Nonlinear prediction based on independent component analysis mixture modelling

[EN] This paper presents a new algorithm for nonlinear prediction based on independent component analysis mixture modelling (ICAMM). The data are considered from several mutually-exclusive classes which are generated by different ICA models. This strategy allows linear local projections that can be adapted to partial segments of a data set while maintaining generalization (capability for nonlinear modelling) given the mixture of several ICAs. The resulting algorithm is a general purpose technique that could be applied to time series prediction, to recover missing data in images, etc. The performance of the proposed method is demonstrated by simulations in comparison with several classical linear and nonlinear methods. © 2011 Springer-Verlag.This work has been supported by the Generalitat Valenciana under grant PROMETEO/2010/040, and the Spanish Administration and the FEDER Programme of the European Union under grant TEC 2008-02975/TEC.Safont Armero, G.; Salazar Afanador, A.; Vergara Domínguez, L. (2011). Nonlinear prediction based on independent component analysis mixture modelling. Lecture Notes in Computer Science. 6691(1):508-515. https://doi.org/10.1007/978-3-642-21498-1_64S50851566911Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. John Wiley & Sons, New York (2001)Lee, T.W., Lewicki, M.S., Sejnowski, T.J.: ICA mixture models for unsupervised classification of non-gaussian classes and automatic context switching in blind signal separation. IEEE Trans. on Patt. Analysis and Mach. Intellig. 22(10), 1078–1089 (2000)Malaroiu, S., Kiviluoto, K., Oja, E.: ICA Preprocessing for Time Series Prediction. In: 2nd International Workshop on ICA and BSS (ICA 2000), pp. 453–457 (2000)Pajunen, P.: Extensions of Linear Independent Component Analysis: Neural and Information-Theoretic Methods. Ph.D. Thesis, Helsinki University of Technology (1998)Gorriz, J.M., Puntonet, C.G., Salmeron, G., Lang, E.W.: Time Series Prediction using ICA Algorithms. In: Proceedings of the 2nd IEEE International Workshop on Intelligent Data Acquisit. and Advanc. Comput. Systems: Technology and Applications, pp. 226–230 (2003)Wang, C.Z., Tan, X.F., Chen, Y.W., Han, X.H., Ito, M., Nishikawa, I.: Independent component analysis-based prediction of O-Linked glycosylation sites in protein using multi-layered neural networks. In: IEEE 10th Internat. Conf. on Signal Processing, pp. 1–4 (2010)Zhang, Y., Teng, Y., Zhang, Y.: Complex process quality prediction using modified kernel partial least squares. Chemical Engineering Science 65, 2153–2158 (2010)Salazar, A., Vergara, L., Serrano, A., Igual, J.: A general procedure for learning mixtures of independent component analyzers. Pattern Recognition 43(1), 69–85 (2010)Bersektas, D.: Nonlinear programming. Athena Scientific, Massachusetts (1999)Cardoso, J.F., Souloumiac, A.: Blind beamforming for non gaussian signals. IEE Proceedings-F 140(6), 362–370 (1993)Salazar, A., Vergara, L., Llinares, R.: Learning material defect patterns by separating mixtures of independent component analyzers from NDT sonic signals. Mechanical Systems and Signal processing 24(6), 1870–1886 (2010)Salazar, A., Vergara, L.: ICA mixtures applied to ultrasonic nondestructive classification of archaeological ceramics. EURASIP Journal on Advances in Signal Processing, vol. 2010, p.11, Article ID 12520111 (2010), doi:10.1155/2010/125201Salazar, A., Vergara, L., Miralles, R.: On including sequential dependence in ICA mixture models. Signal Processing 90(7), 2314–2318 (2010)Raghavan, R.S.: A Model for Spatially Correlated Radar Clutter. IEEE Trans. on Aerospace and Electronic Systems 27, 268–275 (1991

TVICA - Time Varying Independent Component Analysis and Its Application to Financial Data

