Joint<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn fontstyle="italic">1</mml:mn><mml:mo>/</mml:mo><mml:mn fontstyle="italic">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>-Norm Constraint and Graph-Laplacian PCA Method for Feature Extraction

Feng, Chun-Mei; Gao, Ying-Lian; Liu, Jin-Xing; Wang, Juan; Wang, Dongqin; Cheng, Wen

doi:10.1155/2017/5073427

Cited by 14 publications

(9 citation statements)

References 37 publications

(44 reference statements)

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“…In this subsection, we briefly review the classical PCA and gLPCA. PCA finds the new subspace of projected data points H and principal direction U by solving the following optimization problem [7]: …”

Section: Methodsologymentioning

confidence: 99%

“…The basic PCA model cannot recover non-linear structure of data. gLPCA incorporates the geometric manifold information to find the non-linear structure of data [7]. Considering H is the embedding matrix, the gLPCA is formulated as follows: where L = D − W is the graph Laplacian matrix.…”

Section: Methodsologymentioning

confidence: 99%

“…It lays a foundation for further research on the relationship between cancer and genes in the molecular level and improves the efficiency of cancer diagnosis. Among them, Principal Component Analysis (PCA) is a basic tool that has been widely used [6, 7]. The traditional linear PCA method considers the global Euclidean structure of the original data, and when the data points are in a manifold structure, the global Euclidean structure cannot exactly describe the real distance between data points.…”

Section: Introductionmentioning

confidence: 99%

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PCA via joint graph Laplacian and sparse constraint: Identification of differentially expressed genes and sample clustering on gene expression data

Feng

Hou

et al. 2019

BMC Bioinformatics

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BackgroundIn recent years, identification of differentially expressed genes and sample clustering have become hot topics in bioinformatics. Principal Component Analysis (PCA) is a widely used method in gene expression data. However, it has two limitations: first, the geometric structure hidden in data, e.g., pair-wise distance between data points, have not been explored. This information can facilitate sample clustering; second, the Principal Components (PCs) determined by PCA are dense, leading to hard interpretation. However, only a few of genes are related to the cancer. It is of great significance for the early diagnosis and treatment of cancer to identify a handful of the differentially expressed genes and find new cancer biomarkers.ResultsIn this study, a new method gLSPCA is proposed to integrate both graph Laplacian and sparse constraint into PCA. gLSPCA on the one hand improves the clustering accuracy by exploring the internal geometric structure of the data, on the other hand identifies differentially expressed genes by imposing a sparsity constraint on the PCs.ConclusionsExperiments of gLSPCA and its comparison with existing methods, including Z-SPCA, GPower, PathSPCA, SPCArt, gLPCA, are performed on real datasets of both pancreatic cancer (PAAD) and head & neck squamous carcinoma (HNSC). The results demonstrate that gLSPCA is effective in identifying differentially expressed genes and sample clustering. In addition, the applications of gLSPCA on these datasets provide several new clues for the exploration of causative factors of PAAD and HNSC.

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Section: Methodsologymentioning

confidence: 99%

Section: Methodsologymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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PCA via joint graph Laplacian and sparse constraint: Identification of differentially expressed genes and sample clustering on gene expression data

Feng

Hou

et al. 2019

BMC Bioinformatics

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“…(3) L(Z i , X m ) is the load coefficient of the correlation degree between principal component Z i and original variable X m [18]. 50 pixels were randomly selected within the image of each sample, while the spectral information of four adjacent pixels was taken for averaging to exclude the effect of random noise.…”

Section: Spatial Dimensionmentioning

confidence: 99%

Research on Camouflage Recognition in Simulated Operational Environment Based on Hyperspectral Imaging Technology

Zhao

Liu

Xue-feng

et al. 2021

Journal of Spectroscopy

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Hyperspectral imaging technology can obtain the spatial information and spectral information of the simulated operational background and its camouflage materials at the same time and identify and classify them according to their differences. In this paper, we collected the hyperspectral images (400–1000 nm) of the desert background, jungle background, desert camouflage netting, jungle camouflage netting, and jungle camouflage clothing through the hyperspectral imaging system, and the samples were preprocessed by denoising and black-and-white correction. Then, we analysed the region of interest (ROI) of the training samples by principal component analysis (PCA). After the pixels in the region of interest and their surrounding areas were averaged, 60% of the data was used as the training samples, and the remaining 40% was used as the test samples. According to their similarities and differences between them and referenced spectrum, the models of classification were established by combining the Naive Bayes (NB) algorithm, K-nearest neighbour (KNN) algorithm, random forest (RF) algorithm, and support vector machine (SVM) algorithm. The results show that among the four models, SVM model has the highest accuracy of classification and the recognition rate of jungle camouflage clothing is the highest. This study verifies the scientific and feasibility of hyperspectral imaging technology for camouflage identification and classification in a simulated operational environment, which has some practical significance.

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“…Within the given range, the greater the value of γ , the greater the role of the graph Laplacian in the objective function. According to previous research, we set γ = 0.5 to obtain fair results [5], [13], [26]. In practice, we set the parameter ρ = 1.2 in RgLPCA and L 1/2 gLPCA.…”

Section: B Experimental Settingmentioning

confidence: 99%

Dual Graph-Laplacian PCA: A Closed-Form Solution for Bi-Clustering to Find “Checkerboard” Structures on Gene Expression Data

et al. 2019

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In the context of cancer, internal ''checkerboard'' structures are normally found in the matrices of gene expression data, which correspond to genes that are significantly up-or down-regulated in patients with specific types of tumors. In this paper, we propose a novel method, called dual graph-regularization principal component analysis (DGPCA). The main innovation of this method is that it simultaneously considers the internal geometric structures of the condition manifold and the gene manifold. Specifically, we obtain principal components (PCs) to represent the data and approximate the cluster membership indicators through Laplacian embedding. This new method is endowed with internal geometric structures, such as the condition manifold and gene manifold, which are both suitable for bi-clustering. A closed-form solution is provided for DGPCA. We apply this new method to simultaneously cluster genes and conditions (e.g., different samples) with the aim of finding internal ''checkerboard'' structures on gene expression data, if they exist. Then, we use this new method to identify regulatory genes under the particular conditions and to compare the results with those of other state-of-the-art PCA-based methods. Promising results on gene expression data have been verified by extensive experiments. INDEX TERMS Bi-clustering, gene expression data, Laplacian embedding, principal component analysis. I. INTRODUCTION A. BIOLOGICAL ANALYSIS OF PCA

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JointL1/2-Norm Constraint and Graph-Laplacian PCA Method for Feature Extraction

Cited by 14 publications

References 37 publications

PCA via joint graph Laplacian and sparse constraint: Identification of differentially expressed genes and sample clustering on gene expression data

PCA via joint graph Laplacian and sparse constraint: Identification of differentially expressed genes and sample clustering on gene expression data

Research on Camouflage Recognition in Simulated Operational Environment Based on Hyperspectral Imaging Technology

Dual Graph-Laplacian PCA: A Closed-Form Solution for Bi-Clustering to Find “Checkerboard” Structures on Gene Expression Data

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