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

Application of independent component analysis for evaluation of ashlar masonry walls

[EN] This paper presents a novel application of Independent Component Analysis (ICA) to the evaluation of ashlar masonry walls inspected with Ground Penetrating Radar (GPR). ICA is used as preprocessor to eliminate the background from the backscattered signals. Thus, signal-to-noise ratio of the GPR signals is enhanced. Several experiments were made on scale models of historic ashlar masonry walls. These models were loaded with different weights, and the corresponding B-Scans were obtained. ICA shows the best performance to enhance the quality of the B-Scans compared with classical methods used in GPR signal processing.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.Salazar Afanador, A.; Safont Armero, G.; Vergara Domínguez, L. (2011). Application of independent component analysis for evaluation of ashlar masonry walls. Lecture Notes in Computer Science. 6691(1):469-476. https://doi.org/10.1007/978-3-642-21498-1_59S46947666911Salazar, A., Unió, J.M., Serrano, A., Gosalbez, J.: Neural networks for defect detection in non-destructive evaluation by sonic signals. In: Sandoval, F., Prieto, A.G., Cabestany, J., Graña, M. (eds.) IWANN 2007. LNCS, vol. 4507, pp. 638–645. Springer, Heidelberg (2007)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)Zhao, A., Jiang, Y., Wang, W.: Exploring Independent Component Analysis for GPR Signal Processing. In: Progress In Electromagnetics Research Symposium 2005, pp. 750–753. The Electromagnetics Academy, Cambridge (2005)Abujarad, F., Omar, A.: Comparison of Independent-Component Analysis (ICA) Algorithms for GPR Detection of Non-Metallic Land Mines. In: Bruzzone, L. (ed.) Proceedings of SPIE Image and Signal Processing for Remote Sensing XII, vol. 6365, pp. 636516.1–636516.12. SPIE, Bellingham (2006)Liu, J.X., Zhang, B., Wu, R.B.: GPR Ground Bounce Removal Methods Based on Blind Source Separation. In: Progress In Electromagnetics Research Symposium 2006, pp. 256–259. The Electromagnetics Academy, Cambridge (2006)Verma, P.K., Gaikwad, A.N., Sigh, D., Nigam, M.J.: Analysis of Clutter Reduction Techniques for Through Wall Imaging in UWB Range. In: Progres. Electromagnetics Research B 2009, vol. 17, pp. 29–48. The Electromagnetics Academy, Cambridge (2009)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)Cardoso, J.F., Souloumiac, A.: Blind beamforming for non Gaussian signals. IEE Proceedings-F 140(6), 362–370 (1993)Ziehe, A., Muller, K.R.: TDSEP - An Efficient Algorithm for Blind Separation Using Time Structure. In: Proceedings of the Eighth International Conference on Artificial Neural Networks ICANN 1998, Perspectives in Neural Computing, pp. 675–680 (1998)Reynolds, J.M.: An Introduction to Applied and Environmental Geophysics. Wiley, Chichester (1997)Igual, J., Camacho, A., Vergara, L.: A blind source separation technique for extracting sinusoidal interferences in ultrasonic non-destructive testing. Journal of VLSI Signal Processing 38, 25–34 (2004)Salazar, A., Gosálbez, J., Igual, J., Llinares, R., Vergara, L.: Two applications of independent component analysis for non-destructive evaluation by ultrasounds. In: Rosca, J.P., Erdogmus, D., Príncipe, J.C., Haykin, S. (eds.) ICA 2006. LNCS, vol. 3889, pp. 406–413. Springer, Heidelberg (2006)Raghavan, R.S.: A Model for Spatially Correlated Radar Clutter. IEEE Trans. on Aerospace and Electronic Systems 27, 268–275 (1991)Salazar, A., Vergara, L.: ICA mixtures applied to ultrasonic nondestructive classification of archaeological ceramics. EURASIP Journal on Advances in Signal Processing, Article ID 125201, 11 (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

