Related papers: Exponential Convergence of CAVI for Bayesian PCA

In this paper, we study the application of sparse principal component analysis (PCA) to clustering and feature selection problems. Sparse PCA seeks sparse factors, or linear combinations of the data variables, explaining a maximum amount of…

A principal component analysis based on the generalized Gini correlation index is proposed (Gini PCA). The Gini PCA generalizes the standard PCA based on the variance. It is shown, in the Gaussian case, that the standard PCA is equivalent…

Estimating intrinsic dimensionality of data is a classic problem in pattern recognition and statistics. Principal Component Analysis (PCA) is a powerful tool in discovering dimensionality of data sets with a linear structure; it, however,…

We present a stochastic variance-reduced heavy ball power iteration algorithm for solving PCA and provide a convergence analysis for it. The algorithm is an extension of heavy ball power iteration, incorporating a step size so that progress…

Principle Component Analysis PCA is a classical feature extraction and data representation technique widely used in pattern recognition. It is one of the most successful techniques in face recognition. But it has drawback of high…

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…

Incorporating covariates into functional principal component analysis (PCA) can substantially improve the representation efficiency of the principal components and predictive performance. However, many existing functional PCA methods do not…

Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. Consider the points $X_1, X_2,..., X_n$ are vectors drawn i.i.d. from a distribution with mean zero and covariance…

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…

Singular value decomposition (SVD) based principal component analysis (PCA) breaks down in the high-dimensional and limited sample size regime below a certain critical eigen-SNR that depends on the dimensionality of the system and the…

How do statistical dependencies in measurement noise influence high-dimensional inference? To answer this, we study the paradigmatic spiked matrix model of principal components analysis (PCA), where a rank-one matrix is corrupted by…

We study distributed principal component analysis (PCA) in high-dimensional settings under the spiked model. In such regimes, sample eigenvectors can deviate significantly from population ones, introducing a persistent bias. Existing…

Estimating a covariance matrix and its associated principal components is a fundamental problem in contemporary statistics. While optimal estimation procedures have been developed with well-understood properties, the increasing demand for…

Methods for supervised principal component analysis (SPCA) aim to incorporate label information into principal component analysis (PCA), so that the extracted features are more useful for a prediction task of interest. Prior work on SPCA…

Principal component analysis (PCA) defines a reduced space described by PC axes for a given multidimensional-data sequence to capture the variations of the data. In practice, we need multiple data sequences that accurately obey individual…

We present a Bayesian model selection approach to estimate the intrinsic dimensionality of a high-dimensional dataset. To this end, we introduce a novel formulation of the probabilisitic principal component analysis model based on a…

The principal component analysis (PCA), a mathematical tool commonly used in statistics, has recently been employed to interpret the $p_T$-dependent fluctuations of harmonic flow $v_n$ in terms of leading and subleading flow modes in heavy…

Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is…

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 present an unsupervised learning analysis of correlation hierarchies in the quarter-filled simple and extended Hubbard models by applying principal component analysis (PCA) to exact-diagonalization (ED) data on 3x4 and 4x4 cylindrical…