective function is a challenging task because it is non-convex and highly non-smooth. We propose an efficient optimization algorithm to solve the problem based on the block coordinate descent method. Moreover, we have a rigorous proof of the convergence of the algorithm. Extensive experiments are presented to show the superior performance of our method in classification applications.

Visual tracking is an important research topic in computer vision community. Although there are numerous tracking algorithms in the literature, no one performs better than the others under all circumstances, and the best algorithm for a particular dataset may not be known a priori. This motivates a fundamental problem-the necessity of an ensemble learning of different tracking algorithms to overcome their drawbacks and to increase the generalization ability. This paper proposes a multi-modality ranking aggregation framework for fusion of multiple tracking algorithms. In our work, each tracker is viewed as a `ranker' which outputs a rank list of the candidate image patches based on its own appearance model in a particular modality. Then the proposed algorithm aggregates the rankings of different rankers to produce a joint ranking. Moreover, the level of expertise for each `ranker' based on the historical ranking results is also effectively used in our model. The proposed model not only provides a general framework for fusing multiple tracking algorithms on multiple modalities, but also provides a natural way to combine the advantages of the generative model based trackers and the the discriminative model based trackers. It does not need to directly compare the output results obtained by different trackers, and such a comparison is usually heuristic. Extensive experiments demonstrate the effectiveness of our work.

In this paper, we study the low-rank tensor completion problem, where a high-order tensor with missing entries is given and the goal is to complete the tensor. We propose to minimize a new convex objective function, based on log sum of exponentials of nuclear norms, that promotes the low-rankness of unfolding matrices of the completed tensor. We show for the first time that the proximal operator to this objective function is readily computable through a hybrid singular value thresholding scheme. This leads to a new solution to high-order (low-rank) tensor completion via convex relaxation. We show that this convex relaxation and the resulting solution are much more effective than existing tensor completion methods (including those also based on minimizing ranks of unfolding matrices). The hybrid singular value thresholding scheme can be applied to any problem where the goal is to minimize the maximum rank of a set of low-rank matrices.