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Factor models are a class of powerful statistical models that have been widely used to deal with dependent measurements that arise frequently from various applications from genomics and neuroscience to economics and finance. As data are…

Numerous estimators have been proposed for factor analysis, and their statistical properties have been extensively studied. In the early 2000s, a novel matrix factorization-based approach, known as Matrix Decomposition Factor Analysis…

Principal Component Analysis (PCA) is an efficient tool to optimize the multiparameter tests of general relativity (GR) where one tests for simultaneous deviations in multiple post-Newtonian (PN) phasing coefficients by introducing…

Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian…

Our main objective is to develop a denoising strategy to increase the signal to noise ratio of individual spectral lines of stellar spectropolarimetric observations. We use a multivariate statistics technique called Principal Component…

In this paper, we develop an algorithm for federated principal component analysis (PCA) with emphases on both communication efficiency and data privacy. Generally speaking, federated PCA algorithms based on direct adaptations of classic…

Factor Analysis (FA) is a technique of fundamental importance that is widely used in classical and modern multivariate statistics, psychometrics and econometrics. In this paper, we revisit the classical rank-constrained FA problem, which…

In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…

This paper compares two neural network input selection schemes, the Principal Component Analysis (PCA) and the Automatic Relevance Determination (ARD) based on Mac-Kay's evidence framework. The PCA takes all the input data and projects it…

We consider the problem of estimating multiple principal components using the recently-proposed Sparse and Functional Principal Components Analysis (SFPCA) estimator. We first propose an extension of SFPCA which estimates several principal…

We study distributed principal component analysis (PCA) in high-dimensional settings under the spiked model. In such regimes, sample eigenvectors can deviate significantly from population ones, introducing a persistent bias. Existing…

Principle Component Analysis PCA is a classical feature extraction and data representation technique widely used in pattern recognition. It is one of the most successful techniques in face recognition. But it has drawback of high…

In this paper, a new method is proposed for sparse PCA based on the recursive divide-and-conquer methodology. The main idea is to separate the original sparse PCA problem into a series of much simpler sub-problems, each having a closed-form…

This paper proposes a hierarchical approximate-factor approach to analyzing high-dimensional, large-scale heterogeneous time series data using distributed computing. The new method employs a multiple-fold dimension reduction procedure using…

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.…

Spectral methods have been the mainstay in several domains such as machine learning and scientific computing. They involve finding a certain kind of spectral decomposition to obtain basis functions that can capture important structures for…

We propose a novel Decentralized Differentially Private Power Method (D-DP-PM) for performing Principal Component Analysis (PCA) in networked multi-agent settings. Unlike conventional decentralized PCA approaches where each agent accesses…

Developed by Paul Kocher, Joshua Jaffe, and Benjamin Jun in 1999, Differential Power Analysis (DPA) represents a unique and powerful cryptanalysis technique. Insight into the encryption and decryption behavior of a cryptographic device can…

Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional dataset. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional…

Principal Component Analysis (PCA) is a workhorse of modern data science. While PCA assumes the data conforms to Euclidean geometry, for specific data types, such as hierarchical and cyclic data structures, other spaces are more…