Related papers: High-dimensional principal component analysis with…
Principal component analysis (PCA) is perhaps the most widely used method for data dimensionality reduction. A key question in PCA is deciding how many factors to retain. This manuscript describes a new approach to automatically selecting…
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…
The problem of principle component analysis (PCA) is traditionally solved by spectral or algebraic methods. We show how computing the leading principal component could be reduced to solving a \textit{small} number of well-conditioned {\it…
We present a new straightforward principal component analysis (PCA) method based on the diagonalization of the weighted variance-covariance matrix through two spectral decomposition methods: power iteration and Rayleigh quotient iteration.…
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…
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…
Principal Component Analysis (PCA) is one of the most used tools for extracting low-dimensional representations of data, in particular for time series. Performances are known to strongly depend on the quality (amount of noise) and the…
Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional…
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…
Principal component analysis (PCA) is a commonly used pattern analysis method that maps high-dimensional data into a lower-dimensional space maximizing the data variance, that results in the promotion of separability of data. Inspired by…
When the dimension of data is comparable to or larger than the number of data samples, Principal Components Analysis (PCA) may exhibit problematic high-dimensional noise. In this work, we propose an Empirical Bayes PCA method that reduces…
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…
We consider the dimensionality-reduction problem (finding a subspace approximation of observed data) for contaminated data in the high dimensional regime, where the number of observations is of the same magnitude as the number of variables…
Dimension reduction is useful for exploratory data analysis. In many applications, it is of interest to discover variation that is enriched in a "foreground" dataset relative to a "background" dataset. Recently, contrastive principal…
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…
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…
The CP decomposition for high dimensional non-orthogonal spiked tensors is an important problem with broad applications across many disciplines. However, previous works with theoretical guarantee typically assume restrictive incoherence…
A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance…
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…
Principal component analysis (PCA) is by far the most widespread tool for unsupervised learning with high-dimensional data sets. Its application is popularly studied for the purpose of exploratory data analysis and online process…