Source extraction and dimensionality reduction are important in analyzing high dimensional and complex financial time series that are neither Gaussian distributed nor stationary. Independent component analysis (ICA) method can be used to factorize the data into a linear combination of independent compo- nents, so that the high dimensional problem is converted to a set of univariate ones. However conventional ICA methods implicitly assume stationarity or stochastic homogeneity of the analyzed time series, which leads to a low accu- racy of estimation in case of a changing stochastic structure. A time varying ICA (TVICA) is proposed here. The key idea is to allow the ICA filter to change over time, and to estimate it in so-called local homogeneous intervals. The question of how to identify these intervals is solved by the LCP (local change point) method. Compared to a static ICA, the dynamic TVICA pro- vides good performance both in simulation and real data analysis. The data example is concerned with independent signal processing and deals with a portfolio of highly traded stocks.Adaptive Sequential Testing, Independent Component Analysis, Local Homogeneity, Signal Processing, Realized Volatility.

Multichannel dynamic modeling of non-Gaussian mixtures

[EN] This paper presents a novel method that combines coupled hidden Markov models (HMM) and non Gaussian mixture models based on independent component analyzer mixture models (ICAMM). The proposed method models the joint behavior of a number of synchronized sequential independent component analyzer mixture models (SICAMM), thus we have named it generalized SICAMM (G-SICAMM). The generalization allows for flexible estimation of complex data densities, subspace classification, blind source separation, and accurate modeling of both local and global dynamic interactions. In this work, the structured result obtained by G-SICAMM was used in two ways: classification and interpretation. Classification performance was tested on an extensive number of simulations and a set of real electroencephalograms (EEG) from epileptic patients performing neuropsychological tests. G-SICAMM outperformed the following competitive methods: Gaussian mixture models, HMM, Coupled HMM, ICAMM, SICAMM, and a long short-term memory (LSTM) recurrent neural network. As for interpretation, the structured result returned by G-SICAMM on EEGs was mapped back onto the scalp, providing a set of brain activations. These activations were consistent with the physiological areas activated during the tests, thus proving the ability of the method to deal with different kind of data densities and changing non-stationary and non-linear brain dynamics. (C) 2019 Elsevier Ltd. All rights reserved.This work was supported by Spanish Administration (Ministerio de Economia y Competitividad) and European Union (FEDER) under grants TEC2014-58438-R and TEC2017-84743-P.Safont Armero, G.; Salazar Afanador, A.; Vergara Domínguez, L.; Gomez, E.; Villanueva, V. (2019). Multichannel dynamic modeling of non-Gaussian mixtures. Pattern Recognition. 93:312-323. https://doi.org/10.1016/j.patcog.2019.04.022S3123239

