A Selective Overview of Sparse Principal Component Analysis

Zou, Hui; Xue, Lingzhou

doi:10.1109/jproc.2018.2846588

Cited by 129 publications

(62 citation statements)

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“…All computations were made using freely available R statistical software [36]. For principal component calculation the sparse method was considered the more suitable [37,38].…”

Section: Statistical Processingmentioning

confidence: 99%

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Model study of the leather degradation by oxidation and hydrolysis

et al. 2019

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Many objects of culture heritage, comprised of leather, need to receive the right treatment to be restored and to elongate their lifespan. Determination of the degradation degree and even better the type of the degradation is a crucial knowledge for the way of subsequent conservation, exhibition and long-term storage. Collagen based materials are very sensitive to the deterioration and undergo, mainly hydrolysis and oxidation. Namely acid hydrolysis and photooxidation are the most often causes of the disintegration of leather. Contrary to the leather investigation, a few studies dedicated to parchment described some typical features of hydrolysis, oxidation and gelatinization observed applying Attenuated Total Reflection Fourier-Transform Infrared spectroscopy (ATR-FTIR) which is widely used in collagen degradation type research. Except of the collagen secondary structure, followed by IR spectroscopy, we determined the shrinkage temperature of the collagen substrate by Micro Hot Table method (MHT) to reach the degradation level. In this paper, artificially degraded leather samples as a theoretical representative of cultural heritage objects were examined. We discuss the use of both techniques (IR and MHT) as potential methods for fast assessment of oxidation and hydrolysis of vegetable tanned leathers and degradation level. New samples of leather tanned by various vegetable tannins were artificially degraded under controlled conditions. We simulated the photooxidation by means of the Xenon arc lamp exposure, oxidation using the soaking in hydrogen peroxide, acid hydrolysis by the soaking in hydrochloric acid and alkaline hydrolysis using the soaking in natrium hydroxide. ATR-FTIR spectra of reference and tested samples were compared. Oxidation causes increase of the distance between amide I (A I ) and amide II (A II ) wavenumbers (Δν) above 100 cm −1 and the intensity ratio between A I and A II bands (A I /A II ) above 1.6. The A I / A II ratio depends on the type of hydrolysis. The increase above 1.8 proves acid hydrolysis while the decrease under 1 demonstrate alkaline hydrolysis. MHT results are not so obvious. Generally, mainly the hydrolysis causes the decrease of the temperatures. We have found out that knowledge of the whole shrinkage interval is important and provides more appropriate information about the leather disintegration.

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“…All computations were made using freely available R statistical software [36]. For principal component calculation the sparse method was considered the more suitable [37,38].…”

Section: Statistical Processingmentioning

confidence: 99%

“…For principal components calculation more suitable sparse method [37,38] was used (library sparsepca).…”

Section: Statistical Processingmentioning

confidence: 99%

Model study of the leather degradation by oxidation and hydrolysis

et al. 2019

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“…In addition to being di cult to interpret, the PCs generated by applying PCA to high-dimensional data are generally unstable; that is they are subject to major changes under minor perturbations of the data (we refer to Johnstone and Paul [15] for a recent review). Luckily, an abundance of techniques for sparsifying PCA loadings have been developed to mitigate these issues; we direct the interested reader to Zou and Xue [36] for a recent review. Here, we consider the SPCA technique developed by Zou et al [37].…”

Section: Sparse Pcamentioning

confidence: 99%

“…where x i is the i th row of X and V ı p◊k is exactly the loadings matrix of the first k PCs [36]. A sparse loadings matrix can be obtained by imposing an elastic net constraint on a modification of this objective function.…”

Section: Sparse Pcamentioning

confidence: 99%

Exploring High-Dimensional Biological Data with Sparse Contrastive Principal Component Analysis

Boileau

Hejazi

Dudoit

2019

Preprint

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Motivation: Statistical analyses of high-throughput sequencing data have re-shaped the biological sciences. In spite of myriad advances, recovering interpretable biological signal from data corrupted by technical noise remains a prevalent open problem. Several classes of procedures, among them classical dimensionality reduction techniques, and others incorporating subject-matter knowledge, have provided e ective advances; however, no procedure currently satisfies the dual objectives of recovering stable and relevant features simultaneously. Results: Inspired by recent proposals for making use of control data in the removal of unwanted variation, we propose a variant of principal component analysis that extracts sparse, stable, interpretable, and relevant biological signal. The new methodology is compared to competing dimensionality reduction approaches through a simulation study as well as via analyses of several publicly available protein expression, microarray gene expression, and single-cell transcriptome sequencing datasets. Availability:A free and open-source software implementation of the methodology, the scPCA R package, is made available via the Bioconductor Project. Code for all analyses presented in the paper are also made available via GitHub.

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“…For example, it can be applied to the optimal design of the agile supply chain network under an uncertainty [12] and the reduction of the total number of the dimensions of a logistic regression model with the continuous covariates and the avoidance of the multi-collinearity [4]. Second, develop the enhanced versions of the principal component analysis [3] such as the sparse principal component analysis [23], [21] and the robust principal component analysis [19], [10], [5]. The sparse principal component analysis produces the amendatory principal components with the sparse coefficients.…”

mentioning

confidence: 99%

Principal component analysis with drop rank covariance matrix

Guo¹,

Ling²

2021

JIMO

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This paper considers the principal component analysis when the covariance matrix of the input vectors drops rank. This case sometimes happens when the total number of the input vectors is very limited. First, it is found that the eigen decomposition of the covariance matrix is not uniquely defined. This implies that different transform matrices could be obtained for performing the principal component analysis. Hence, the generalized form of the eigen decomposition of the covariance matrix is given. Also, it is found that the matrix with its columns being the eigenvectors of the covariance matrix is not necessary to be unitary. This implies that the transform for performing the principal component analysis may not be energy preserved. To address this issue, the necessary and sufficient condition for the matrix with its columns being the eigenvectors of the covariance matrix to be unitary is derived. Moreover, since the design of the unitary transform matrix for performing the principal component analysis is usually formulated as an optimization problem, the necessary and sufficient condition for the first order derivative of the Lagrange function to be equal to the zero vector is derived. In fact, the unitary matrix with its columns being the eigenvectors of the covariance matrix is only a particular case of the condition. Furthermore, the necessary and sufficient condition for the second order derivative of the Lagrange function to be a positive definite function is derived. It is found that the unitary matrix with its columns being the eigenvectors of the covariance matrix does not satisfy this condition. Computer numerical simulation results are given to valid the results.2010 Mathematics Subject Classification. Primary: 58F15, 58F17; Secondary: 53C35.

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A Selective Overview of Sparse Principal Component Analysis

Cited by 129 publications

References 50 publications

Model study of the leather degradation by oxidation and hydrolysis

Model study of the leather degradation by oxidation and hydrolysis

Exploring High-Dimensional Biological Data with Sparse Contrastive Principal Component Analysis

Principal component analysis with drop rank covariance matrix

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