Related papers: Data driven approach to study the transition from …
Dimension reduction for high-dimensional compositional data plays an important role in many fields, where the principal component analysis of the basis covariance matrix is of scientific interest. In practice, however, the basis variables…
When synthesizing multi-source high-dimensional data, a key objective is to extract low-dimensional representations that effectively approximate the original features across different sources. Such representations facilitate the discovery…
Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional dataset. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional…
We propose novel methods for predictive (sparse) PCA with spatially misaligned data. These methods identify principal component loading vectors that explain as much variability in the observed data as possible, while also ensuring the…
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,…
Principal Component Analysis (PCA) is a well-known linear dimension-reduction technique designed for Euclidean data. In a wide spectrum of applied fields, however, it is common to observe multivariate circular data (also known as toroidal…
We propose a new high dimensional semiparametric principal component analysis (PCA) method, named Copula Component Analysis (COCA). The semiparametric model assumes that, after unspecified marginally monotone transformations, the…
To mitigate the severe information loss arising from widely adopted linear scale cuts in constraints on modified gravity parameterisations with Weak Lensing (WL) and Large-Scale Structure (LSS) data, we introduce a novel alternative method…
Principal Component Analysis (PCA) is a widely used method for dimensionality reduction, but it often overlooks fairness, especially when working with data that includes demographic characteristics. This can lead to biased representations…
High-fidelity modeling of blood flow is crucial for enhancing our understanding of cardiovascular disease. Despite significant advances in computational and experimental characterization of blood flow, the knowledge that we can acquire from…
In this paper, we propose a novel approach named by Discriminative Principal Component Analysis which is abbreviated as Discriminative PCA in order to enhance separability of PCA by Linear Discriminant Analysis (LDA). The proposed method…
Functional data typically contains amplitude and phase variation. In many data situations, phase variation is treated as a nuisance effect and is removed during preprocessing, although it may contain valuable information. In this note, we…
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…
Multiway data are becoming more and more common. While there are many approaches to extending principal component analysis (PCA) from usual data matrices to multiway arrays, their conceptual differences from the usual PCA, and the…
The idea of representation has been used in various fields of study from data analysis to political science. In this paper, we define representativeness and describe a method to isolate data points that can represent the entire data set.…
We explore the physical implications of applying principal component analysis (PCA) to translationally invariant classical systems defined on a $d$-dimensional hypercubic lattice. Using Rayleigh-Schr\"odinger perturbation theory, we…
Principal component analysis (PCA) represents a standard approach to identify collective variables $\{x_i\}\!=\!\boldsymbol{x}$, which can be used to construct the free energy landscape $\Delta G(\boldsymbol{x})$ of a molecular system.…
Principal component analysis (PCA) is one of the most widely used dimension reduction and multivariate statistical techniques. From a probabilistic perspective, PCA seeks a low-dimensional representation of data in the presence of…
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…
We derive direct data-driven dissipativity analysis methods for Linear Parameter-Varying (LPV) systems using a single sequence of input-scheduling-output data. By means of constructing a semi-definite program subject to linear matrix…