Separation of independent sources from correlated inputs

Modified Herault–Jutten Algorithms for Blind Separation of Sources

“…Recently, Cardoso and his co-workers independently developed a similar algorithm, also with the equivariant property [7,8]. Unfortunately the simple local learning rule (23) does not have this desirable property. Further analysis of the learning rules Eqs.…”

On the behavior of current second and higher order blind source separation methods for cyclostationary sources

“…Most of the blind source separators developed these last years exploit either the SO [1], [21], [32], [34] or the FO [14] or both the SO and FO [3], [11], [13], [15], [21], [25], [28] statistics of the data. Under the previous assumptions, the SO statistics of the data are characterized by the correlation matrices that are defined by (3) where is the SO correlation function of the noise on each sensor, is the identity matrix, , diagonal under the previous hypotheses, is the correlation matrix of the vector , and is the correlation matrix of the sources.…”

“…F OR MORE than a decade, blind source separation methods exploiting either the second-order (SO) [1], [21], [32], [34] or the higher order (HO) [14], [24] or both the SO and HO [3], [11], [13], [15], [21], [25], [28] statistics of the data have been strongly developed. These methods aim at blindly separating several statistically independent sources that are assumed zero-mean, stationary, and ergodic.…”

“…Limiting the analysis to the blind separators exploiting the information contained in either the SO [1], [21], [32], [34] or the FO [14] or both the SO and the FO cumulants of the data [3], [11], [13], [15], [21], [25], [28], the purpose of this paper is precisely to bring some answers to the previous important question through the behavior analysis of the empirical SO and FO cumulants estimators in the presence of zero-mean nonstationary and more precisely (quasi)-cyclostationary sources.…”

A First Application of Independent Component Analysis to Extracting Structure from Stock Returns

“…A wide variety of on-line algorithms have been proposed , Bell and Sejnowski 1995, Cichocki and Moszczyriski 1992, Cichocki and Unbehauen 1993, Cichocki, Unbehauen and Rummert 1994, Cichocki, Amari and Thawonmas 1996, Cichocki, Thawonmas and Amari 1997, Choi, Liu and Cichocki 1998, Comon 1994, Delfosse and Loubaton 1995, Girolami and Fyfe 199713, Girolami and Fyfe 1997a, Hyvarinen 1996, Karhunen 1996, Lacoume and Ruiz 1992, Lee, Girolami, Bell and Sejnowski 1998, Li and Sejnowski 1995, Ling, Huang and Liu 1994, Moreau and Macchi 1994, Oja and Karhunen 1995, Pham, Garat and Jutten 1992. Many of these algorithms are sometimes referred to as "neural" learning algorithms.…”