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We explore the physical implications of applying principal component analysis (PCA) to translationally invariant classical systems defined on a $d$-dimensional hypercubic lattice. Using Rayleigh-Schr\"odinger perturbation theory, we…

We propose a new high dimensional semiparametric principal component analysis (PCA) method, named Copula Component Analysis (COCA). The semiparametric model assumes that, after unspecified marginally monotone transformations, the…

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…

We propose a multiple imputation method based on principal component analysis (PCA) to deal with incomplete continuous data. To reflect the uncertainty of the parameters from one imputation to the next, we use a Bayesian treatment of the…

Principal Component Analysis (PCA) is a commonly used tool for dimension reduction and denoising. Therefore, it is also widely used on the data prior to training a neural network. However, this approach can complicate the explanation of…

Transition edge sensor microcalorimeters can measure x-ray and gamma-ray energies with very high energy resolution and high photon-collection efficiency. For this technology to reach its full potential in future x-ray observatories, each…

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,…

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…

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…

Cellular Automata are discrete dynamical systems that evolve following simple and local rules. Despite of its local simplicity, knowledge discovery in CA is a NP problem. This is the main motivation for using data mining techniques for CA…

Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal,…

We outline how principal component analysis (PCA) can be applied to particle configuration data to detect a variety of phase transitions in off-lattice systems, both in and out of equilibrium. Specifically, we discuss its application to…

Principal component analysis (PCA) is a widely used technique for data analysis and dimension reduction with numerous applications in science and engineering. However, the standard PCA suffers from the fact that the principal components…

Principal Component Analysis (PCA) and its nonlinear extension Kernel PCA (KPCA) are widely used across science and industry for data analysis and dimensionality reduction. Modern deep learning tools have achieved great empirical success,…

We present a novel approach for adaptive, differentiable parameterization of large-scale random fields. If the approach is coupled with any gradient-based optimization algorithm, it can be applied to a variety of optimization problems,…

Functional data analysis is concerned with the analysis of infinite-dimensional data functions. Functional principal component analysis (FPCA) is a key method to obtain finite-dimensional summaries. Consistency of FPCA has been…

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 one of the most popular dimension reduction techniques in statistics and is especially powerful when a multivariate distribution is concentrated near a lower-dimensional subspace. Multivariate extreme…

In this paper, we consider the problem of forming machine cell in cellular manufacturing (CM). The major problem in the design of a CM system is to identify the part families and machine groups and consequently to form manufacturing cells.…

Given a matrix of observed data, Principal Components Analysis (PCA) computes a small number of orthogonal directions that contain most of its variability. Provably accurate solutions for PCA have been in use for a long time. However, to…