Sparse PCA
View article: Principal component eigenvalues derived from PCA of morphological variables in <i>Iris meda</i> accessions.
Principal component eigenvalues derived from PCA of morphological variables in <i>Iris meda</i> accessions. Open
Principal component eigenvalues derived from PCA of morphological variables in Iris meda accessions.
View article: Sparse outlier-robust PCA for multi-source data
Sparse outlier-robust PCA for multi-source data Open
Sparse and outlier-robust principal component analysis (PCA) has been a very active field of research recently. Yet, most existing methods apply PCA to a single data set whereas multi-source data—i.e. multiple related data sets requiring j…
View article: A comprehensive review of Principal Component Analysis
A comprehensive review of Principal Component Analysis Open
PCA (Principal Component Analysis) is a method aiming to reduce the dimensions among data analysis, with various applications in neurosciences, finance, and beyond. Data normalization, covariance matrix decomposition, eigenvalue-driven com…
View article: Sparse dynamic principal components analysis in the frequency domain
Sparse dynamic principal components analysis in the frequency domain Open
The main focus of this paper will be the sparsity treatment of dynamic principal components analysis (DPCA), which is an extension of principal components analysis (PCA) in a time series setting. Several sparse extensions for the high-dime…
View article: Least angle sparse principal component analysis for ultrahigh dimensional data
Least angle sparse principal component analysis for ultrahigh dimensional data Open
Principal component analysis (PCA) has been a widely used technique for dimension reduction while retaining essential information. However, the ordinary PCA lacks interpretability, especially when dealing with large scale data. To address …
View article: Multivariate Linear Model for Data Analysis and Machine Learning and the Theory and Practice of Eigenvalues in Mitigating Multicollinearity
Multivariate Linear Model for Data Analysis and Machine Learning and the Theory and Practice of Eigenvalues in Mitigating Multicollinearity Open
The chapter introduces a multivariate high dimensional linear model for large dataset analytics and machine learning and the mathematical derivation of its parameters. We covered regression techniques and analysis for multidimensional data…
View article: Model-Fitting Weighted Least Squares as an Alternative to Principal Component Analysis for Analyzing Energy-Dispersive X-ray Spectroscopy Spectrum Images
Model-Fitting Weighted Least Squares as an Alternative to Principal Component Analysis for Analyzing Energy-Dispersive X-ray Spectroscopy Spectrum Images Open
Spectrum imaging with energy-dispersive X-ray spectroscopy (EDS) has become ubiquitous in material characterization using electron microscopy. Multivariate statistical methods, commonly principal component analysis (PCA), are often used to…
View article: Cellwise robust and sparse principal component analysis
Cellwise robust and sparse principal component analysis Open
A first proposal of a sparse and cellwise robust PCA method is presented. Robustness to single outlying cells in the data matrix is achieved by substituting the squared loss function for the approximation error by a robust version. The int…
View article: RankPCA: Rank of Variables Based on Principal Component Analysis for Mixed Data Types
RankPCA: Rank of Variables Based on Principal Component Analysis for Mixed Data Types Open
Principal Component Analysis (PCA) is a statistical technique used to reduce the dimensionality of a dataset while preserving as much variability as possible. By transforming the original variables into a new set of uncorrelated variables …
View article: Adaptive Latent Feature Sharing for Piecewise Linear Dimensionality Reduction
Adaptive Latent Feature Sharing for Piecewise Linear Dimensionality Reduction Open
Linear Gaussian exploratory tools such as principal component analysis (PCA) and factor analysis (FA) are widely used for exploratory analysis, pre-processing, data visualization, and related tasks. Because the linear-Gaussian assumption i…
View article: Tensor robust principal component analysis via dual l quasi-norm sparse constraints
Tensor robust principal component analysis via dual l quasi-norm sparse constraints Open
As a pioneering method, tensor robust principal component analysis (TRPCA) can separate an underlying low-rank component and a sparse component from the original data by minimizing a convex objective function composed of tensor nuclear nor…
View article: GT-PCA: Effective and Interpretable Dimensionality Reduction with General Transform-Invariant Principal Component Analysis
GT-PCA: Effective and Interpretable Dimensionality Reduction with General Transform-Invariant Principal Component Analysis Open
Data analysis often requires methods that are invariant with respect to specific transformations, such as rotations in case of images or shifts in case of images and time series. While principal component analysis (PCA) is a widely-used di…
View article: Sparse PCA with False Discovery Rate Controlled Variable Selection
Sparse PCA with False Discovery Rate Controlled Variable Selection Open
Sparse principal component analysis (PCA) aims at mapping large dimensional data to a linear subspace of lower dimension. By imposing loading vectors to be sparse, it performs the double duty of dimension reduction and variable selection. …
View article: Principal Component Analysis for Equation Discovery
Principal Component Analysis for Equation Discovery Open
Principal Component Analysis (PCA) is one of the most commonly used statistical methods for data exploration, and for dimensionality reduction wherein the first few principal components account for an appreciable proportion of the variabil…
View article: An Exploration of the Application of Principal Component Analysis in Big Data Processing
An Exploration of the Application of Principal Component Analysis in Big Data Processing Open
With the arrival of the significant data era, efficiently processing large-scale multidimensional data has become challenging. As a powerful data dimensionality reduction tool, Principal Component Analysis (PCA) plays a vital role in big d…
