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Higher-order principal component pursuit via tensor approximation and convex optimization 被引量:1
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作者 Sijia Cai Ping Wang +1 位作者 Linhao Li Chuhan Zhang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2014年第3期523-530,共8页
Recovering the low-rank structure of data matrix from sparse errors arises in the principal component pursuit (PCP). This paper exploits the higher-order generalization of matrix recovery, named higher-order princip... Recovering the low-rank structure of data matrix from sparse errors arises in the principal component pursuit (PCP). This paper exploits the higher-order generalization of matrix recovery, named higher-order principal component pursuit (HOPCP), since it is critical in multi-way data analysis. Unlike the convexification (nuclear norm) for matrix rank function, the tensorial nuclear norm is stil an open problem. While existing preliminary works on the tensor completion field provide a viable way to indicate the low complexity estimate of tensor, therefore, the paper focuses on the low multi-linear rank tensor and adopt its convex relaxation to formulate the convex optimization model of HOPCP. The paper further propose two algorithms for HOPCP based on alternative minimization scheme: the augmented Lagrangian alternating direction method (ALADM) and its truncated higher-order singular value decomposition (ALADM-THOSVD) version. The former can obtain a high accuracy solution while the latter is more efficient to handle the computationally intractable problems. Experimental results on both synthetic data and real magnetic resonance imaging data show the applicability of our algorithms in high-dimensional tensor data processing. 展开更多
关键词 tensor recovery principal component pursuit alternating direction method tensor approximation.
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PROJECTION PURSUIT PRINCIPAL COMPONENT ANALYSIS AND ITS APPLICATION TO METEOROLOGY 被引量:3
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作者 常红 史久恩 陈忠琏 《Acta meteorologica Sinica》 SCIE 1990年第2期254-263,共10页
Projection Pursuit (PP) Principal Component Analysis (PCA) method is herein introduced and applied to the field of meteorology for the first time. Some problems relevant to meteorological application are dis- cussed i... Projection Pursuit (PP) Principal Component Analysis (PCA) method is herein introduced and applied to the field of meteorology for the first time. Some problems relevant to meteorological application are dis- cussed in detail and comparisons with EOF method are made with the emphasis on robustness. 展开更多
关键词 PP PROJECTION pursuit principal component ANALYSIS AND ITS APPLICATION TO METEOROLOGY
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