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In this work, we develop a novel principal component analysis (PCA) for semimartingales by introducing a suitable spectral analysis for the quadratic variation operator. Motivated by high-dimensional complex systems typically found in…
Principal component analysis (PCA) is a widely used method for dimension reduction. In high dimensional data, the "signal" eigenvalues corresponding to weak principal components (PCs) do not necessarily separate from the bulk of the "noise"…
We present a method using principal component analysis (PCA) to process x-ray pulses with severe shape variation where traditional optimal filter methods fail. We demonstrate that PCA is able to noise-filter and extract energy information…
Previous versions of sparse principal component analysis (PCA) have presumed that the eigen-basis (a $p \times k$ matrix) is approximately sparse. We propose a method that presumes the $p \times k$ matrix becomes approximately sparse after…
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…
Principal component analysis (PCA) frequently suffers from the disturbance of outliers and thus a spectrum of robust extensions and variations of PCA have been developed. However, existing extensions of PCA treat all samples equally even…
We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to…
A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance…
Neural networks-based learning of the distribution of non-dispatchable renewable electricity generation from sources such as photovoltaics (PV) and wind as well as load demands has recently gained attention. Normalizing flow density models…
Machine Learning models are prone to fail when test data are different from training data, a situation often encountered in real applications known as distribution shift. While still valid, the training-time knowledge becomes less…
Terahertz (THz) systems inherently introduce frequency-dependent degradation effects, resulting in low-frequency blurring and high-frequency noise in amplitude images. Conventional image processing techniques cannot simultaneously address…
Aims: We show the use of principal component analysis (PCA) and Fourier decomposition (FD) method as tools for variable star diagnostics and compare their relative performance in studying the changes in the light curve structures of…
Multivariate Functional Principal Component Analysis (MFPCA) is a valuable tool for exploring relationships and identifying shared patterns of variation in multivariate functional data. However, controlling the roughness of the extracted…
We analyze the nonlinear Carr\'e 4-steps algorithm including its frequency response, signal-to-noise ratio, and harmonics rejection using linear systems theory. At first sight the previous statement as well as the title of this paper seems…
Factor-based forecasting using Principal Component Analysis (PCA) is an effective machine learning tool for dimension reduction with many applications in statistics, economics, and finance. This paper introduces a Supervised Screening and…
Searching for departures from general relativity (GR) in more than one post-Newtonian (PN) phasing coefficients, called a \emph{multi-parameter test}, is known to be ineffective given the sensitivity of the present generation of…
The standard particle-in-cell algorithm suffers from grid heating. There exists a gridless alternative which bypasses the deposition step and calculates each Fourier mode of the charge density directly from the particle positions. We show…
Recently, introducing Tensor Decomposition (TD) techniques into unsupervised feature selection (UFS) has been an emerging research topic. A tensor structure is beneficial for mining the relations between different modes and helps relieve…
Principal component analysis (PCA) is a simple and popular tool for processing high-dimensional data. We investigate its effectiveness for matrix denoising. We consider the clean data are generated from a low-dimensional subspace, but…
Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is…