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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…
When the dimension of data is comparable to or larger than the number of data samples, Principal Components Analysis (PCA) may exhibit problematic high-dimensional noise. In this work, we propose an Empirical Bayes PCA method that reduces…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an…
There is growing interest in using the close connection between differential geometry and statistics to model smooth manifold-valued data. In particular, much work has been done recently to generalize principal component analysis (PCA), the…
Gravitational-wave (GW) parameter estimation typically assumes that instrumental noise is Gaussian and stationary. Obvious departures from this idealization are typically handled on a case-by-case basis, e.g., through bespoke procedures to…
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…
Principal component analysis (PCA) is a widely used unsupervised dimensionality reduction technique in machine learning, applied across various fields such as bioinformatics, computer vision and finance. However, when the response variables…
Multiway data are becoming more and more common. While there are many approaches to extending principal component analysis (PCA) from usual data matrices to multiway arrays, their conceptual differences from the usual PCA, and the…
Principal component analysis (PCA) is an important tool in exploring data. The conventional approach to PCA leads to a solution which favours the structures with large variances. This is sensitive to outliers and could obfuscate interesting…
Matrix factor models have been growing popular dimension reduction tools for large-dimensional matrix time series. However, the heteroscedasticity of the idiosyncratic components has barely received any attention. Starting from the pseudo…
Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low…
We propose a multiple imputation method based on principal component analysis (PCA) to deal with incomplete continuous data. To reflect the uncertainty of the parameters from one imputation to the next, we use a Bayesian treatment of the…
In this work we analyze the variational problem emerging from the Gutzwiller approach to strongly correlated systems. This problem comprises the two main steps: evaluation and minimization of the ground state energy $W$ for the postulated…
We show that the gravitational wave source counts distribution can test how gravitational radiation propagates on cosmological scales. This test does not require obtaining redshifts for the sources. If the signal-to-noise ratio (SNR,…
The problem of radiation by the charged particles of the intergalactic medium (IGM) when a passing gravitational wave (GW) accelerate them is investigated. The largest acceleration (taking a charge from rest to a maximum speed which remains…
Principal component analysis (PCA) is a classical feature extraction method, but it may be adversely affected by outliers, resulting in inaccurate learning of the projection matrix. This paper proposes a robust method to estimate both the…
Waves play an essential role in many aspects of plasma science, such as plasma manipulation and diagnostics. Due to the complexity of the governing equations, approximate models are often necessary to describe wave dynamics. In this…
Gravitational-wave astronomy provides a promising avenue for the discovery of new physics beyond general relativity as it probes extreme curvature and ultra-relativistic dynamics. However, in the absence of a compelling alternative to…
Principal component regression (PCR) is a widely used two-stage procedure: principal component analysis (PCA), followed by regression in which the selected principal components are regarded as new explanatory variables in the model. Note…
This paper introduces the use of Principal Component Analysis as a method to decompose the waveform catalogues to produce a set of orthonormal basis vectors. We apply this method to a set of supernova waveforms and compare the basis vectors…