Two novel methods for the determination of the number of components in independent components analysis models

Independent Components Analysis is a Blind Source Separation method that aims to find the pure source signals mixed together in unknown proportions in the observed signals under study. It does this by searching for factors which are mutually statistically independent. It can thus be classified among the latent-variable based methods. Like other methods based on latent variables, a careful investigation has to be carried out to find out which factors are significant and which are not. Therefore, it is important to dispose of a validation procedure to decide on the optimal number of independent components to include in the final model. This can be made complicated by the fact that two consecutive models may differ in the order and signs of similarly-indexed ICs. As well, the structure of the extracted sources can change as a function of the number of factors calculated. Two methods for determining the optimal number of ICs are proposed in this article and applied to simulated and real datasets to demonstrate their performance.

[1]  T. Næs,et al.  Principal component regression in NIR analysis: Viewpoints, background details and selection of components , 1988 .

[2]  Erkki Oja,et al.  Independent component analysis: algorithms and applications , 2000, Neural Networks.

[3]  R. Kass,et al.  Automatic correction of ocular artifacts in the EEG: a comparison of regression-based and component-based methods. , 2004, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[4]  Guoqing Wang,et al.  Independent component analysis and its applications in signal processing for analytical chemistry , 2008 .

[5]  J. Cardoso,et al.  Blind beamforming for non-gaussian signals , 1993 .

[6]  Alexander Kraskov,et al.  Least-dependent-component analysis based on mutual information. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Eugenio Martinelli,et al.  Counteraction of environmental disturbances of electronic nose data by independent component analysis , 2002 .

[8]  Frank Westad,et al.  Cross validation and uncertainty estimates in independent component analysis , 2003 .

[9]  Terrence J. Sejnowski,et al.  An Information-Maximization Approach to Blind Separation and Blind Deconvolution , 1995, Neural Computation.

[10]  Aapo Hyvärinen,et al.  A Fast Fixed-Point Algorithm for Independent Component Analysis , 1997, Neural Computation.

[11]  Theodoros N. Arvanitis,et al.  A comparative study of feature extraction and blind source separation of independent component analysis (ICA) on childhood brain tumour 1H magnetic resonance spectra , 2009, NMR in biomedicine.

[12]  J. Vandewalle,et al.  An introduction to independent component analysis , 2000 .

[13]  R. Kass,et al.  Automatic correction of ocular artifacts in the EEG: a comparison of regression-based and component-based methods , 2004 .

[14]  Shinji Umeyama,et al.  Blind deconvolution of blurred images by use of ICA , 2001 .

[15]  Pilar Poncela.  DiscussionFurther research on independent component analysis , 2012 .

[16]  S. Wold.  Cross-Validatory Estimation of the Number of Components in Factor and Principal Components Models , 1978 .

[17]  António S. Barros,et al.  Generalised PLS_Cluster: an extension of PLS_Cluster for interpretable hierarchical clustering of multivariate data , 2007 .

[18]  Paul Geladi,et al.  Principal Component Analysis , 1987, Comprehensive Chemometrics.

[19]  Douglas N. Rutledge,et al.  Independent components analysis applied to 3D-front-face fluorescence spectra of edible oils to study the antioxidant effect of Nigella sativa L. extract on the thermal stability of heated oils , 2012 .

[20]  M. Stone.  Cross‐Validatory Choice and Assessment of Statistical Predictions , 1976 .

[21]  D. Jouan-Rimbaud Bouveresse,et al.  Two novel methods for the determination of the number of components in independent components analysis models , 2012 .

[22]  Robert Tibshirani,et al.  Estimating the number of clusters in a data set via the gap statistic , 2000 .

[23]  B. Kowalski,et al.  Partial least-squares regression: a tutorial , 1986 .

[24]  Douglas N. Rutledge,et al.  Durbin–Watson statistic as a morphological estimator of information content , 2002 .

[25]  Fei Liu,et al.  Variable selection in visible/near infrared spectra for linear and nonlinear calibrations: a case study to determine soluble solids content of beer. , 2009, Analytica chimica acta.

[26]  Michael I. Jordan,et al.  Kernel independent component analysis , 2003 .

[27]  Lutgarde M. C. Buydens,et al.  Application of independent component analysis to 1H MR spectroscopic imaging exams of brain tumours , 2005 .

[28]  Guoqing Wang,et al.  Estimation of source spectra profiles and simultaneous determination of polycomponent in mixtures from ultraviolet spectra data using kernel independent component analysis and support vector regression. , 2007, Analytica chimica acta.

[29]  Alexander Kraskov,et al.  Monte Carlo Algorithm for Least Dependent Non-Negative Mixture Decomposition , 2006, Analytical chemistry.

[30]  Jian Yang,et al.  Kernel ICA: An alternative formulation and its application to face recognition , 2005, Pattern Recognit..

[31]  Yulia B. Monakhova,et al.  Independent components in spectroscopic analysis of complex mixtures , 2010, 1009.0534.

[32]  K Ramadoss,et al.  Comparison of Independent Component Analysis Algorithms for Removal of Ocular Artifacts from Electroencephalogram , 2005 .

[33]  Ole Winther,et al.  Mean-Field Approaches to Independent Component Analysis , 2002, Neural Computation.

[34]  D. Massart,et al.  Determination of the number of components during mixture analysis using the Durbin–Watson criterion in the Orthogonal Projection Approach and in the SIMPLe-to-use Interactive Self-modelling Mixture Analysis approach , 2002 .

[35]  Xueguang Shao,et al.  A primary study on resolution of overlapping GC-MS signal using mean-field approach independent component analysis , 2006 .

[36]  Ganesh R. Naik,et al.  Introduction: Independent Component Analysis , 2012 .

[37]  Maryam Vosough,et al.  Using mean field approach independent component analysis to fatty acid characterization with overlapped GC-MS signals. , 2007, Analytica chimica acta.

[38]  J. Durbin,et al.  Testing for serial correlation in least squares regression. I. , 1950, Biometrika.

[39]  Nikos Pasadakis,et al.  Identifying constituents in commercial gasoline using Fourier transform-infrared spectroscopy and independent component analysis. , 2006, Analytica chimica acta.

[40]  P. Barreiro,et al.  Prospects for the rapid detection of mealiness in apples by nondestructive NMR relaxometry , 2002 .

[41]  Klaus-Robert Müller,et al.  Inlier‐based ICA with an application to superimposed images , 2005, Int. J. Imaging Syst. Technol..

[42]  Chih-Chou Chiu,et al.  Process monitoring with ICA‐based signal extraction technique and CART approach , 2009, Qual. Reliab. Eng. Int..

[43]  Delphine Jouan-Rimbaud Bouveresse,et al.  Independent component analysis as a pretreatment method for parallel factor analysis to eliminate artefacts from multiway data. , 2007, Analytica chimica acta.

[44]  M. P. Gómez-Carracedo,et al.  Selecting the optimum number of partial least squares components for the calibration of attenuated total reflectance-mid-infrared spectra of undesigned kerosene samples. , 2007, Analytica chimica acta.

[45]  J. Durbin,et al.  Testing for serial correlation in least squares regression. II. , 1950, Biometrika.

[46]  Athanasios Mouchtaris,et al.  Linear predictive spectral coding and independent component analysis in identifying gasoline constituents using infrared spectroscopy , 2007 .