This paper is concerned with screening features in ultrahigh dimensional data analysis, which has become increasingly important in diverse scientific fields. We develop a sure independence screening procedure based on the distance correlation (DC-SIS, for short). The DC-SIS can be implemented as easily as the sure independence screening procedure based on the Pearson correlation (SIS, for short) proposed by Fan and Lv (2008). However, the DC-SIS can significantly improve the SIS. Fan and Lv (2008) established the sure screening property for the SIS based on linear models, but the sure screening property is valid for the DC-SIS under more general settings including linear models. Furthermore, the implementation of the DC-SIS does not require model specification (e.g., linear model or generalized linear model) for responses or predictors. This is a very appealing property in ultrahigh dimensional data analysis. Moreover, the DC-SIS can be used directly to screen grouped predictor variables and for multivariate response variables. We establish the sure screening property for the DC-SIS, and conduct simulations to examine its finite sample performance. Numerical comparison indicates that the DC-SIS performs much better than the SIS in various models. We also illustrate the DC-SIS through a real data example.

In this paper we propose a robust object tracking algorithm using a collaborative model. As the main challenge for object tracking is to account for drastic appearance change, we propose a robust appearance model that exploits both holistic templates and local representations. We develop a sparsity-based discriminative classifier (SD-C) and a sparsity-based generative model (SGM). In the S-DC module, we introduce an effective method to compute the confidence value that assigns more weights to the foreground than the background. In the SGM module, we propose a novel histogram-based method that takes the spatial information of each patch into consideration with an occlusion handing scheme. Furthermore, the update scheme considers both the latest observations and the original template, thereby enabling the tracker to deal with appearance change effectively and alleviate the drift problem. Numerous experiments on various challenging videos demonstrate that the proposed tracker performs favorably against several state-of-the-art algorithms.

Abstract-In this paper, we propose a robust object tracking algorithm based on a sparse collaborative model that exploits both holistic templates and local representations to account for drastic appearance changes. Within the proposed collaborative appearance model, we develop a sparse discriminative classifier (SDC) and sparse generative model (SGM) for object tracking. In the SDC module, we present a classifier that separates the foreground object from the background based on holistic templates. In the SGM module, we propose a histogram-based method that takes the spatial information of each local patch into consideration. The update scheme considers both the most recent observations and original templates, thereby enabling the proposed algorithm to deal with appearance changes effectively and alleviate the tracking drift problem. Numerous experiments on various challenging videos demonstrate that the proposed tracker performs favorably against several state-of-the-art algorithms.

In this paper, multiagent systems and genetic algorithms are integrated to form a new algorithm, multiagent genetic algorithm (MAGA), for solving the global numerical optimization problem. An agent in MAGA represents a candidate solution to the optimization problem in hand. All agents live in a latticelike environment, with each agent fixed on a lattice-point. In order to increase energies, they compete or cooperate with their neighbors, and they can also use knowledge. Making use of these agent-agent interactions, MAGA realizes the purpose of minimizing the objective function value. Theoretical analyzes show that MAGA converges to the global optimum. In the first part of the experiments, ten benchmark functions are used to test the performance of MAGA, and the scalability of MAGA along the problem dimension is studied with great care. The results show that MAGA achieves a good performance when the dimensions are increased from 20-10,000. Moreover, even when the dimensions are increased to as high as 10,000, MAGA still can find high quality solutions at a low computational cost. Therefore, MAGA has good scalability and is a competent algorithm for solving high dimensional optimization problems. To the best of our knowledge, no researchers have ever optimized the functions with 10,000 dimensions by means of evolution. In the second part of the experiments, MAGA is applied to a practical case, the approximation of linear systems, with a satisfactory result.

This work is concerned with marginal sure independence feature screening for ultra-high dimensional discriminant analysis. The response variable is categorical in discriminant analysis. This enables us to use conditional distribution function to construct a new index for feature screening. In this paper, we propose a marginal feature screening procedure based on empirical conditional distribution function. We establish the sure screening and ranking consistency properties for the proposed procedure without assuming any moment condition on the predictors. The proposed procedure enjoys several appealing merits. First, it is model-free in that its implementation does not require specification of a regression model. Second, it is robust to heavy-tailed distributions of predictors and the presence of potential outliers. Third, it allows the categorical response having a diverging number of classes in the order of O(nκ) with some κ ≥ 0. We assess the finite sample property of the proposed procedure by Monte Carlo simulation studies and numerical comparison. We further illustrate the proposed methodology by empirical analyses of two real-life data sets.