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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…

Principal component analysis (PCA) is a tool to capture factors that explain variation in data. Across domains, data are now collected across multiple contexts (for example, individuals with different diseases, cells of different types, or…

We seek a generalization of regression and principle component analysis (PCA) in a metric space where data points are distributions metrized by the Wasserstein metric. We recast these analyses as multimarginal optimal transport problems.…

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…

Hyperspectral optical imaging provides rich spectral information for estimating continuous environmental and material parameters; however, its high dimensionality and strong feature correlation pose significant challenges for machine…

Classical Principal Component Analysis (PCA) approximates data in terms of projections on a small number of orthogonal vectors. There are simple procedures to efficiently compute various functions of the data from the PCA approximation. The…

In many CAD-based applications, complex geometries are defined by a high number of design parameters. This leads to high-dimensional design spaces that are challenging for downstream engineering processes like simulations, optimization, and…

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 fields such as ecology, microbiology, and genomics, non-Euclidean distances are widely applied to describe pairwise dissimilarity between samples. Given these pairwise distances, principal coordinates analysis (PCoA) is commonly used to…

Principal component analysis (PCA) is a standard tool for dimensional reduction of a set of $n$ observations (samples), each with $p$ variables. In this paper, using a matrix perturbation approach, we study the nonasymptotic relation…

In the past decade, sparse principal component analysis has emerged as an archetypal problem for illustrating statistical-computational tradeoffs. This trend has largely been driven by a line of research aiming to characterize the…

Principal Component Analysis (PCA) and K-means constitute fundamental techniques in multivariate analysis. Although they are frequently applied independently or sequentially to cluster observations, the relationship between them, especially…

With the development of high-throughput technologies, principal component analysis (PCA) in the high-dimensional regime is of great interest. Most of the existing theoretical and methodological results for high-dimensional PCA are based on…

Principal component analysis (PCA) is a fundamental tool in multivariate statistics, yet its sensitivity to outliers and limitations in distributed environments restrict its effectiveness in modern large-scale applications. To address these…

Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…

Principal component analysis (PCA) is one of the most fundamental tools in machine learning with broad use as a dimensionality reduction and denoising tool. In the later setting, while PCA is known to be effective at subspace recovery and…

Principal components analysis (PCA) is a widely used dimension reduction technique with an extensive range of applications. In this paper, an online distributed algorithm is proposed for recovering the principal eigenspaces. We further…

Principal component analysis (PCA) is one of the most widely used dimensionality reduction methods in scientific data analysis. In many applications, for additional interpretability, it is desirable for the factor loadings to be sparse,…

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,…

Discovering dominant patterns and exploring dynamic behaviors especially critical state transitions and tipping points in high-dimensional time-series data are challenging tasks in study of real-world complex systems, which demand…