Related papers: Singular Value Decomposition and Principal Compone…

Singular value decomposition is widely used in modal analysis, such as proper orthogonal decomposition and resolvent analysis, to extract key features from complex problems. SVD derivatives need to be computed efficiently to enable the…

Covariances from categorical variables are defined using a regular simplex expression for categories. The method follows the variance definition by Gini, and it gives the covariance as a solution of simultaneous equations. The calculated…

We discuss spectral principal component analysis (SPCA) and show examples of its application in analyzing AGN spectra in both small and large samples. It can be used to identify peculiar spectra and classify AGN spectra. Its application to…

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…

By singular value decomposition (SVD) of a numerically singular Hessian matrix and a numerically singular system of linear equations for the experimental data (accumulated in the respective ${\chi ^2}$ function) and constraints, least…

Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of…

Sparse principal component analysis (PCA) is an important technique for dimensionality reduction of high-dimensional data. However, most existing sparse PCA algorithms are based on non-convex optimization, which provide little guarantee on…

Correspondence analysis, multiple correspondence analysis and their discriminant counterparts (i.e., discriminant simple correspondence analysis and discriminant multiple correspondence analysis) are methods of choice for analyzing…

Principal component analysis (PCA) is a dimensionality reduction method in data analysis that involves diagonalizing the covariance matrix of the dataset. Recently, quantum algorithms have been formulated for PCA based on diagonalizing a…

Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of many kind of high-dimensional data. It is used in signal processing, mechanical engineering, psychometrics, and other fields under different…

Principal component analysis (PCA) is widely used for dimension reduction and embedding of real data in social network analysis, information retrieval, and natural language processing, etc. In this work we propose a fast randomized PCA…

We study the convergence properties of the VR-PCA algorithm introduced by \cite{shamir2015stochastic} for fast computation of leading singular vectors. We prove several new results, including a formal analysis of a block version of the…

Principal component analysis (PCA) is arguably the most widely used dimension-reduction method for vector-type data. When applied to a sample of images, PCA requires vectorization of the image data, which in turn entails solving an…

We present a new approach to solve the exponential retrieval problem. We derive a stable technique, based on the singular value decomposition (SVD) of lag-covariance and crosscovariance matrices consisting of covariance coefficients…

Singular value decomposition (SVD) is a widely used technique for dimensionality reduction and computation of basis vectors. In many applications, especially in fluid mechanics and image processing the matrices are dense, but low-rank…

We introduce the Singular Value Representation (SVR), a new method to represent the internal state of neural networks using SVD factorization of the weights. This construction yields a new weighted graph connecting what we call spectral…

We propose an approximation method for thresholding of singular values using Chebyshev polynomial approximation (CPA). Many signal processing problems require iterative application of singular value decomposition (SVD) for minimizing the…

Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…

When functional data manifest amplitude and phase variations, a commonly-employed framework for analyzing them is to take away the phase variation through a function alignment and then to apply standard tools to the aligned functions. A…

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…