An Efficient Algorithm for Tensor Principal Component Analysis via Proximal Linearized Alternating Direction Method of Multipliers

2016 ◽  
Author(s):  
Linbo Qiao ◽  
Bofeng Zhang ◽  
Lei Zhuang ◽  
Jinshu Su
Keyword(s):  
Principal Component Analysis ◽  
Efficient Algorithm ◽  
Principal Component ◽  
Component Analysis ◽  
Alternating Direction Method ◽  
Method Of Multipliers ◽  
Alternating Direction

scholarly journals Kernel Principal Component Analysis Allowing Sparse Representation and Sample Selection

2019 ◽  
Vol 13 (1) ◽  
pp. 9-20 ◽  
Author(s):  
Duo Wang ◽  
Toshihisa Tanaka
Keyword(s):  
Principal Component Analysis ◽  
Sparse Representation ◽  
Sample Selection ◽  
Principal Component ◽  
Real Data ◽  
Component Analysis ◽  
Kernel Functions ◽  
Kernel Principal Component Analysis ◽  
Alternating Direction ◽  
Sparse Kernel

Kernel principal component analysis (KPCA) is a kernelized version of principal component analysis (PCA). A kernel principal component is a superposition of kernel functions. Due to the number of kernel functions equals the number of samples, each component is not a sparse representation. Our purpose is to sparsify coefficients expressing in linear combination of kernel functions, two types of sparse kernel principal component are proposed in this paper. The method for solving sparse problem comprises two steps: (a) we start with the Pythagorean theorem and derive an explicit regression expression of KPCA and (b) two types of regularization $l_1$-norm or $l_{2,1}$-norm are added into the regression expression in order to obtain two different sparsity form, respectively. As the proposed objective function is different from elastic net-based sparse PCA (SPCA), the SPCA method cannot be directly applied to the proposed cost function. We show that the sparse representations are obtained in its iterative optimization by conducting an alternating direction method of multipliers. Experiments on toy examples and real data confirm the performance and effectiveness of the proposed method.

An efficient algorithm for Kernel two-dimensional principal component analysis

2007 ◽  
Vol 17 (1) ◽  
pp. 59-64 ◽  
Author(s):  
Ning Sun ◽  
Hai-xian Wang ◽  
Zhen-hai Ji ◽  
Cai-rong Zou ◽  
Li Zhao
Keyword(s):  
Principal Component Analysis ◽  
Efficient Algorithm ◽  
Principal Component ◽  
Component Analysis ◽  
Two Dimensional
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