Independent component analysis: recent advances

Aapo Hyvärinen1
1Department of Computer Science, Department of Mathematics and Statistics, and HIIT, University of Helsinki, Helsinki, Finland

Tóm tắt

Independent component analysis is a probabilistic method for learning a linear transform of a random vector. The goal is to find components that are maximally independent and non-Gaussian (non-normal). Its fundamental difference to classical multi-variate statistical methods is in the assumption of non-Gaussianity, which enables the identification of original, underlying components, in contrast to classical methods. The basic theory of independent component analysis was mainly developed in the 1990s and summarized, for example, in our monograph in 2001. Here, we provide an overview of some recent developments in the theory since the year 2000. The main topics are: analysis of causal relations, testing independent components, analysing multiple datasets (three-way data), modelling dependencies between the components and improved methods for estimating the basic model.

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Tài liệu tham khảo

10.1016/0165-1684(91)90079-X

10.1016/S0893-6080(00)00026-5

10.1002/0471221317

Comon P, 2010, Handbook of blind source separation.

10.1016/0165-1684(94)90029-9

10.1109/LSP.2004.830118

10.1109/78.599941

10.1162/neco.1995.7.6.1129

10.1088/0954-898X/5/4/008

10.1109/97.566704

10.1109/72.761722

Amari S-I, 1996, Advances in neural information processing systems

Hyvärinen A, 2010, In Proc. Asian Conf. Machine Learning, Tokyo, Japan, 1

Hyvärinen A& Smith SM. Submitted. Pairwise likelihood ratios for estimation of non-Gaussian structural equation models.

10.1198/000313001300339932

Shimizu S, 2006, A linear non-Gaussian acyclic model for causal discovery, J. Mach. Learn. Res., 7, 2003

Lacerda G, 2008, In Proc. 24th Conf. Uncertainty in Artificial Intelligence (UAI2008), Helsinki, Finland.

Shimizu S, 2011, DirectLiNGAM: a direct method for learning a linear non-Gaussian structural equation model, J. Mach. Learn. Res., 12, 1225

Hyvärinen A, 2010, Estimation of a structural vector autoregression model using non-Gaussianity, J. Mach. Learn. Res., 11, 1709

10.1016/j.neuroimage.2011.06.068

10.1016/j.neucom.2011.11.005

Hoyer PO, 2009, Advances in neural information processing systems

Zhang K, 2009, In Proc. 25th Conf. on Uncertainty in Artificial Intelligence (UAI2009), Montréal, Canada, 647

10.1016/j.neuroimage.2004.03.027

10.1109/TBME.2002.805480

10.1016/j.neuroimage.2011.05.086

10.1016/j.neuroimage.2004.10.042

Hyvärinen A& Ramkumar P. Submitted. Testing independent components by inter-subject or inter-session consistency.

10.1016/j.neuroimage.2008.10.057

Varoquaux G, 2011, Information processing in medical imaging, 562, 10.1007/978-3-642-22092-0_46

Hyvärinen A, 2012, In Human Brain Mapping Meeting, Beijing, China, 10–14 June 2012.

Harshman RA, 1970, Foundations of the PARAFAC procedure: models and conditions for an explanatory multimodal factor analysis, UCLA Working Papers Phonetics, 16, 1

10.1016/j.neuroimage.2004.10.043

10.1109/78.554307

10.1109/78.942614

Yeredor A, 2010, Handbook of blind source separation

10.1109/JSTSP.2008.2005346

10.1007/978-1-84882-491-1

10.1162/089976600300015312

10.1162/089976601750264992

Hyvärinen A, 2006, In Proc. Eur. Symp. Artificial Neural Networks, Bruges, Belgium.

Gruber P, 2009, Proc. Int. Conf. on Independent Component Analysis and Blind Signal Separation (ICA2009), Paraty, Brazil, 259, 10.1007/978-3-642-00599-2_33

10.1162/0899766053011474

10.1038/nature07481

Ranzato M, 2010, In Proc. 13th Int. Conf. on Artificial Intelligence and Statistics (AISTATS2010), Sardinia, Italy, 13–15 May 2010.

10.1162/089976606775093936

10.1162/NECO_a_00010

10.1162/089976602760128018

Hyvärinen A, 2005, Estimation of non-normalized statistical models using score matching, J. Mach. Learn. Res., 6, 695

Gutmann MU, 2012, Noise-contrastive estimation of unnormalized statistical models, with applications to natural image statistics, J. Mach. Learn. Res., 13, 307

10.1016/j.sigpro.2003.10.010

Kawanabe M, 2005, Estimating functions for blind separation when sources have variance dependencies, J. Mach. Learn. Res., 6, 453

Hyvärinen A, 1998, In Proc. Int. Conf. on Artificial Neural Networks (ICANN’98), Skövde, Sweden, 135

10.1016/j.neuroimage.2008.07.032

Zhang K& Hyvärinen A. 2011 A general linear non-Gaussian state-space model: identifiability identification applications. Proc. Asian Conf. on Machine Learning Tokyo Japan pp. 113–128.

10.1109/TBME.2010.2046325

10.1162/089976606774841620

Lahat D, 2012, Latent variable analysis and signal separation, 155, 10.1007/978-3-642-28551-6_20

Sasaki H, 2012, In Proc. Asian Conf. on Machine Learning, Singapore.

Bach FR, 2003, Beyond independent components: trees and clusters, J. Mach. Learn. Res., 4, 1205

Zoran D, 2010, Advances in neural information processing systems, 22

10.1016/j.tics.2007.09.004

10.1126/science.1127647

10.1145/2001269.2001295

10.1109/31.76486

10.1162/089976601300014394

10.1016/j.sigpro.2005.02.003

Pham D-T, 2002, In Proc. Int. Conf. on Digital Signal Processing (DSP2002), 151

10.1214/aoms/1177706099

10.1162/089976601300014385

Pham D-T& Cardoso J-F. 2003 Source adaptive blind source separation: Gaussian models and sparsity. In. In SPIE Conf. Wavelets: Applications in Signal and Image Processing. SPIE.

Kisilev P, 2003, A multiscale framework for blind separation of linearly mixed signals, J. Mach. Learn. Res., 4, 1339

Gribonval R, 2010, Handbook of blind source separation

10.1016/j.neuroimage.2009.08.028

10.1109/TIT.2005.864440

10.1142/SO129065700000028

10.1023/A:1018647011077

10.1214/009053606000000939

10.1109/72.925558

Hastie T, 2003, In Advances in neural information processing 15 (Proc. NIPS*2002).

Learned-Miller EG, 2003, ICA using spacings estimates of entropy, J. Mach. Learn. Res., 4, 1271

Bach FR, 2002, Kernel independent component analysis, J. Mach. Learn. Res., 3, 1

Gretton A, 2008, Advances in neural information processing systems

10.1103/PhysRevE.70.066123

10.1002/env.3170050203

10.1016/S0169-7439(96)00044-5

10.1038/44565

10.1016/S0042-6989(02)00017-2

10.1002/9780470747278

Donoho DL, 2004, In Advances in neural information processing 16 (Proc. NIPS*2003)

Hoyer PO, 2004, Non-negative matrix factorization with sparseness constraints, J. Mach. Learn. Res., 5, 1457

10.1109/TNN.2003.810616

Plumbley MD, 2010, Handbook of blind source separation