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For many image processing and computer vision problems, data points are in matrix form. Traditional methods often convert a matrix into a vector and then use vector-based approaches. They will ignore the location of matrix elements and the converted vector often has high dimensionality. How to select features for 2D matrix data directly is still an uninvestigated important issue. In this paper, we propose an algorithm named sparse matrix regression (SMR) for direct feature selection on matrix data. It employs the matrix regression model to accept matrix as input and bridges each matrix to its label. Based on the intrinsic property of regression coefficients, we design some sparse constraints on the coefficients to perform feature selection. An effective optimization method with provable convergence behavior is also proposed. We reveal that the number of regression vectors can be regarded as a tradeoff parameter to balance the capacity of learning and generalization in essence. To examine the effectiveness of SMR, we have compared it with several vector-based approaches on some benchmark data sets. Furthermore, we have also evaluated SMR in the application of scene classification. They all validate the effectiveness of our method.

High-dimensional non-Gaussian data are ubiquitous in many real applications. Face recognition is a typical example of such scenarios. The sampled face images of each person in the original data space are more closely located to each other than to those of the same individuals due to the changes of various conditions like illumination, pose variation, and facial expression. They are often non-Gaussian and differentiating the importance of each data point has been recognized as an effective approach to process the high-dimensional non-Gaussian data. In this paper, to embed non-Gaussian data well, we propose a novel unified framework named adaptive discriminative analysis (ADA), which combines the sample's importance measurement and subspace learning in a unified framework. Therefore, our ADA can preserve the within-class local structure and learn the discriminative transformation functions simultaneously by minimizing the distances of the projected samples within the same classes while maximizing the between-class separability. Meanwhile, an efficient method is developed to solve our formulated problem. Comprehensive analyses, including convergence behavior and parameter determination, together with the relationship to other related approaches, are as well presented. Systematical experiments are conducted to understand the work of our proposed ADA. Promising experimental results on various types of real-world benchmark data sets are provided to examine the effectiveness of our algorithm. Furthermore, we have also evaluated our method in face recognition. They all validate the effectiveness of our method on processing the high-dimensional non-Gaussian data.

Inferring the network structure from limited observable data is significant in molecular biology, communication and many other areas. It is challenging, primarily because the observable data are sparse, finite and noisy. The development of machine learning and network structure study provides a great chance to solve the problem. In this paper, we propose an iterative smoothing algorithm with structure sparsity (ISSS) method. The elastic penalty in the model is introduced for the sparse solution, identifying group features and avoiding over-fitting, and the total variation (TV) penalty in the model can effectively utilize the structure information to identify the neighborhood of the vertices. Due to the non-smoothness of the elastic and structural TV penalties, an efficient algorithm with the Nesterov's smoothing optimization technique is proposed to solve the non-smooth problem. The experimental results on both synthetic and real-world networks show that the proposed model is robust against insufficient data and high noise. In addition, we investigate many factors that play important roles in identifying the performance of ISSS.Almost everything in our daily life can be modeled as complex networks, such as the social network 1, 2 , transportation network 3 , protein-to-protein network 4 and knowledge graph 5 . The interactions in these networks play an important role in identifying the networks' structure, functionality and dynamics. Hence, many researchers utilize the detailed interaction information to do a lot of interesting research works, such as the centrality measures 6, 7 , community detection 8 , robustness analysis 9-11 , controllability 12 and network game [13][14][15] . However, the link information of networks is often invisible in many cases. Hence, it's very important to propose a robust method in inferring the network structure from very few observed values (measurements) with noise, which are indirectly generated from the network.Many researchers have made great efforts in solving the network inference problem. For instance, Han and Di et al. 16 proposed the state-of-art method i.e., Lasso (Least Absolute Shrinkage and Selection Operator) 17 , which provides an estimation of a network with limited connectivity and low model prediction error. Hempe 18 proposed an inference algorithm based on inner composition alignment to identify the network structure 19, 20 on the time series data 21 . Timme 22 and Domenico Napoletani et al. 23 inferred the complete connectivity of a network from its stable response dynamics. Daniel Marbach et al. 24 summarized many robust gene network inference methods and compared their performances. Soheil Feizi et al. 25 proposed network deconvolution as a general method to distinguish direct dependencies in gene expression regulatory networks.Though many researchers have made great efforts in solving the network inference problem, it is still very challenging mainly on the following reasons. Firstly, the interactions in the network are very sparse. For most of the vertices...

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Moving target detection is a fundamental problem in computer vision. Most target detection methods only detect the rough area of the target. However, there are also many applications (e.g., advanced video surveillance system, hybrid video camera system, etc.) need to detect the accurate target area for analyzing the movement or behavior. These applications always product noisy video frames and will lead to high false rates using previous method. In this paper, a two-step accurate moving target detection method is proposed. This method obtains a rough target area using a color background subtraction method with a feedback to background estimation, followed by a modified SUSAN method to estimate the accurate target edge. The modified SUSAN method uses the grads magnitudes to achieve an adaptive threshold and the gray barycenter criterion for denoising. Experimental results demonstrate the proposed method is effective for accurate moving target detection in different noise level video frames compare to several competitive methods proposed in the literature.

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