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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) for binary data, known as logistic PCA, has become a popular alternative to dimensionality reduction of binary data. It is motivated as an extension of ordinary PCA by means of a matrix factorization, akin…

Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…

The first order behavior of multivariate heavy-tailed random vectors above large radial thresholds is ruled by a limit measure in a regular variation framework. For a high dimensional vector, a reasonable assumption is that the support of…

Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. While PCA is often thought of as a dimensionality reduction method, the purpose of PCA is actually two-fold: dimension reduction…

Sparse Principal Component Analysis (PCA) is a dimensionality reduction technique wherein one seeks a low-rank representation of a data matrix with additional sparsity constraints on the obtained representation. We consider two…

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,…

We develop a new principal components analysis (PCA) type dimension reduction method for binary data. Different from the standard PCA which is defined on the observed data, the proposed PCA is defined on the logit transform of the success…

The main shortage of principle component analysis (PCA) based anomaly detection models is their interpretability. In this paper, our goal is to propose an interpretable PCA-based model for anomaly detection and interpretation. The propose…

Sparse Principal Component Analysis (sparse PCA) is a fundamental dimension-reduction tool that enhances interpretability in various high-dimensional settings. An important variant of sparse PCA studies the scenario when samples are…

Compressed sensing is a recent set of mathematical results showing that sparse signals can be exactly reconstructed from a small number of linear measurements. Interestingly, for ideal sparse signals with no measurement noise, random…

Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…

Linear projections are widely used in the analysis of high-dimensional data. In unsupervised settings where the data harbour latent classes/clusters, the question of whether class discriminatory signals are retained under projection is…

We present a novel class of projected methods, to perform statistical analysis on a data set of probability distributions on the real line, with the 2-Wasserstein metric. We focus in particular on Principal Component Analysis (PCA) and…

We study the distributed computing setting in which there are multiple servers, each holding a set of points, who wish to compute functions on the union of their point sets. A key task in this setting is Principal Component Analysis (PCA),…

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…

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…

As tensors become widespread in modern data analysis, Tucker low-rank Principal Component Analysis (PCA) has become essential for dimensionality reduction and structural discovery in tensor datasets. Motivated by the common scenario where…

Principal Component Analysis (PCA) is a well-known multivariate technique used to decorrelate a set of vectors. PCA has been extensively applied in the past to the classification of stellar and galaxy spectra. Here we apply PCA to the…

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…