Related papers: aPCoA: Covariate Adjusted Principal Coordinates An…
The distance covariance of Sz\'ekely, et al. [23] and Sz\'ekely and Rizzo [21], a powerful measure of dependence between sets of multivariate random variables, has the crucial feature that it equals zero if and only if the sets are mutually…
In climate studies, detecting spatial patterns that largely deviate from the sample mean still remains a statistical challenge. Although a Principal Component Analysis (PCA), or equivalently a Empirical Orthogonal Functions (EOF)…
PCA is often used in anomaly detection and statistical process control tasks. For bivariate data, we prove that the minor projection (the least varying projection) of the PCA-rotated data is the most sensitive to distributional changes,…
Canonical Correlation Analysis (CCA) has been widely applied to jointly embed multiple views of data in a maximally correlated latent space. However, the alignment between various data perspectives, which is required by traditional…
Linking between two data sources is a basic building block in numerous computer vision problems. In this paper, we set to answer a fundamental cognitive question: are prior correspondences necessary for linking between different domains?…
PCA can be used for rotation invariant features, describing a shape with its $p_{ab}=E[(x_i-E[x_a])(x_b-E[x_b])]$ covariance matrix approximating shape by ellipsoid, allowing for rotation invariants like its traces of powers. However, real…
Principal component analysis (PCA) is one of the most widely used dimension reduction and multivariate statistical techniques. From a probabilistic perspective, PCA seeks a low-dimensional representation of data in the presence of…
This paper presents an algebro-geometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points. We represent the subspaces with a set of homogeneous polynomials whose…
Principal Component Analysis (PCA) is a well-known technique used to decorrelate a set of vectors. It has been applied to explore the star formation history of galaxies or to determine distances of mass-lossing stars. Here we apply PCA to…
Physics has been transforming our view of nature for centuries. While combining physical knowledge with computational approaches has enabled detailed modeling of physical systems' evolution, understanding the emergence of patterns and…
In recent years, Artificial Intelligence techniques have proved to be very successful when applied to problems in physical sciences. Here we apply an unsupervised Machine Learning (ML) algorithm called Principal Component Analysis (PCA) as…
Principal component analysis (PCA) is a powerful method that can identify patterns in large, complex data sets by constructing low-dimensional order parameters from higher-dimensional feature vectors. There are increasing efforts to use…
We consider the problem of identifying patterns in a data set that exhibit anomalous behavior, often referred to as anomaly detection. In most anomaly detection algorithms, the dissimilarity between data samples is calculated by a single…
In recent years microbiome studies have become increasingly prevalent and large-scale. Through high-throughput sequencing technologies and well-established analytical pipelines, relative abundance data of operational taxonomic units and…
\texttt{rCOSA} is a software package interfaced to the R language. It implements statistical techniques for clustering objects on subsets of attributes in multivariate data. The main output of COSA is a dissimilarity matrix that one can…
In many CAD-based applications, complex geometries are defined by a high number of design parameters. This leads to high-dimensional design spaces that are challenging for downstream engineering processes like simulations, optimization, and…
Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain…
Joint analysis of multiple phenotypes can increase statistical power in genetic association studies. Principal component analysis, as a popular dimension reduction method, especially when the number of phenotypes is high-dimensional, has…
Sparse principal component analysis (sPCA) enhances the interpretability of principal components (PCs) by imposing sparsity constraints on loading vectors (LVs). However, when used as a precursor to independent component analysis (ICA) for…
Principal components (PCA) and hierarchical clustering are two of the most heavily used techniques for analyzing the differences between nucleic acid sequence samples sampled from a given environment. However, a classical application of…