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

Nonlinear estimators from ICA mixture models

"NOTICE: this is the author's version of a work that was accepted for publication in Signal Processing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Signal Processing, 155, (2019) https://doi.org/10.1016/j.sigpro.2018.10.003"[EN] Independent Component Analyzers Mixture Models (ICAMM) are versatile and general models for a large variety of probability density functions. In this paper we assume ICAMM to derive new MAP and LMSE estimators. The first one (MAP-ICAMM) is obtained by an iterative gradient algorithm, while the second (LMSE-ICAMM) admits a closed-form solution. Both estimators can be combined by using LMSE-ICAMM to initialize the iterative computation of MAP-ICAMM .The new estimators are applied to the reconstruction of missed channels in EEG multichannel analysis. The experiments demonstrate the superiority of the new estimators with respect to: Spherical Splines, Hermite, Partial Least Squares, Support Vector Regression, and Random Forest Regression. (C) 2018 Elsevier B.V. All rights reserved.This work was supported by Spanish Administration (Ministerio de Economia y Competitividad) and European Union (FEDER) under grant TEC2014-58438-R, and Generalitat Valenciana under grant PROMETEO II/2014/032.Safont Armero, G.; Salazar Afanador, A.; Vergara Domínguez, L.; Rodriguez Martinez, A. (2019). Nonlinear estimators from ICA mixture models. Signal Processing. 155:281-286. https://doi.org/10.1016/j.sigpro.2018.10.003S28128615

Estimating the Laplacian matrix of Gaussian mixtures for signal processing on graphs

[EN] Recent works in signal processing on graphs have been driven to estimate the precision matrix and to use it as the graph Laplacian matrix. The normalized elements of the precision matrix are the partial correlation coefficients which measure the pairwise conditional linear dependencies of the graph. However, the non-linear dependencies inherent in any non-Gaussian model cannot be captured. We propose in this paper a generalized partial correlation coefficient which is derived by assuming an underlying multivariate Gaussian Mixture Model of the observations. Exact and approximate methods are proposed to estimate the generalized partial correlation coefficients from estimates of the Gaussian Mixture Model parameters. Thus it may find application in any non-Gaussian scenario where the Laplacian matrix is to be learned from training signals. (C) 2018 Elsevier B.V. All rights reserved.This work was supported by Spanish Administration (Ministerio de Economia y Competitividad) and European Union (FEDER) under grant TEC2014-58438-R, and Generalitat Valenciana under grant PROMETEO II/2014/032.Belda, J.; Vergara Domínguez, L.; Salazar Afanador, A.; Safont Armero, G. (2018). Estimating the Laplacian matrix of Gaussian mixtures for signal processing on graphs. Signal Processing. 148:241-249. https://doi.org/10.1016/j.sigpro.2018.02.017S24124914

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

Probabilistic Distance for Mixtures of Independent Component Analyzers

© 2018 IEEE. Personal use of this material is permitted. Permissíon from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertisíng or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.[EN] Independent component analysis (ICA) is a blind source separation technique where data are modeled as linear combinations of several independent non-Gaussian sources. The independence and linear restrictions are relaxed using several ICA mixture models (ICAMM) obtaining a two-layer artificial neural network structure. This allows for dependence between sources of different classes, and thus a myriad of multidimensional probability density functions (PDFs) can be accurate modeled. This paper proposes a new probabilistic distance (PDI) between the parameters learned for two ICA mixture models. The PDI is computed explicitly, unlike the popular Kullback-Leibler divergence (KLD) and other similar metrics, removing the need for numerical integration. Furthermore, the PDI is symmetric and bounded within 0 and 1, which enables its use as a posterior probability in fusion approaches. In this work, the PDI is employed for change detection by measuring the distance between two ICA mixture models learned in consecutive time windows. The changes might be associated with relevant states from a process under analysis that are explicitly reflected in the learned ICAMM parameters. The proposed distance was tested in two challenging applications using simulated and real data: (i) detecting flaws in materials using ultrasounds and (ii) detecting changes in electroencephalography signals from humans performing neuropsychological tests. The results demonstrate that the PDI outperforms the KLD in change-detection capabilitiesThis work was supported by the Spanish Administration and European Union under grant TEC2014-58438-R, and Generalitat Valenciana under Grant PROMETEO II/2014/032 and Grant GV/2014/034.Safont Armero, G.; Salazar Afanador, A.; Vergara Domínguez, L.; Gomez, E.; Villanueva, V. (2018). Probabilistic Distance for Mixtures of Independent Component Analyzers. IEEE Transactions on Neural Networks and Learning Systems. 29(4):1161-1173. https://doi.org/10.1109/TNNLS.2017.2663843S1161117329

