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Principal Component Analysis (PCA) is a well-known technique used to decorrelate a set of vectors. It has been applied to explore the star formation history of galaxies or to determine distances of mass-lossing stars. Here we apply PCA to…

Principal Component Analysis (PCA) is a well-known linear dimension-reduction technique designed for Euclidean data. In a wide spectrum of applied fields, however, it is common to observe multivariate circular data (also known as toroidal…

The ability to manipulate complex systems, such as the brain, to modify specific outcomes has far-reaching implications, particularly in the treatment of psychiatric disorders. One approach to designing appropriate manipulations is to…

In recent years, Artificial Intelligence techniques have proved to be very successful when applied to problems in physical sciences. Here we apply an unsupervised Machine Learning (ML) algorithm called Principal Component Analysis (PCA) as…

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…

Functional data typically contains amplitude and phase variation. In many data situations, phase variation is treated as a nuisance effect and is removed during preprocessing, although it may contain valuable information. In this note, we…

The present paper applied Principal Component Analysis (PCA) for grouping of machines and parts so that the part families can be processed in the cells formed by those associated machines. An incidence matrix with binary entries has been…

Principal Component Analysis (PCA) is applied to a variety of blazars to examine X-ray spectral variability. Data from nine different objects are analysed in two ways: long-term, which examines variability trends across years or decades,…

In the era of big data, reducing data dimensionality is critical in many areas of science. Widely used Principal Component Analysis (PCA) addresses this problem by computing a low dimensional data embedding that maximally explain variance…

Principal component regression (PCR) is a popular technique for fixed-design error-in-variables regression, a generalization of the linear regression setting in which the observed covariates are corrupted with random noise. We provide the…

Principal Component Analysis (PCA) is a classical method for reducing the dimensionality of data by projecting them onto a subspace that captures most of their variation. Effective use of PCA in modern applications requires understanding…

A set of curves or images of similar shape is an increasingly common functional data set collected in the sciences. Principal Component Analysis (PCA) is the most widely used technique to decompose variation in functional data. However, the…

Principal component analysis (PCA) is the most commonly used statistical procedure for dimension reduction. An important issue for applying PCA is to determine the rank, which is the number of dominant eigenvalues of the covariance matrix.…

Principal Component Analysis (PCA) is a popular tool for dimensionality reduction and feature extraction in data analysis. There is a probabilistic version of PCA, known as Probabilistic PCA (PPCA). However, standard PCA and PPCA are not…

This paper proposes an extension of principal component analysis for Gaussian process (GP) posteriors, denoted by GP-PCA. Since GP-PCA estimates a low-dimensional space of GP posteriors, it can be used for meta-learning, which is a…

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…

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…

The increasing integration of data science techniques into quantitative finance has enabled more systematic and data-driven approaches to portfolio construction. This paper investigates the use of Principal Component Analysis (PCA) in…

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 a commonly used tool for dimension reduction and denoising. Therefore, it is also widely used on the data prior to training a neural network. However, this approach can complicate the explanation of…