11,810 research outputs found
An Extension of Slow Feature Analysis for Nonlinear Blind Source Separation
We present and test an extension of slow feature analysis as a novel approach to nonlinear blind source separation. The algorithm relies on temporal correlations and iteratively reconstructs a set of statistically independent sources from arbitrary nonlinear instantaneous mixtures. Simulations show that it is able to invert a complicated nonlinear mixture of two audio signals with a reliability of more than \%. The algorithm is based on a mathematical analysis of slow feature analysis for the case of input data that are generated from statistically independent sources
BMICA-independent component analysis based on B-spline mutual information estimator
The information theoretic concept of mutual information provides a general framework to evaluate dependencies between variables. Its estimation however using B-Spline has not been used before in creating an approach for Independent Component Analysis. In this paper we present a B-Spline estimator for mutual information to find the independent components in mixed signals. Tested using electroencephalography (EEG) signals the resulting BMICA (B-Spline Mutual Information Independent Component Analysis)
exhibits better performance than the standard Independent Component Analysis algorithms of FastICA, JADE, SOBI and EFICA in similar simulations. BMICA was found to be also more reliable than the 'renown' FastICA
Non-negative mixtures
This is the author's accepted pre-print of the article, first published as M. D. Plumbley, A. Cichocki and R. Bro. Non-negative mixtures. In P. Comon and C. Jutten (Ed), Handbook of Blind Source Separation: Independent Component Analysis and Applications. Chapter 13, pp. 515-547. Academic Press, Feb 2010. ISBN 978-0-12-374726-6 DOI: 10.1016/B978-0-12-374726-6.00018-7file: Proof:p\PlumbleyCichockiBro10-non-negative.pdf:PDF owner: markp timestamp: 2011.04.26file: Proof:p\PlumbleyCichockiBro10-non-negative.pdf:PDF owner: markp timestamp: 2011.04.2
Differential fast fixed-point algorithms for underdetermined instantaneous and convolutive partial blind source separation
This paper concerns underdetermined linear instantaneous and convolutive
blind source separation (BSS), i.e., the case when the number of observed mixed
signals is lower than the number of sources.We propose partial BSS methods,
which separate supposedly nonstationary sources of interest (while keeping
residual components for the other, supposedly stationary, "noise" sources).
These methods are based on the general differential BSS concept that we
introduced before. In the instantaneous case, the approach proposed in this
paper consists of a differential extension of the FastICA method (which does
not apply to underdetermined mixtures). In the convolutive case, we extend our
recent time-domain fast fixed-point C-FICA algorithm to underdetermined
mixtures. Both proposed approaches thus keep the attractive features of the
FastICA and C-FICA methods. Our approaches are based on differential sphering
processes, followed by the optimization of the differential nonnormalized
kurtosis that we introduce in this paper. Experimental tests show that these
differential algorithms are much more robust to noise sources than the standard
FastICA and C-FICA algorithms.Comment: this paper describes our differential FastICA-like algorithms for
linear instantaneous and convolutive underdetermined mixture
Mathematical tools for identifying the fetal response to physical exercise during pregnancy
In the applied mathematics literature there exist a significant number of tools that can reveal the interaction between mother and fetus during rest and also during and after exercise. These tools are based on techniques from a number of areas such as signal processing, time series analysis, neural networks, heart rate variability as well as dynamical systems and chaos. We will briefly review here some of these methods, concentrating on a method of extracting the fetal heart rate from the mixed maternal-fetal heart rate signal, that is based on phase space reconstructio
Decorrelation of Neutral Vector Variables: Theory and Applications
In this paper, we propose novel strategies for neutral vector variable
decorrelation. Two fundamental invertible transformations, namely serial
nonlinear transformation and parallel nonlinear transformation, are proposed to
carry out the decorrelation. For a neutral vector variable, which is not
multivariate Gaussian distributed, the conventional principal component
analysis (PCA) cannot yield mutually independent scalar variables. With the two
proposed transformations, a highly negatively correlated neutral vector can be
transformed to a set of mutually independent scalar variables with the same
degrees of freedom. We also evaluate the decorrelation performances for the
vectors generated from a single Dirichlet distribution and a mixture of
Dirichlet distributions. The mutual independence is verified with the distance
correlation measurement. The advantages of the proposed decorrelation
strategies are intensively studied and demonstrated with synthesized data and
practical application evaluations
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