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Block Principle Component Analysis with lp-norm for Robust and Sparse Modelling

Journal of Shanghai Jiaotong university(Science) 2018年第3期23卷 398-403页

作者：唐肝翌卢桂馥 School of Computer and Information Anhui Polytechnic University

Block principle component analysis(BPCA) is a recently developed technique in computer vision and pattern classification. In this paper, we propose a robust and sparse BPCA with lp-norm, referred to as BPCAlp-S, which inherits the robustness of BPCA-L1 due to the employment of adjustable lp-norm. In order to perform a sparse modelling, the elastic net is integrated into the objective function. An iterative algorithm which extracts feature vectors one by one greedily is elaborately designed. The monotonicity of the proposed iterative procedure is theoretically guaranteed. Experiments of image classification and reconstruction on several benchmark sets show the effectiveness of the proposed approach.

关键词： block principle component analysis(BPCA) lp-norm robust modelling sparse modelling

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L1-norm and lp-norm Optimization for Bearing-Only Positioning in Presence of Unreliable Measurements

L1-Norm and Lp-Norm Optimization for Bearing-Only Positionin...

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第32届中国控制与决策会议

作者： Ji-An Luo Feng Fang Yi-Fang Shi Han Shen-Tu Yun-Fei Guo Key Lab for IOT and Information Fusion Technology of Zhejiang Hangzhou Dianzi University Institute of information and control School of AutomationHangzhou Dianzi University

Consider the problem of locating a stationary target using bearing measurements in presence of outliers collected from spatially distributed *** standard pseudo-linear estimate requires that the sum of squares of least-squares residuals is ***,the L-norm optimization is not resistance to isolated gross *** this paper,we consider more suitable procedures corresponding to replacing the L2-norm to be L-norm and L-norm(1 norm and L-norm optimization can be solved using existing CVX software and iteratively reweighted least-squares algorithm *** simulations validate the performance of the proposed methods.

关键词： Passive Localization Bearing-Only L1-norm lp-norm Robust Estimation

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Extremal Problems Related to Gauss-John Position

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Acta Mathematica Sinica,English Series 2012年第12期28卷 2527-2534页

作者： Ai Jun LI Gang Song LENG School of Mathematics and Information Science Henan Polytechnic University Department of Mathematics Shanghai University

In this paper, we consider the extremal problem of the ;p-norm： min{;p（TK）, o E TK C L, T E GL（n）}, where K, L are two convex bodies in Rn. Using the optimization theorem of John, we give necessary conditions for K to be in extremal position in terms of a decomposition of the identity. Fhrthermore, the weaker optimization problem, min{（lp（TK））p ： TK C B2n,TK Sn-1 ≠ O,T E GL（n）}, is also considered. As an application, the geometric distance between the unit ball B2n and a centrally symmetric convex body K is obtained.

关键词： Gauss-John position optimization theorem of John lp-norm contact pair

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P-norm Regularized SVM Classifier by Non-convex Conjugate Gradient Algorithm

P-norm Regularized SVM Classifier by Non-convex Conjugate Gr...

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第25届中国控制与决策会议

作者： ZUO Xin HUANG Hailong LI Haien LIU Jianwei Research Institute of Automation China University of Petroleum

ISBN: (纸本)9781467355339

Classical classification algorithm of SVM via p norm regularization usually takes p as 0, 1 or 2. However, these parameters can’t always achieve the best classification results. Some scholars have discussed the situations of p∈{0,1, 2} , where the problem is transformed into the standard quadratic programming. However, when p∈(0,1], the object is non-convex, and the method of quadratic programming is not suitable. From the point of optimization, we use Conjugate Gradient Algorithm to solve the problem. In this paper, two different kinds of SVM have been discussed and the classification results are shown by the experiments on three cancer datasets. At last, we discussed the problem of feature selection. The experiment results show that, feature selection can not only keep the precision of the prediction but also reduce model complexity.

关键词： lp-norm 0 SVM Conjugate gradient algorithm Feature Selection

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