Related papers: Principal Component Analysis of Spectral Line Data…
Brillouin microscopy has recently emerged as a new bio-imaging modality that provides information on the micromechanical properties of biological materials, cells and tissues. The data collected in a typical Brillouin microscopy experiment…
A system with many degrees of freedom can be characterized by a covariance matrix; principal components analysis (PCA) focuses on the eigenvalues of this matrix, hoping to find a lower dimensional description. But when the spectrum is…
Principal component analysis (PCA) is a fundamental tool for analyzing multivariate data. Here the focus is on dimension reduction to the principal subspace, characterized by its projection matrix. The classical principal subspace can be…
Principal component analysis (PCA) is a classical feature extraction method, but it may be adversely affected by outliers, resulting in inaccurate learning of the projection matrix. This paper proposes a robust method to estimate both the…
As machine learning models are increasingly considered for high-stakes domains, effective explanation methods are crucial to ensure that their prediction strategies are transparent to the user. Over the years, numerous metrics have been…
Supersonic turbulence in molecular clouds is a dominant agent that strongly affects the clouds' evolution and star formation activity. Turbulence may be initiated and maintained by a number of processes, acting at a wide range of physical…
Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to…
Independent component analysis (ICA) has become a standard data analysis technique applied to an array of problems in signal processing and machine learning. This tutorial provides an introduction to ICA based on linear algebra formulating…
This work explores the potential of an information-theoretical causality detection method for unraveling the relation between fluctuating variables in complex nonlinear systems. The method is tested on some simple though nonlinear models,…
Principal component analysis is a useful dimension reduction and data visualization method. However, in high dimension, low sample size asymptotic contexts, where the sample size is fixed and the dimension goes to infinity,a paradox has…
A variety of interstellar complex organic molecules (COMs) have been detected in various physical conditions. However, in the protostellar and protoplanetary environments, their complex kinematics make line profiles blend each other and the…
Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…
We discuss a new technique for studying astrophysical turbulence that utilizes the statistics of Doppler-broadened spectral lines. The technique relates the power Velocity Coordinate Spectrum (VCS), i.e. the spectrum of fluctuations…
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.…
The geometrical structure is among the most fundamental ingredients in understanding complex systems. Is there any systematic approach in defining structures quantitatively, rather than illustratively? If yes, what are the basic principles…
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…
I develop a feasible weighted projected principal component (FPPC) analysis for factor models in which observable characteristics partially explain the latent factors. This novel method provides more efficient and accurate estimators than…
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…
Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and…
Magnetic reconnection is a fundamental process for releasing magnetic energy in space physics and astrophysics. At present, the usual way to investigate the reconnection process is through analytical studies or first-principles numerical…