Related papers: Intrinsic dimension estimation of data by principa…

Principal Component Analysis (PCA) is a workhorse of modern data science. While PCA assumes the data conforms to Euclidean geometry, for specific data types, such as hierarchical and cyclic data structures, other spaces are more…

Principal component analysis (PCA) is a fundamental dimension reduction tool in statistics and machine learning. For large and high-dimensional data, computing the PCA (i.e., the singular vectors corresponding to a number of dominant…

Traditional principal component analysis (PCA) is well known in high-dimensional data analysis, but it requires to express data by a matrix with observations to be continuous. To overcome the limitations, a new method called flexible PCA…

Principal component analysis (PCA) is a commonly used pattern analysis method that maps high-dimensional data into a lower-dimensional space maximizing the data variance, that results in the promotion of separability of data. Inspired by…

Principal Component Analysis (PCA) finds the best linear representation of data, and is an indispensable tool in many learning and inference tasks. Classically, principal components of a dataset are interpreted as the directions that…

Principal component analysis (PCA) is often used to analyze multivariate data together with cluster analysis, which depends on the number of principal components used. It is therefore important to determine the number of significant…

Sparse principal component analysis (PCA) is a well-established dimensionality reduction technique that is often used for unsupervised feature selection (UFS). However, determining the regularization parameters is rather challenging, and…

In the era of big data, reducing data dimensionality is critical in many areas of science. Widely used Principal Component Analysis (PCA) addresses this problem by computing a low dimensional data embedding that maximally explain variance…

Principal component analysis (PCA) is a popular tool for linear dimensionality reduction and feature extraction. Kernel PCA is the nonlinear form of PCA, which better exploits the complicated spatial structure of high-dimensional features.…

Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…

We develop a new principal components analysis (PCA) type dimension reduction method for binary data. Different from the standard PCA which is defined on the observed data, the proposed PCA is defined on the logit transform of the success…

Data reconciliation (DR) and Principal Component Analysis (PCA) are two popular data analysis techniques in process industries. Data reconciliation is used to obtain accurate and consistent estimates of variables and parameters from…

Autoencoders have long been considered a nonlinear extension of Principal Component Analysis (PCA). Prior studies have demonstrated that linear autoencoders (LAEs) can recover the ordered, axis-aligned principal components of PCA by…

The statistical analysis of tree structured data is a new topic in statistics with wide application areas. Some Principal Component Analysis (PCA) ideas were previously developed for binary tree spaces. In this study, we extend these ideas…

Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear relationships in data. Although nonlinear variants…

Recently years, the attempts on distilling mobile data into useful knowledge has been led to the deployment of machine learning algorithms at the network edge. Principal component analysis (PCA) is a classic technique for extracting the…

PCA (Principal Component Analysis) and its variants areubiquitous techniques for matrix dimension reduction and reduced-dimensionlatent-factor extraction. One significant challenge in using PCA, is thechoice of the number of principal…

We consider the dimensionality-reduction problem (finding a subspace approximation of observed data) for contaminated data in the high dimensional regime, where the number of observations is of the same magnitude as the number of variables…

Learning augmented is a machine learning concept built to improve the performance of a method or model, such as enhancing its ability to predict and generalize data or features, or testing the reliability of the method by introducing noise…

Principal component analysis (PCA), a ubiquitous dimensionality reduction technique in signal processing, searches for a projection matrix that minimizes the mean squared error between the reduced dataset and the original one. Since…