Related papers: aPCoA: Covariate Adjusted Principal Coordinates An…
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…
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…
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…
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…
Even with the rise in popularity of over-parameterized models, simple dimensionality reduction and clustering methods, such as PCA and k-means, are still routinely used in an amazing variety of settings. A primary reason is the combination…
A general asymptotic framework is developed for studying consis- tency properties of principal component analysis (PCA). Our frame- work includes several previously studied domains of asymptotics as special cases and allows one to…
Distance covariance is a widely used statistical methodology for testing the dependency between two groups of variables. Despite the appealing properties of consistency and superior testing power, the testing results of distance covariance…
Mahalanobis distance between treatment group and control group covariate means is often adopted as a balance criterion when implementing a rerandomization strategy. However, this criterion may not work well for high-dimensional cases…
We introduce the notion of Principal Component Analysis (PCA) of image gradient orientations. As image data is typically noisy, but noise is substantially different from Gaussian, traditional PCA of pixel intensities very often fails to…
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) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of…
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…
Principal Component Analysis (PCA) is a classical method for reducing the dimensionality of data by projecting them onto a subspace that captures most of their variation. Effective use of PCA in modern applications requires understanding…
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…
Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear relationships in data. Although nonlinear variants…
In this on-going work, I explore certain theoretical and empirical implications of data transformations under the PCA. In particular, I state and prove three theorems about PCA, which I paraphrase as follows: 1). PCA without discarding…
Principal Component Analysis and biplots are so well-established and readily implemented that it is just too tempting to give for granted their internal workings. In this note I get back to basics in comparing how PCA and biplots are…
Machine learning (ML) methods have proved to be a very successful tool in physical sciences, especially when applied to experimental data analysis. Artificial intelligence is particularly good at recognizing patterns in high dimensional…
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…
Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…