Related papers: Principal Components for Model-Agnostic Modified G…

Retrieval-Augmented Generation (RAG) has emerged as a powerful paradigm for grounding large language models in external knowledge sources, improving the precision of agents responses. However, high-dimensional language model embeddings,…

We use measurements from the Planck satellite mission and galaxy redshift surveys over the last decade to test three of the basic assumptions of the standard model of cosmology, $\Lambda$CDM: the spatial curvature of the universe, the…

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 been widely applied to dimensionality reduction and data pre-processing for different applications in engineering, biology and social science. Classical PCA and its variants seek for linear projections…

We present a comprehensive assessment of multiparameter tests of general relativity (GR) in the inspiral regime of compact binary coalescences using principal component analysis (PCA). Our analysis is based on an extensive set of simulated…

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…

Principal Component Analysis (PCA) is a highly useful topic within an introductory Linear Algebra course, especially since it can be used to incorporate a number of applied projects. This method represents an essential application and…

Using the linear Gaussian latent variable model as a starting point we relax some of the constraints it imposes by deriving a nonparametric latent feature Gaussian variable model. This model introduces additional discrete latent variables…

Traditional principal component analysis (PCA) is well known in high-dimensional data analysis, but it requires to express data by a matrix with observations to be continuous. To overcome the limitations, a new method called flexible PCA…

Data compression can be achieved by reducing the dimensionality of high-dimensional but approximately low-rank datasets, which may in fact be described by the variation of a much smaller number of parameters. It often serves as a…

Determination of cosmological parameters is a major goal in cosmology at present. The availability of improved data sets necessitates the development of novel statistical tools to interpret the inference from a cosmological model. In this…

Artificial neural networks that learn to perform Principal Component Analysis (PCA) and related tasks using strictly local learning rules have been previously derived based on the principle of similarity matching: similar pairs of inputs…

The performance of principal component analysis (PCA) suffers badly in the presence of outliers. This paper proposes two novel approaches for robust PCA based on semidefinite programming. The first method, maximum mean absolute deviation…

Principal component analysis (PCA) is a tool to capture factors that explain variation in data. Across domains, data are now collected across multiple contexts (for example, individuals with different diseases, cells of different types, or…

Dimension reduction is useful for exploratory data analysis. In many applications, it is of interest to discover variation that is enriched in a "foreground" dataset relative to a "background" dataset. Recently, contrastive principal…

The cosmic acceleration problem remains one of the most significant challenges in cosmology. One of the proposed solutions to this problem is the modification of gravity on large scales. In this paper, we explore the well-known…

We study degeneracies between cosmological parameters and measurement errors from cosmic shear surveys using a principal component analysis of the Fisher matrix. We simulate realistic survey topologies with non-uniform sky coverage, and…

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…

We applied principal component analysis (PCA) to the study of five ground level enhancement (GLE) of cosmic ray (CR) events. The nature of the multivariate data involved makes PCA a useful tool for this study. A subroutine program written…

This paper proposes an innovative extension of Principal Component Analysis (PCA) that transcends the traditional assumption of data lying in Euclidean space, enabling its application to data on Riemannian manifolds. The primary challenge…