View article: Robust Principal Component Analysis Integrating Sparse and Low-Rank Priors
Robust Principal Component Analysis Integrating Sparse and Low-Rank Priors Open
Principal Component Analysis (PCA) is a widely used technique for data analysis and dimensionality reduction, but its sensitivity to feature scale and outliers limits its applicability. Robust Principal Component Analysis (RPCA) addresses …
View article: Exploring the Impact of the New Crown Epidemic on Tourism in Qiannan, Guizhou Using Principal Component Analysis Methods
Exploring the Impact of the New Crown Epidemic on Tourism in Qiannan, Guizhou Using Principal Component Analysis Methods Open
Principal component analysis is usually a linear combination of all variables, which is very detrimental to the interpretation of the results. Therefore, this paper proposes sparse principal component analysis for analyzing the impact of t…
View article: <strong></strong>Data Reduction Using Principal Component Analysis: Theoretical Underpinnings and Practical Applications in Public Health
<strong></strong>Data Reduction Using Principal Component Analysis: Theoretical Underpinnings and Practical Applications in Public Health Open
Big datasets are becoming increasingly common and can be challenging to understand and apply in public health. One method for lowering the dimensionality of these datasets and improving interpretability while minimizing information loss is…
View article: Empirical Bayes Covariance Decomposition, and a solution to the Multiple Tuning Problem in Sparse PCA
Empirical Bayes Covariance Decomposition, and a solution to the Multiple Tuning Problem in Sparse PCA Open
Sparse Principal Components Analysis (PCA) has been proposed as a way to improve both interpretability and reliability of PCA. However, use of sparse PCA in practice is hindered by the difficulty of tuning the multiple hyperparameters that…
View article: Federated Learning for Sparse Principal Component Analysis
Federated Learning for Sparse Principal Component Analysis Open
In the rapidly evolving realm of machine learning, algorithm effectiveness often faces limitations due to data quality and availability. Traditional approaches grapple with data sharing due to legal and privacy concerns. The federated lear…
View article: Ensemble Principal Component Analysis
Ensemble Principal Component Analysis Open
Efficient representations of data are essential for processing, exploration, and human understanding, and Principal Component Analysis (PCA) is one of the most common dimensionality reduction techniques used for the analysis of large, mult…
View article: Cauchy robust principal component analysis with applications to high-dimensional data sets
Cauchy robust principal component analysis with applications to high-dimensional data sets Open
Principal component analysis (PCA) is a standard dimensionality reduction technique used in various research and applied fields. From an algorithmic point of view, classical PCA can be formulated in terms of operations on a multivariate Ga…
View article: $e^{\text{RPCA}}$: Robust Principal Component Analysis for Exponential Family Distributions
$e^{\text{RPCA}}$: Robust Principal Component Analysis for Exponential Family Distributions Open
Robust Principal Component Analysis (RPCA) is a widely used method for recovering low-rank structure from data matrices corrupted by significant and sparse outliers. These corruptions may arise from occlusions, malicious tampering, or othe…
View article: Fast Sparse PCA via Positive Semidefinite Projection for Unsupervised Feature Selection
Fast Sparse PCA via Positive Semidefinite Projection for Unsupervised Feature Selection Open
In the field of unsupervised feature selection, sparse principal component analysis (SPCA) methods have attracted more and more attention recently. Compared to spectral-based methods, SPCA methods don’t rely on the construction of a simila…
View article: When Collaborative Filtering is not Collaborative: Unfairness of PCA for Recommendations
When Collaborative Filtering is not Collaborative: Unfairness of PCA for Recommendations Open
We study the fairness of dimensionality reduction methods for recommendations. We focus on the fundamental method of principal component analysis (PCA), which identifies latent components and produces a low-rank approximation via the leadi…
View article: SuSiE PCA: A scalable Bayesian variable selection technique for principal component analysis
SuSiE PCA: A scalable Bayesian variable selection technique for principal component analysis Open
View article: Comparison of Supervised Learning Algorithms on a 5G Dataset Reduced via Principal Component Analysis (PCA)
Comparison of Supervised Learning Algorithms on a 5G Dataset Reduced via Principal Component Analysis (PCA) Open
Improving the quality of service (QoS) and meeting service level agreements (SLAs) are critical objectives in next-generation networks. This article presents a study on applying supervised learning (SL) algorithms in a 5G/B5G service datas…
View article: Fast Sparse PCA via Positive Semidefinite Projection for Unsupervised Feature Selection
Fast Sparse PCA via Positive Semidefinite Projection for Unsupervised Feature Selection Open
In the field of unsupervised feature selection, sparse principal component analysis (SPCA) methods have attracted more and more attention recently. Compared to spectral-based methods, SPCA methods don't rely on the construction of a simila…
View article: A Bi-Directional Two-Dimensional Deep Subspace Learning Network with Sparse Representation for Object Recognition
A Bi-Directional Two-Dimensional Deep Subspace Learning Network with Sparse Representation for Object Recognition Open
A principal component analysis network (PCANet), as one of the representative deep subspace learning networks, utilizes principal component analysis (PCA) to learn filters that represent the dominant structural features of objects. However…
View article: A critical assessment of sparse PCA (research): why (one should acknowledge that) weights are not loadings
A critical assessment of sparse PCA (research): why (one should acknowledge that) weights are not loadings Open