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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 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…
Clustering is one of the most widely used procedures in the analysis of microarray data, for example with the goal of discovering cancer subtypes based on observed heterogeneity of genetic marks between different tissues. It is well-known…
Our aim is to evaluate fundamental parameters from the analysis of the electromagnetic spectra of stars. We may use $10^3$-$10^5$ spectra; each spectrum being a vector with $10^2$-$10^4$ coordinates. We thus face the so-called "curse of…
The robust PCA problem, wherein, given an input data matrix that is the superposition of a low-rank matrix and a sparse matrix, we aim to separate out the low-rank and sparse components, is a well-studied problem in machine learning. One…
Differentially private synthetic data provide a powerful mechanism to enable data analysis while protecting sensitive information about individuals. However, when the data lie in a high-dimensional space, the accuracy of the synthetic data…
We propose a robust principal component analysis (RPCA) framework to recover low-rank and sparse matrices from temporal observations. We develop an online version of the batch temporal algorithm in order to process larger datasets or…
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…
This work explores a novel approach for adaptive, differentiable parametrization of large-scale non-stationary random fields. Coupled with any gradient-based algorithm, the method can be applied to variety of optimization problems,…
Commonly used in computer vision and other applications, robust PCA represents an algorithmic attempt to reduce the sensitivity of classical PCA to outliers. The basic idea is to learn a decomposition of some data matrix of interest into…
Principal component analysis (PCA) is an exploratory tool widely used in data analysis to uncover dominant patterns of variability within a population. Despite its ability to represent a data set in a low-dimensional space, the…
Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy --- even on parallel processors --- unlike the classical (deterministic) alternatives. We adapt one of…
Probabilistic principal component analysis (PPCA) is a probabilistic reformulation of principal component analysis (PCA), under the framework of a Gaussian latent variable model. To improve the robustness of PPCA, it has been proposed to…
In an era where big and high-dimensional data is readily available, data scientists are inevitably faced with the challenge of reducing this data for expensive downstream computation or analysis. To this end, we present here a new method…
Bayesian variable selection methods are powerful techniques for fitting and inferring on sparse high-dimensional linear regression models. However, many are computationally intensive or require restrictive prior distributions on model…
Principal component regression (PCR) is a two-stage procedure: the first stage performs principal component analysis (PCA) and the second stage constructs a regression model whose explanatory variables are replaced by principal components…
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…
Streaming principal component analysis (PCA) is an integral tool in large-scale machine learning for rapidly estimating low-dimensional subspaces from very high-dimensional data arriving at a high rate. However, modern datasets increasingly…
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…
The implementation of conventional sparse principal component analysis (SPCA) on high-dimensional data sets has become a time consuming work. In this paper, a series of subspace projections are constructed efficiently by using Household QR…