Search results for "Independent component analysi"

2019

In the independent component model, the multivariate data are assumed to be a mixture of mutually independent latent components. The independent component analysis (ICA) then aims at estimating these latent components. In this article, we study an ICA method which combines the use of linear and quadratic autocorrelations to enable efficient estimation of various kinds of stationary time series. Statistical properties of the estimator are studied by finding its limiting distribution under general conditions, and the asymptotic variances are derived in the case of ARMA-GARCH model. We use the asymptotic results and a finite sample simulation study to compare different choices of a weight coef…

Affine-invariant rank tests for multivariate independence in independent component models

2016

We consider the problem of testing for multivariate independence in independent component (IC) models. Under a symmetry assumption, we develop parametric and nonparametric (signed-rank) tests. Unlike in independent component analysis (ICA), we allow for the singular cases involving more than one Gaussian independent component. The proposed rank tests are based on componentwise signed ranks, à la Puri and Sen. Unlike the Puri and Sen tests, however, our tests (i) are affine-invariant and (ii) are, for adequately chosen scores, locally and asymptotically optimal (in the Le Cam sense) at prespecified densities. Asymptotic local powers and asymptotic relative efficiencies with respect to Wilks’…

On the usage of joint diagonalization in multivariate statistics

2022

Scatter matrices generalize the covariance matrix and are useful in many multivariate data analysis methods, including well-known principal component analysis (PCA), which is based on the diagonalization of the covariance matrix. The simultaneous diagonalization of two or more scatter matrices goes beyond PCA and is used more and more often. In this paper, we offer an overview of many methods that are based on a joint diagonalization. These methods range from the unsupervised context with invariant coordinate selection and blind source separation, which includes independent component analysis, to the supervised context with discriminant analysis and sliced inverse regression. They also enco…

Fourth Moments and Independent Component Analysis

2015

In independent component analysis it is assumed that the components of the observed random vector are linear combinations of latent independent random variables, and the aim is then to find an estimate for a transformation matrix back to these independent components. In the engineering literature, there are several traditional estimation procedures based on the use of fourth moments, such as FOBI (fourth order blind identification), JADE (joint approximate diagonalization of eigenmatrices), and FastICA, but the statistical properties of these estimates are not well known. In this paper various independent component functionals based on the fourth moments are discussed in detail, starting wi…

Steady-state and tracking analysis of a robust adaptive filter with low computational cost

2007

This paper analyses a new adaptive algorithm that is robust to impulse noise and has a low computational load [E. Soria, J.D. Martin, A.J. Serrano, J. Calpe, and J. Chambers, A new robust adaptive algorithm with low computacional cost, Electron. Lett. 42 (1) (2006) 60-62]. The algorithm is based on two premises: the use of the cost function often used in independent component analysis and a fuzzy modelling of the hyperbolic tangent function. The steady-state error and tracking capability of the algorithm are analysed using conservation methods [A. Sayed, Fundamentals of Adaptive Filtering, Wiley, New York, 2003], thus verifying the correspondence between theory and experimental results.

An identifiable model to assess frequency-domain Granger causality in the presence of significant instantaneous interactions

2010

We present a new approach for the investigation of Granger causality in the frequency domain by means of the partial directed coherence (PDC). The approach is based on the utilization of an extended multivariate autoregressive (MVAR) model, including instantaneous effects in addition to the lagged effects traditionally studied, to fit the observed multiple time series prior to PDC computation. Model identification is performed combining standard MVAR coefficient estimation with a recent technique for instantaneous causal modeling based on independent component analysis. The approach is first validated on simulated MVAR processes showing that, in the presence of instantaneous effects, only t…

Syntagmatic and Paradigmatic Associations in Information Retrieval

2003

It is shown that unconscious associative processes taking place in the memory of a searcher during the formulation of a search query in information retrieval — such as the production of free word associations and the generation of synonyms — can be simulated using statistical models that analyze the distribution of words in large text corpora. The free word associations as produced by subjects on presentation of stimulus words can be predicted by applying first-order statistics to the frequencies of word co-occurrences as observed in texts. The generation of synonyms can also be conducted on co-occurrence data but requires second-order statistics. Both approaches are compared and validated …

Complex-Valued Independent Component Analysis of Natural Images

2011

Linear independent component analysis (ICA) learns simple cell receptive fields fromnatural images. Here,we showthat linear complex-valued ICA learns complex cell properties from Fourier-transformed natural images, i.e. two Gabor-like filters with quadrature-phase relationship. Conventional methods for complex-valued ICA assume that the phases of the output signals have uniform distribution. We show here that for natural images the phase distributions are, however, often far from uniform. We thus relax the uniformity assumption and model also the phase of the sources in complex-valued ICA. Compared to the original complex ICA model, the new model provides a better fit to the data, and leads…

Técnicas de análisis de posproceso en resonancia magnetica parael estudio de la conectividad cerebral

2011

Brain connectivity is a key concept for understanding brain function. Current methods to detect and quantify different types of connectivity with neuroimaging techniques are fundamental for understanding the pathophysiology of many neurologic and psychiatric disorders. This article aims to present a critical review of the magnetic resonance imaging techniques used to measure brain connectivity within the context of the Human Connectome Project. We review techniques used to measure: a) structural connectivity b) functional connectivity (main component analysis, independent component analysis, seed voxel, meta-analysis), and c) effective connectivity (psychophysiological interactions, causal …

Spatially variant dimensionality reduction for the visualization of multi/hyperspectral images

2011

International audience; In this paper, we introduce a new approach for color visu- alization of multi/hyperspectral images. Unlike traditional methods, we propose to operate a local analysis instead of considering that all the pixels are part of the same population. It takes a segmentation map as an input and then achieves a dimensionality reduction adaptively inside each class of pixels. Moreover, in order to avoid unappealing discon- tinuities between regions, we propose to make use of a set of distance transform maps to weigh the mapping applied to each pixel with regard to its relative location with classes' centroids. Results on two hyperspec- tral datasets illustrate the efficiency of…