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We present a new straightforward principal component analysis (PCA) method based on the diagonalization of the weighted variance-covariance matrix through two spectral decomposition methods: power iteration and Rayleigh quotient iteration.…

Principal component analysis (PCA) is commonly used in genetics to infer and visualize population structure and admixture between populations. PCA is often interpreted in a way similar to inferred admixture proportions, where it is assumed…

Multivariate data are typically represented by a rectangular matrix (table) in which the rows are the objects (cases) and the columns are the variables (measurements). When there are many variables one often reduces the dimension by…

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…

Ecological Momentary Assessments (EMA) capture real-time thoughts and behaviors in natural settings, producing rich longitudinal data for statistical and physiological analyses. However, the robustness of these analyses can be compromised…

High dimensional data has introduced challenges that are difficult to address when attempting to implement classical approaches of statistical process control. This has made it a topic of interest for research due in recent years. However,…

Principal component regression (PCR) is a two-stage procedure: the first stage performs principal component analysis (PCA) and the second stage constructs a regression model whose explanatory variables are replaced by principal components…

Principal Component Analysis (PCA) is widely used for dimensionality reduction and data analysis. However, PCA results are adversely affected by outliers often observed in real-world data. Existing robust PCA methods are often…

A new framework for many multiblock component methods (including consensus and hierarchical PCA) is proposed. It is based on the consensus PCA model: a scheme connecting each block of variables to a superblock obtained by concatenation of…

Missing data present challenges in data analysis. Naive analyses such as complete-case and available-case analysis may introduce bias and loss of efficiency, and produce unreliable results. Multiple imputation (MI) is one of the most widely…

Missing data theory deals with the statistical methods in the occurrence of missing data. Missing data occurs when some values are not stored or observed for variables of interest. However, most of the statistical theory assumes that data…

Principal component analysis (PCA) is largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the…

We study the estimation of a high dimensional approximate factor model in the presence of both cross sectional dependence and heteroskedasticity. The classical method of principal components analysis (PCA) does not efficiently estimate the…

Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is…

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…

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…

The idea of representation has been used in various fields of study from data analysis to political science. In this paper, we define representativeness and describe a method to isolate data points that can represent the entire data set.…

Principal Component Analysis (PCA) has been used to study the pathogenesis of diseases. To enhance the interpretability of classical PCA, various improved PCA methods have been proposed to date. Among these, a typical method is the…

Multiple imputation is a common approach for dealing with missing values in statistical databases. The imputer fills in missing values with draws from predictive models estimated from the observed data, resulting in multiple, completed…

Missing observations are pervasive throughout empirical research, especially in the social sciences. Despite multiple approaches to dealing adequately with missing data, many scholars still fail to address this vital issue. In this paper,…