Improving Sparse Representation-Based Classification Using Local Principal Component Analysis

This study proposes an image denoising algorithm based on sparse representation and Principal Component Analysis (PCA). The proposed algorithm includes the following steps. First, the noisy image is divided into overlapped [Formula: see text] blocks. Second, the discrete cosine transform is applied as a dictionary for the sparse representation of the vectors created by the overlapped blocks. To calculate the sparse vector, the orthogonal matching pursuit algorithm is used. Then, the dictionary is updated by means of the PCA algorithm to achieve the sparsest representation of vectors. Since the signal energy, unlike the noise energy, is concentrated on a small dataset by transforming into the PCA domain, the signal and noise can be well distinguished. The proposed algorithm was implemented in a MATLAB environment and its performance was evaluated on some standard grayscale images under different levels of standard deviations of white Gaussian noise by means of peak signal-to-noise ratio, structural similarity indexes, and visual effects. The experimental results demonstrate that the proposed denoising algorithm achieves significant improvement compared to dual-tree complex discrete wavelet transform and K-singular value decomposition image denoising methods. It also obtains competitive results with the block-matching and 3D filtering method, which is the current state-of-the-art for image denoising.

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Kernel Principal Component Analysis Allowing Sparse Representation and Sample Selection

ECTI Transactions on Computer and Information Technology (ECTI-CIT) ◽

10.37936/ecti-cit.2019131.187506 ◽

2019 ◽

Vol 13 (1) ◽

pp. 9-20 ◽

Cited By ~ 1

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.

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Dimensionality Reduction with Sparse Locality for Principal Component Analysis

Mathematical Problems in Engineering ◽

10.1155/2020/9723279 ◽

2020 ◽

Vol 2020 ◽

pp. 1-12

Author(s):

Pei Heng Li ◽

Taeho Lee ◽

Hee Yong Youn

Keyword(s):

Principal Component Analysis ◽

Dimensionality Reduction ◽

Sparse Representation ◽

Principal Component ◽

Original Data ◽

Component Analysis ◽

Reconstruction Error ◽

Dimensional Representation ◽

Weighted Matrix ◽

Low Dimensional

Various dimensionality reduction (DR) schemes have been developed for projecting high-dimensional data into low-dimensional representation. The existing schemes usually preserve either only the global structure or local structure of the original data, but not both. To resolve this issue, a scheme called sparse locality for principal component analysis (SLPCA) is proposed. In order to effectively consider the trade-off between the complexity and efficiency, a robust L2,p-norm-based principal component analysis (R2P-PCA) is introduced for global DR, while sparse representation-based locality preserving projection (SR-LPP) is used for local DR. Sparse representation is also employed to construct the weighted matrix of the samples. Being parameter-free, this allows the construction of an intrinsic graph more robust against the noise. In addition, simultaneous learning of projection matrix and sparse similarity matrix is possible. Experimental results demonstrate that the proposed scheme consistently outperforms the existing schemes in terms of clustering accuracy and data reconstruction error.

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