Related papers: Principal Component Analysis of Spectral Line Data…
Unsupervised learning makes manifest the underlying structure of data without curated training and specific problem definitions. However, the inference of relationships between data points is frustrated by the `curse of dimensionality' in…
In this paper the exact linear relation between the leading eigenvectors of the modularity matrix and the singular vectors of an uncentered data matrix is developed. Based on this analysis the concept of a modularity component is defined,…
Numerical and experimental turbulence simulations are nowadays reaching the size of the so-called big data, thus requiring refined investigative tools for appropriate statistical analyses and data mining. We present a new approach based on…
Principal Component Analysis (PCA) is a commonly used tool for dimension reduction in analyzing high dimensional data; Multilinear Principal Component Analysis (MPCA) has the potential to serve the similar function for analyzing tensor…
A principal component analysis (PCA) of clean microcalorimeter pulse records can be a first step beyond statistically optimal linear filtering of pulses towards a fully non-linear analysis. For PCA to be practical on spectrometers with…
Principal component analysis (PCA) is an important tool in exploring data. The conventional approach to PCA leads to a solution which favours the structures with large variances. This is sensitive to outliers and could obfuscate interesting…
Principal component analysis (PCA), the most popular dimension-reduction technique, has been used to analyze high-dimensional data in many areas. It discovers the homogeneity within the data and creates a reduced feature space to capture as…
Functional principal component analysis has become the most important dimension reduction technique in functional data analysis. Based on B-spline approximation, functional principal components (FPCs) can be efficiently estimated by the…
We propose a stable version of Principal Component Analysis (PCA) in the general framework of a separable Hilbert space. It consists in interpreting the projection on the first eigenvectors as a step function applied to the spectrum of the…
The present paper applied Principal Component Analysis (PCA) for grouping of machines and parts so that the part families can be processed in the cells formed by those associated machines. An incidence matrix with binary entries has been…
Quantum principal component analysis (QPCA) ignited a new development toward quantum machine learning algorithms. Initially showcasing as an active way for analyzing a quantum system using the quantum state itself, QPCA also found potential…
Functional data analysis on nonlinear manifolds has drawn recent interest. Sphere-valued functional data, which are encountered for example as movement trajectories on the surface of the earth, are an important special case. We consider an…
Functional principal component analysis is one of the most commonly employed approaches in functional and longitudinal data analysis and we extend it to analyze functional/longitudinal data observed on a general $d$-dimensional domain. The…
The Dynamic State Index is a scalar quantity designed to identify atmospheric developments such as fronts, hurricanes or specific weather pattern. The DSI is defined as Jacobian-determinant of three constitutive quantities that characterize…
Small-scale fluctuations of different tracers of the interstellar the medium can be used to study the nature of turbulence in astrophysical scales. Of these, the `continuum' emission traces the fluctuations integrated along the line of…
Generalized principal component analysis (GLM-PCA) facilitates dimension reduction of non-normally distributed data. We provide a detailed derivation of GLM-PCA with a focus on optimization. We also demonstrate how to incorporate…
Principal Component Analysis (PCA) is one of the most used tools for extracting low-dimensional representations of data, in particular for time series. Performances are known to strongly depend on the quality (amount of noise) and the…
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…
When working with large biological data sets, exploratory analysis is an important first step for understanding the latent structure and for generating hypotheses to be tested in subsequent analyses. However, when the number of variables is…
We explore the use of principal component analysis (PCA) to characterize high-fidelity simulations and interferometric observations of the millimeter emission that originates near the horizons of accreting black holes. We show…