Related papers: A note on the variance in principal component regr…
In a regression model with multiple response variables and multiple explanatory variables, if the difference of the mean vectors of the response variables for different values of explanatory variables is always in the direction of the first…
Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…
Multiway data are becoming more and more common. While there are many approaches to extending principal component analysis (PCA) from usual data matrices to multiway arrays, their conceptual differences from the usual PCA, and the…
Linear principal component analysis (PCA) can be extended to a nonlinear PCA by using artificial neural networks. But the benefit of curved components requires a careful control of the model complexity. Moreover, standard techniques for…
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…
Principal component regression (PCR) is a popular technique for fixed-design error-in-variables regression, a generalization of the linear regression setting in which the observed covariates are corrupted with random noise. We provide 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…
We present a method for performing Principal Component Analysis (PCA) on noisy datasets with missing values. Estimates of the measurement error are used to weight the input data such that compared to classic PCA, the resulting eigenvectors…
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 a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…
Functional data typically contains amplitude and phase variation. In many data situations, phase variation is treated as a nuisance effect and is removed during preprocessing, although it may contain valuable information. In this note, we…
Principal loading analysis is a dimension reduction method that discards variables which have only a small distorting effect on the covariance matrix. As a special case, principal loading analysis discards variables that are not correlated…
We study principal components analyses in multivariate random and mixed effects linear models, assuming a spherical-plus-spikes structure for the covariance matrix of each random effect. We characterize the behavior of outlier sample…
Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of many kind of high-dimensional data. It is used in signal processing, mechanical engineering, psychometrics, and other fields under different…
How does missing data affect our ability to learn signal structures? It has been shown that learning signal structure in terms of principal components is dependent on the ratio of sample size and dimensionality and that a critical number of…
Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting…
The regression of principal component scores (RPCS) on covariates is a widely used analytic approach to detect and test for associations between functional measurements and study participant characteristics. Here we show that: (1) RPCS…
Principal component analysis (PCA) is fundamental to statistical machine learning. It extracts latent principal factors that contribute to the most variation of the data. When data are stored across multiple machines, however, communication…
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 study regression using functional predictors in situations where these functions contain both phase and amplitude variability. In other words, the functions are misaligned due to errors in time measurements, and these errors can…