Mixtures of independent component analyzers for EEG prediction

This paper presents a new application of independent component analysis mixture modeling (ICAMM) for prediction of electroencephalographic (EEG) signals. Demonstrations in prediction of missing EEG data in a working memory task using classic methods and an ICAMM-based algorithm are included. The performance of the methods is measured by using four error indicators: signal-to-interference (SIR) ratio, Kullback-Leibler divergence, correlation at lag zero and mean structural similarity index. The results show that the ICAMM-based algorithm outperforms the classical spherical splines method which is commonly used in EEG signal processing. Hence, the potential of using mixtures of independent component analyzers (ICAs) to improve prediction, as opposed on estimating only one ICA is demonstrated.This work has been supported by Generalitat Valenciana under grants PROMETEO/2010/040 and ISIC/2012/006Safont Armero, G.; Salazar Afanador, A.; Vergara Domínguez, L.; Gonzalez, A.; Vidal Maciá, AM. (2012). Mixtures of independent component analyzers for EEG prediction. En Green and smart technology with sensor applications. Springer Verlag (Germany). 338:328-335. doi:10.1007/978-3-642-35251-5_46S328335338Common, P., Jutten, C.: Handbook of Blind Source Separation: Independent Component Analysis and Applications. Academic Press, USA (2010)Salazar, A., Vergara, L., Serrano, A., Igual, J.: A general procedure for learning mixtures of independent component analyzers. Pattern Recognition 43(1), 69–85 (2010)Lee, T.W., Lewicki, M.S., Sejnowski, T.J.: ICA mixture models for unsupervised classification of non-gaussian classes and automatic context switching in blind signal separation. IEEE Transactions on Pattern Analysis and Machine Intelligence 22(10), 1078–1089 (2000)Salazar, A., Vergara, L.: ICA mixtures applied to ultrasonic nondestructive classification of archaeological ceramics. Eurasip Journal on Advances in Signal Processing 2010, article ID 125201, 11 pages (2010), doi:10.1155/2010/125201Klein, C., Feige, B.: An independent component analysis (ICA) approach to the study of developmental differences in the saccadic contingent negative variation. Biological Psychology 70, 105–114 (2005)Makeig, S., Westerfield, M., Jung, T.P., Covington, J., Townsend, J., Sejnowski, T.J., Courchesne, E.: Functionally Independent Components of the Late Positive Event-Related Potential during Visual Spatial Attention. Journal of Neuroscience 19(7), 2665–2680 (1999)Wibral, M., Turi, G., Linden, D.E.J., Kaiser, J., Bledowski, C.: Decomposition of working memory-related scalp ERPs: Crossvalidation of fMRI-constrained source analysis and ICA. Internt J. of Psychol. 67, 200–211 (2008)Castellanos, N.P., Makarov, V.A.: Recovering EEG brain signals: Artifact suppression with wavelet enhanced independent component analysis. Journal of Neuroscience Methods 158, 300–312 (2006)Salazar, A., Vergara, L., Miralles, R.: On including sequential dependence in ICA mixture models. Signal Processing 90, 2314–2318 (2010)Dayan, P., Abbot, L.F.: Theoretical neuroscience: computational and mathematical modeling of neural systems. The MIT Press (2001)Sternberg, S.: High-speed scanning in human memory. Science 153(3736), 652–654 (1966)Raghavachari, S., Lisman, J.E., Tully, M., Madsen, J.R., Bromfield, E.B., Kahana, M.J.: Theta oscillations in human cortex during a working-memory task: evidence for local generators. J. of Neurophys. 95, 1630–1638 (2006)Gorriz, J.M., Puntonet, C.G., Salmeron, G., Lang, E.W.: Time series prediction using ICA algorithms. In: Proc. of 2nd IEEE Internat. W. on Intellig Data Acquisition and Advanc. Comp. Systems: Tech. and App., pp. 226–230 (2003)Lin, C.-T., Cheng, W.-C., Liang, S.-F.: An On-line ICA-Mixture-Model-Based Self-Constructing Fuzzy Neural Network. IEEE Transactions on Circuits and Systems I: Regular Papers 52(1), 207–221 (2005)Lee, T.W., Girolami, M., Sejnowski, T.J.: Independent component analysis using an extended InfoMax algorithm for mixed sub-gaussian and super-gaussian sources. Neural Computation 11(2), 417–441 (1999)Perrin, F., Pernier, J., Bertrand, D., Echallier, J.F.: Spherical splines for scalp potential and current density matching. Electroencep. and Clin. Neurophys. 72, 184–187 (1989)Wang, Z., Bovik, A., Sheikh, H., Simoncelli, E.: Image quality assessment: from error visibility to structural similarity. IEEE Transactions on Image Processing 13(4), 600–612 (2004

RETRASO, a code for modeling reactive transport in saturated and unsaturated porous media

The code RETRASO (REactive TRAnsport of SOlutes) simulates reactive transport of dissolved and gaseous species in non-isothermal saturated or unsaturated problems. Possible chemical reactions include aqueous complexation (including redox reactions), sorption, precipitation-dissolution of minerals and gas dissolution. Various models for sorption of solutes on solids are available, from experimental relationships (linear KD, Freundlich and Langmuir isotherms) to cation exchange and surface complexation models (constant capacitance, diffuse layer and triple layer models). Precipitation-dissolution and aqueous complexation can be modelled in equilibrium or according to kinetic laws. For the numerical solution of the reactive transport equations it uses the Direct Substitution Approach. The use of the code is demonstrated by three examples. The first example models various sorption processes in a smectite barrier. The second example models a complex chemical system in a two dimensional cross-section. The last example models pyrite weathering in an unsaturated medium

Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models are first discussed. Signal-subspace, geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms are described. Mathematical problems and potential solutions are described. Algorithm characteristics are illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensin