A survey of the performance indexes of ICA algorithms

This paper deals with the problem of blind separation of sources (BSS). In the literature, one can find many Independent Component Algorithms (ICA) to solve the BSS. To demonstrate the performances of their algorithms, researchers often use different methods or performance indexes depending on their source signals and their applications. Many methods and performance indexes can not be used to compare two different algorithms applied to different signals. Most of the widely used performance indexes or methods are mentioned and discussed hereafter. We also give many examples to show limitations or drawbacks of some performance indexes or methods. keywords: Blind Separation of Sources, BSS, ICA, Crosstalk, SNR, SINR, Gap or Distance to Diagonal Matrix, Performance Indexes, Crosstalk Error, Rejection Level, Global Index, Symbol Error Rate, Scatter Plot, Error Signals, Real World Applications.

[1]  P. Comon Separation Of Stochastic Processes , 1989, Workshop on Higher-Order Spectral Analysis.

[2]  Shun-ichi Amari,et al.  Adaptive Online Learning Algorithms for Blind Separation: Maximum Entropy and Minimum Mutual Information , 1997, Neural Computation.

[3]  J. Hérault,et al.  Réseau de neurones à synapses modifiables: décodage de messages sensoriels composites par apprentissage non supervisé et permanent , 1984 .

[4]  Reinhold Orglmeister,et al.  Blind source separation of real world signals , 1997, Proceedings of International Conference on Neural Networks (ICNN'97).

[5]  Terrence J. Sejnowski,et al.  Blind source separation of more sources than mixtures using overcomplete representations , 1999, IEEE Signal Processing Letters.

[6]  Henrik Sahlin,et al.  Separation of real-world signals , 1998, Signal Process..

[7]  J. Cardoso On the Performance of Orthogonal Source Separation Algorithms , 1994 .

[8]  Noboru Ohnishi,et al.  Blind separation for instantaneous mixture of speech signals: algorithms and performances , 2000, 2000 TENCON Proceedings. Intelligent Systems and Technologies for the New Millennium (Cat. No.00CH37119).

[9]  Eric Moreau,et al.  Adaptive unsupervised separation of discrete sources , 1999, Signal Process..

[10]  Meir Feder,et al.  Multi-channel signal separation by decorrelation , 1993, IEEE Trans. Speech Audio Process..

[11]  Christian Jutten,et al.  Independent components analysis versus principal components analysis , 1988 .

[12]  Christian Jutten,et al.  Fourth-order criteria for blind sources separation , 1995, IEEE Trans. Signal Process..

[13]  Shun-ichi Amari,et al.  Neural Learning in Structured Parameter Spaces - Natural Riemannian Gradient , 1996, NIPS.

[14]  Noboru Ohnishi,et al.  A simple ICA algorithm based on geometrical approach , 2001, Proceedings of the Sixth International Symposium on Signal Processing and its Applications (Cat.No.01EX467).

[15]  A. Mansour,et al.  Discussion of Simple Algorithms and Methods to Separate Non-stationary Signals. , 2000 .

[16]  Terrence J. Sejnowski,et al.  Adaptive separation of mixed broadband sound sources with delays by a beamforming Herault-Jutten network , 1995 .

[17]  Comon 5 - Analyse en composantes indépendantes et identification aveugle , 1990 .

[18]  Pierre Comon,et al.  Separation Of Sources Using Higher-Order Cumulants , 1989, Optics & Photonics.

[19]  Eric Moulines,et al.  A blind source separation technique using second-order statistics , 1997, IEEE Trans. Signal Process..

[20]  Christian Jutten,et al.  A direct solution for blind separation of sources , 1996, IEEE Trans. Signal Process..

[21]  Christian Jutten,et al.  Blind source separation for convolutive mixtures , 1995, Signal Process..

[22]  Erkki Oja,et al.  Independent component analysis by general nonlinear Hebbian-like learning rules , 1998, Signal Process..

[23]  Eric Moreau,et al.  Separation auto-adaptative de sources sans blanchiment prealable , 1993 .

[24]  Noboru Ohnishi,et al.  Multichannel blind separation of sources algorithm based on cross-cumulant and the Levenberg-Marquardt method , 1999, IEEE Trans. Signal Process..

[25]  Beate H. Laheld,et al.  Séparation adaptative de sources en aveugle. Implantation complexe sans contraintes , 1993 .

[26]  Carlos J. Escudero,et al.  A blind signal separation method for multiuser communications , 1997, IEEE Trans. Signal Process..

[27]  Terrence J. Sejnowski,et al.  Independent Component Analysis Using an Extended Infomax Algorithm for Mixed Subgaussian and Supergaussian Sources , 1999, Neural Computation.

[28]  Eric Moreau,et al.  High order contrasts for self-adaptive source separation criteria for complex source separation , 1996 .

[29]  Pierre Comon,et al.  Independent component analysis, A new concept? , 1994, Signal Process..

[30]  Ali Mansour,et al.  Blind separation of sources : Methods, assumptions and applications , 2000 .

[31]  Jutten,et al.  1 - Une solution neuromimétique au problème de séparation de sources , 1988 .

[32]  Christian Jutten,et al.  Adaptive Optimization of Neural Algorithms , 1991, IWANN.

[33]  Dirk Van Compernolle,et al.  Blind separation of sources : a comparative study of a 2-nd and a 4-th order solution , 1994 .

[34]  Terrence J. Sejnowski,et al.  Blind separation and blind deconvolution: an information-theoretic approach , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[35]  Ali Mansour,et al.  Adaptive blind elimination of artifacts in ECG signals , 1998 .

[36]  A. Belouchrani,et al.  Séparation aveugle au second ordre de sources corrélées , 1993 .

[37]  Ehud Weinstein,et al.  Multichannel signal separation: methods and analysis , 1996, IEEE Trans. Signal Process..

[38]  Adel Belouchrani,et al.  A new composite criterion for adaptive and iterative blind source separation , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[39]  H. H. Yang,et al.  Serial updating rule for blind separation derived from the method of scoring , 1999, IEEE Trans. Signal Process..

[40]  Allan Kardec Barros,et al.  Real world blind separation of convolved non-stationary signals , 1999 .

[41]  A. Cichocki,et al.  Self-adaptive independent component analysis for sub-Gaussian and super-Gaussian mixtures with an un , 1997 .

[42]  Andrzej Cichocki,et al.  Robust neural networks with on-line learning for blind identification and blind separation of sources , 1996 .

[43]  Jean-Francois Cardoso,et al.  Performances en séparation de sources , 1993 .

[44]  Christian Jutten,et al.  Detection de grandeurs primitives dans un message composite par une architecture de calcul neuromime , 1985 .

[45]  Jacek M. Zurada,et al.  Nonlinear Blind Source Separation Using a Radial Basis Function Network , 2001 .

[46]  Andrzej Cichocki,et al.  Information-theoretic approach to blind separation of sources in non-linear mixture , 1998, Signal Process..

[47]  Ali Mansour,et al.  A new geometrical blind separation of sources algorithm. , 2001 .

[48]  Kiyotoshi Matsuoka,et al.  A neural net for blind separation of nonstationary signals , 1995, Neural Networks.

[49]  Shun-ichi Amari,et al.  Multi-Layer Neural Networks with a Local Adaptive Learning Rule for Blind Separation of Source Signa , 1995 .

[50]  Lang Tong,et al.  Waveform-preserving blind estimation of multiple independent sources , 1993, IEEE Trans. Signal Process..

[51]  Eric Moreau,et al.  Self-adaptive source separation. II. Comparison of the direct, feedback, and mixed linear network , 1998, IEEE Trans. Signal Process..

[52]  P. Comon,et al.  Blind separation of discrete sources , 1998, IEEE Signal Processing Letters.

[53]  Julio Ortega Lopera,et al.  Separation of sources: A geometry-based procedure for reconstruction of n-valued signals , 1995, Signal Process..

[54]  Allan Kardec Barros,et al.  independent , 2006, Gumbo Ya Ya.

[55]  Shun-ichi Amari,et al.  Blind separation of uniformly distributed signals: a general approach , 1999, IEEE Trans. Neural Networks.

[56]  Dong-Jo Park,et al.  Blind separation of sources using higher-order cumulants , 1999, Signal Process..