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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…
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,…
We propose a spectral clustering method based on local principal components analysis (PCA). After performing local PCA in selected neighborhoods, the algorithm builds a nearest neighbor graph weighted according to a discrepancy between the…
Principal Component Analysis (PCA) is a transform for finding the principal components (PCs) that represent features of random data. PCA also provides a reconstruction of the PCs to the original data. We consider an extension of PCA which…
Modeling cross-sectional correlations between thousands of stocks, across countries and industries, can be challenging. In this paper, we demonstrate the advantages of using Hierarchical Principal Component Analysis (HPCA) over the classic…
This paper examines several applications of principal component analysis (PCA) to physical systems. The first of these demonstrates that the principal components in a basis of appropriate system variables can be employed to identify…
Principal component analysis (PCA) is a popular dimension reduction technique often used to visualize high-dimensional data structures. In genomics, this can involve millions of variables, but only tens to hundreds of observations.…
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 method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data.…
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…
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…
Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…
Principal Component Analysis (PCA) has been used to study the pathogenesis of diseases. To enhance the interpretability of classical PCA, various improved PCA methods have been proposed to date. Among these, a typical method is the…
Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal,…
Ongoing and upcoming galaxy surveys are providing precision measurements of galaxy clustering. However a major obstacle in its cosmological application is the stochasticity in the galaxy bias. We explore whether the principal component…
Traditional load analysis is facing challenges with the new electricity usage patterns due to demand response as well as increasing deployment of distributed generations, including photovoltaics (PV), electric vehicles (EV), and energy…
We perform a principal component analysis (PCA) of two one-dimensional lattice models belonging to distinct nonequilibrium universality classes - directed bond percolation and branching and annihilating random walks with even number of…
Principal Components Analysis (PCA) and Independent Component Analysis (ICA) are used to identify global patterns in solar and space data. PCA seeks orthogonal modes of the two-point correlation matrix constructed from a data set. It…
Principal component analysis (PCA) is a fundamental tool for analyzing multivariate data. Here the focus is on dimension reduction to the principal subspace, characterized by its projection matrix. The classical principal subspace can be…
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…