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Principal Components Analysis (PCA) and Independent Component Analysis (ICA) are used to identify global patterns in solar and space data. PCA seeks orthogonal modes of the two-point correlation matrix constructed from a data set. It…
In many atmospheric and earth sciences, it is of interest to identify dominant spatial patterns of variation based on data observed at $p$ locations and $n$ time points with the possibility that $p>n$. While principal component analysis…
In 2019, Yoshida et al. introduced a notion of tropical principal component analysis (PCA). The output is a tropical polytope with a fixed number of vertices that best fits the data. We here apply tropical PCA to dimension reduction and…
Data analysis often requires methods that are invariant with respect to specific transformations, such as rotations in case of images or shifts in case of images and time series. While principal component analysis (PCA) is a widely-used…
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…
Principal component analysis (PCA) has achieved great success in unsupervised learning by identifying covariance correlations among features. If the data collection fails to capture the covariance information, PCA will not be able to…
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…
A topological computation method, called the MGSTD method, is applied to time-series data obtained from meteorological measurement. The method gives decomposition of the dynamics into invariant sets and gradient-like transitions between…
Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…
Spatiotemporal Graph Neural Networks (ST-GNNs) and Transformers have shown significant promise in traffic forecasting by effectively modeling temporal and spatial correlations. However, rapid urbanization in recent years has led to dynamic…
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…
Principal Component Analysis (PCA) is a widely used technique in exploratory data analysis, visualization, and data preprocessing, leveraging the concept of variance to identify key dimensions in datasets. In this study, we focus on the…
Principal Component Analysis (PCA) is one of the most commonly used statistical methods for data exploration, and for dimensionality reduction wherein the first few principal components account for an appreciable proportion of the…
This work addresses a procedure to estimate fundamental stellar parameters such as T eff , logg, [Fe/H], and v sin i using a dimensionality reduction technique called Principal Component Analysis (PCA), applied to a large database of…
To simultaneously address the rising need of expressing uncertainties in deep learning models along with producing model outputs which are consistent with the known scientific knowledge, we propose a novel physics-guided architecture (PGA)…
We propose a novel method of finding principal components in multivariate data sets that lie on an embedded nonlinear Riemannian manifold within a higher-dimensional space. Our aim is to extend the geometric interpretation of PCA, while…
When modeling multivariate data, one might have an extra parameter of contextual information that could be used to treat some observations as more similar to others. For example, images of faces can vary by age, and one would expect the…
Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance-correlation matrix of the analyzed data. However to properly work with high-dimensional data, PCA poses severe mathematical…
Principal component analysis (PCA) is routinely used in population genetics to assess genetic structure. With chromosomal reference genomes and population-scale whole genome-sequencing becoming increasingly accessible, contemporary studies…
Principal Component Analysis (PCA) is a method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data.…