Related papers: Principal Component Analysis: A Natural Approach t…
We consider estimation of large approximate factor models in high-dimensional panels of stationary time series using Principal Component Analysis (PCA). We review the key results establishing the necessary and sufficient conditions for…
This paper proposes an innovative extension of Principal Component Analysis (PCA) that transcends the traditional assumption of data lying in Euclidean space, enabling its application to data on Riemannian manifolds. The primary challenge…
Principal component analysis has been widely adopted to reduce the dimension of data while preserving the information. The quantum version of PCA (qPCA) can be used to analyze an unknown low-rank density matrix by rapidly revealing the…
Classical Principal Component Analysis (PCA) approximates data in terms of projections on a small number of orthogonal vectors. There are simple procedures to efficiently compute various functions of the data from the PCA approximation. The…
Motivation: Although principal component analysis is frequently applied to reduce the dimensionality of matrix data, the method is sensitive to noise and bias and has difficulty with comparability and interpretation. These issues are…
The principal component analysis (PCA) is a staple statistical and unsupervised machine learning technique in finance. The application of PCA in a financial setting is associated with several technical difficulties, such as numerical…
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…
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…
Principal Component Analysis (PCA) finds a linear mapping and maximizes the variance of the data which makes PCA sensitive to outliers and may cause wrong eigendirection. In this paper, we propose techniques to solve this problem; we use…
Machine learning (ML) methods have proved to be a very successful tool in physical sciences, especially when applied to experimental data analysis. Artificial intelligence is particularly good at recognizing patterns in high dimensional…
The research detailed in this paper scrutinizes Principal Component Analysis (PCA), a seminal method employed in statistics and machine learning for the purpose of reducing data dimensionality. Singular Value Decomposition (SVD) is often…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an…
Principal Subspace Analysis (PSA) -- and its sibling, Principal Component Analysis (PCA) -- is one of the most popular approaches for dimensionality reduction in signal processing and machine learning. But centralized PSA/PCA solutions are…
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…
In the course of the last century, Principal Component Analysis (PCA) have become one of the pillars of modern scientific methods. Although PCA is normally addressed as a statistical tool aiming at finding orthogonal directions on which the…
In recent times, functional data analysis (FDA) has been successfully applied in the field of high dimensional data classification. In this paper, we present a novel classification framework using functional data and classwise Principal…
Principal component analysis (PCA) has been widely used in analyzing high-dimensional data. It converts a set of observed data points of possibly correlated variables into a set of linearly uncorrelated variables via an orthogonal…
Principal component analysis (PCA) is very popular to perform dimension reduction. The selection of the number of significant components is essential but often based on some practical heuristics depending on the application. Only few works…
Principal component analysis (PCA) is fundamental to statistical machine learning. It extracts latent principal factors that contribute to the most variation of the data. When data are stored across multiple machines, however, communication…
Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…