| Comon, P., Jutten, C., & Herault, J. (1991). Blind separation of sources, Part II: Problem statement. Signal Processing, 24, 11--20. |
....is required. We achieve this factorization by transforming # into a new feature vector # whose components are (mostly) independent. This is where Independent Component Analysis (ICA) comes in. 2.2. Density Factorization with ICA ICA originated in the context of blind source separation [13, 14] to separate independent causes of a complex signal or mixture. It is usually implemented by pushing the vector components away from Gaussianity by minimizing high order statistics such as the 4 order cross cumulants. ICA is in general not perfect therefore the IC s obtained are not ....
C. Jutten and J. Herault, "Blind separation of sources," Signal Processing, vol. 24, pp. 1--10, 1991.
.... of minimizing reconstruction error to learn appropriate features from multivariate data [1, 2] Independent components analysis (ICA) can similarly be understood as maximizing the likelihood of the data under a non Gaussian generative model, and thus is related to minimizing a reconstruction cost [3, 4, 5]. On the other hand, the same ICA algorithm can also be derived without regard to a particular generative model by maximizing the mutual information between the data and a nonlinearly transformed version of the data [6] This principle of information maximization has also been previously applied ....
Jutten, C & Herault, J (1991). Blind separation of sources, part I: An adaptive algorithm based on neuromimetic architecture. Signal Processing 24, 1--10.
....thus recovering the original sources. In contrast to correlation based transformations such as principal component analysis, ICA renders the output signals as statistically independent as possible by evaluating higherorder statistics. The idea of ICA was first expressed by Jutten and Herault [13] [14] while the term ICA was later coined by Comon in [8] However the field became popular only with the seminal paper by Bell and Sejnowski [4] who elaborated upon the Infomax principle first advocated by Linsker [20] 21] Amari [1] as well as Cardoso and Laheld [6] later simplified the Infomax ....
C. Jutten, J. Herault, P. Comon, and E. Sorouchiary. Blind separation of sources, parts I, II and III. Signal Processing, 24:1--29, 1991.
....by a phase shift. Most of the methods developed in the last share an analysis based on the pdf and their related cumulants to obtain independence properties: the precursors used the cumulants in several ways: straightforward [1] through a cost function [2] or using a non lineal neural network[3];Also the maximum likelihood estimator is based on pdf [4] More recently other approaches deal with a non linearity (building in base to some conditions over the pdf) in order to minimize the entropy (Infomax) 5] or the mean squared error (PCA non linear) 6] By our own, let s recall that the ....
.-C.Jutten and J. Herault. Blind separation of sources, part I: . Signal processing, 24, (1991) vol 1. page 1-10
....and the final objective in every method is to force the maximisation of an independence measure of the involved signals to extract the original sources. Most of the methods developed in the last years share an analysis based on the pdf and their related cumulants to obtain independence properties, [1,2,3,4]. More recently other approaches deal with a non linearity (building in base to some conditions over the pdf in order to minimize the entropy (Infomax) 5] or the mean squared error (non linear PCA) 6] zN wN w 1 z 1 yN x N ICA Instantenous mixing matrix H Spatial Decorrelation matrix D ....
.-C.Jutten and J. Herault. Blind separation of sources, part I: . Signal processing, 24, (1991) vol 1. page 1-10
....those directions that are independent across all statistical orders. However, in practical situations this is often impossible, in which case the minimization of di erent contrast functions can be used to emphasize di erent aspects of the data. The problem was rst addressed by Jutten and Herault (Jutten and Herault, 1991). Other important landmarks were established by Amari et al. Amari et al. 1996) Cardoso and Laheld (Cardoso and Laheld, 1996) Comon (Comon, 1994) Hyv arinen (Hyv arinen, 1997) Girolami and Fyfe (Girolami and Fyfe, 1997) Oja (Oja, 1997) Pearlmutter and Parra (Pearlmutter and Parra, 1996) ....
Jutten, C. and Herault, J. (1991). Blind separation of sources, part 1: An adaptive algorithm based on neuromimetic architechture. Signal Processing, 24:1-10.
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Comon, P., Jutten, C., & Herault, J. (1991). Blind separation of sources, Part II: Problem statement. Signal Processing, 24, 11--20.
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Jutten C. & Herault J. 1991. Blind separation of sources, part I: an adaptive algorithm based on neuromimetic architecture, Signal processing 24, 1-10
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Comon P., Jutten C. & Herault J. 1991. Blind separation of sources, part II: problems statement, Signal processing 24, 11-21
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C. Jutten, J. Herault, Blind separation of sources, Signal Process. 24 (1991) 1--10.
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Jutten, C., Herault, J., Comon, P., & Sorouchiary, E. (1991). Blind separation of sources, parts I, II, and III. Signal Processing, 24, 1--29.
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C. Jutten and J. Herault, "Blind separation of sources," Signal Processing, vol. 24, pp. 1--10, 1991.
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C. Jutten and J. Herault. Blind separation of sources. Signal processing, 24:1-10, 1991.
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C. Jutten and J. Herault. Blind separation of sources. Signal processing, 24:1-10, 1991.
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C. Jutten, J. Herault, P. Comon, and E. Sorouchiary. Blind separation of sources, parts I, II and III. Signal Processing, 24:1--29, 1991.
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C. Jutten, and J. Herault, " Blind separation of sources," Signal Processing, 24:1-10, 1991
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Jutten, C., Herault, J., 1991. Blind separation of sources. Signal Processing 24, 1--10.
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C. Jutten, and J. Herault, " Blind separation of sources," Signal Processing, 24:1-10, 1991
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Jutten, C. and Herault, J. (1991). Blind separation of sources, part I: An adaptive algorithm based on neuromimetic architecture. Signal Processing, 24:1--10.
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C. Jutten, and J. Herault, " Blind separation of sources," Signal Processing, 24:1-10, 1991
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C. Jutten and J. Herault. Blind separation of sources. Signal Processing, 24:1--10, 1991.
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C. Jutten and J. Herault, "Blind separation of sources," Signal Processing, vol. 24, pp. 1--10, 1991.
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Jutten, C. & Herault, J. (1991) Blind separation of sources, part I: an adaptive algorithm based on neuromimetic architecture, Signal Processing, 24:110.
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C. Jutten and J. Herault. Blind separation of sources. Signal processing, 24:1-10, 1991.
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C. Jutten, and J. Herault, " Blind separation of sources," Signal Processing, 24:1-10, 1991
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