A framework named Copula Component Analysis for blind source separation is proposed as a generalization of ICA. It differs from ICA which assumes independence of sources that the underlying components may be dependent with certain structure which is represented by Copula. By incorporating dependency structure, much accurate estimation can be made in principle in the case that the assumption of ...

This article presents a unified theory for analysis of components in discrete data, and compares the methods with techniques such as independent component analysis (ICA), non-negative matrix factorisation (NMF) and latent Dirichlet allocation (LDA). The main families of algorithms discussed are mean field, Gibbs sampling, and Rao-Blackwellised Gibbs sampling. Applications are presented for voti...

We study the extraction of nonlinear data models in high dimensional spaces with modi ed self organizing maps We present a general algorithm which maps low dimensional lattices into high dimensional data manifolds without violation of topology The approach is based on a new principle exploiting the speci c dynamical properties of the rst order phase tran sition induced by the noise of the data ...

Independent component analysis (ICA) has been widely used for blind source separation in many fields, such as brain imaging analysis, signal processing and telecommunication. Many statistical techniques based on Mestimates have been proposed for estimating the mixing matrix. Recently, several nonparametric methods have been developed, but in-depth analysis of asymptotic efficiency has not been ...

A new methodology to aid interpretation of a principal component analysis is presented. While preserving orthogonality, each eigenvector is replaced by a vector, close to it in angle terms, whose entries are small integers. We call such vectors simple. The approach is exploratory, a range of sets of pairwise orthogonal simple components being systematically obtained, from which the user may cho...

Principal component analysis (PCA) is a multivariate technique that analyzes a data table in which observations are described by several inter-correlated quantitative dependent variables. Its goal is to extract the important information from the table, to represent it as a set of new orthogonal variables called principal components, and to display the pattern of similarity of the observations a...

R esum e : L'ACC est un r eseau de neurones auto-organis e qui donne une carte de la sous-vari et e d'un nuage de donn ees en grandes dimensions non lin eairement d ependantes. Le principe est de construire une relation entre un espace d'entr ee (les don-n ees) et un espace de sortie (la carte) au moyen d'un ensemble de neurones ayant chacun deux vecteurs-poids : un pour l'entr ee et l'autre po...

Principal component analysis (PCA) has been applied to analyze random fields in various scientific disciplines. However, the explainability of PCA remains elusive unless strong domain-specific knowledge is available. This paper provides a theoretical framework that builds duality between eigenmodes field and eigenstates Schr\"odinger equation. Based on we propose algorithm replace expensive sol...

Problem Statement Experimental data to be analyzed is often represented as a number of vectors of fixed dimensionality. A single vector could for example be a set of temperature measurements across Germany. Taking such a vector of measurements at different times results in a number of vectors that altogether constitute the data. Each vector can also be interpreted as a point in a high dimension...

Principal component analysis (PCA) is widely used in data processing and dimensionality reduction. However, PCA suffers from the fact that each principal component is a linear combination of all the original variables, thus it is often difficult to interpret the results. We introduce a new method called sparse principal component analysis (SPCA) using the lasso (elastic net) to produce modified...