Yajing Li

Hongbing Zhang, Xinyi Liu, Chang Liu et al. · microsoft-research, tsinghua

Non-convex relaxation methods have been widely used in tensor recovery problems, and compared with convex relaxation methods, can achieve better recovery results. In this paper, a new non-convex function, Minimax Logarithmic Concave Penalty (MLCP) function, is proposed, and some of its intrinsic properties are analyzed, among which it is interesting to find that the Logarithmic function is an upper bound of the MLCP function. The proposed function is generalized to tensor cases, yielding tensor MLCP and weighted tensor $Lγ$-norm. Consider that its explicit solution cannot be obtained when applying it directly to the tensor recovery problem. Therefore, the corresponding equivalence theorems to solve such problem are given, namely, tensor equivalent MLCP theorem and equivalent weighted tensor $Lγ$-norm theorem. In addition, we propose two EMLCP-based models for classic tensor recovery problems, namely low-rank tensor completion (LRTC) and tensor robust principal component analysis (TRPCA), and design proximal alternate linearization minimization (PALM) algorithms to solve them individually. Furthermore, based on the Kurdyka-Łojasiwicz property, it is proved that the solution sequence of the proposed algorithm has finite length and converges to the critical point globally. Finally, Extensive experiments show that proposed algorithm achieve good results, and it is confirmed that the MLCP function is indeed better than the Logarithmic function in the minimization problem, which is consistent with the analysis of theoretical properties.

Luoma Ke, Guangpeng Zhang, Jibo He et al.

With the rapid growth of the aviation industry, there is a need for a large number of flight crew. How to select the right pilots in a cost-efficient manner has become an important research question. In the current study, twenty-three pilots were recruited from China Eastern Airlines, and 23 novices were from the community of Tsinghua University. A novel approach incorporating machine learning and virtual reality technology was applied to distinguish features between these participants with different flight skills. Results indicate that SVM with the MIC feature selection method consistently achieved the highest prediction performance on all metrics with an Accuracy of 0.93, an AUC of 0.96, and an F1 of 0.93, which outperforms four other classifier algorithms and two other feature selection methods. From the perspective of feature selection methods, the MIC method can select features with a nonlinear relationship to sampling labels, instead of a simple filter-out. Our new implementation of the SVM + MIC algorithm outperforms all existing pilot selection algorithms and perhaps provides the first implementation based on eye tracking and flight dynamics data. This study's VR simulation platforms and algorithms can be used for pilot selection and training.

Hongbing Zhang, Xinyi Liu, Hongtao Fan et al.

The low rank tensor completion (LRTC) problem has attracted great attention in computer vision and signal processing. How to acquire high quality image recovery effect is still an urgent task to be solved at present. This paper proposes a new tensor $L_{2,1}$ norm minimization model (TLNM) that integrates sum nuclear norm (SNN) method, differing from the classical tensor nuclear norm (TNN)-based tensor completion method, with $L_{2,1}$ norm and Qatar Riyal decomposition for solving the LRTC problem. To improve the utilization rate of the local prior information of the image, a total variation (TV) regularization term is introduced, resulting in a new class of tensor $L_{2,1}$ norm minimization with total variation model (TLNMTV). Both proposed models are convex and therefore have global optimal solutions. Moreover, we adopt the Alternating Direction Multiplier Method (ADMM) to obtain the closed-form solution of each variable, thus ensuring the feasibility of the algorithm. Numerical experiments show that the two proposed algorithms are convergent and outperform compared methods. In particular, our method significantly outperforms the contrastive methods when the sampling rate of hyperspectral images is 2.5\%.