On Recovering Missing Ground Penetrating Radar Traces by Statistical Interpolation Methods

Missing traces in ground penetrating radar (GPR) B-scans (radargrams) may appear because of limited scanning resolution, failures during the acquisition process or the lack of accessibility to some areas under test. Four statistical interpolation methods for recovering these missing traces are compared in this paper: Kriging, Wiener structures, Splines and the expectation assuming an independent component analyzers mixture model (E-ICAMM). Kriging is an adaptation to the spatial context of the linear least mean squared error estimator. Wiener structures improve the linear estimator by including a nonlinear scalar function. Splines are a commonly used method to interpolate GPR traces. This consists of piecewise-defined polynomial curves that are smooth at the connections (or knots) between pieces. E-ICAMM is a new method proposed in this paper. E-ICAMM consists of computing the optimum nonlinear estimator (the conditional mean) assuming a non-Gaussian mixture model for the joint probability density in the observation space. The proposed methods were tested on a set of simulated data and a set of real data, and four performance indicators were computed. Real data were obtained by GPR inspection of two replicas of historical walls. Results show the superiority of E-ICAMM in comparison with the other three methods in the application of reconstructing incomplete B-scans.This research was supported by Universitat Politecnica de Valencia (Vice-Rectorate for Research, Innovation and Transfer) under Grant SP20120646; Generalitat Valenciana under Grants PROMETEOII/2014/032, GV/2014/034 (Emergent Research Groups), and ISIC/2012/006; and the Spanish Administration and European Union FEDER Programme under Grant TEC2011-23403.Safont Armero, G.; Salazar Afanador, A.; Rodriguez, A.; Vergara Domínguez, L. (2014). On Recovering Missing Ground Penetrating Radar Traces by Statistical Interpolation Methods. Remote Sensing. 6(8):7546-7565. https://doi.org/10.3390/rs6087546S7546756568Le Bastard, C., Baltazart, V., Yide Wang, & Saillard, J. (2007). Thin-Pavement Thickness Estimation Using GPR With High-Resolution and Superresolution Methods. IEEE Transactions on Geoscience and Remote Sensing, 45(8), 2511-2519. doi:10.1109/tgrs.2007.900982Schafer, R. W., & Rabiner, L. R. (1973). A digital signal processing approach to interpolation. Proceedings of the IEEE, 61(6), 692-702. doi:10.1109/proc.1973.9150Salazar, A., Vergara, L., Serrano, A., & Igual, J. (2010). A general procedure for learning mixtures of independent component analyzers. Pattern Recognition, 43(1), 69-85. doi:10.1016/j.patcog.2009.05.013Vincent, E., Gribonval, R., & Fevotte, C. (2006). Performance measurement in blind audio source separation. IEEE Transactions on Audio, Speech and Language Processing, 14(4), 1462-1469. doi:10.1109/tsa.2005.858005Kullback, S., & Leibler, R. A. (1951). On Information and Sufficiency. The Annals of Mathematical Statistics, 22(1), 79-86. doi:10.1214/aoms/1177729694Wang, Z., Bovik, A. C., Sheikh, H. R., & Simoncelli, E. P. (2004). Image Quality Assessment: From Error Visibility to Structural Similarity. IEEE Transactions on Image Processing, 13(4), 600-612. doi:10.1109/tip.2003.819861Raghavan, R. S. (1991). A model for spatially correlated radar clutter. IEEE Transactions on Aerospace and Electronic Systems, 27(2), 268-275. doi:10.1109/7.78302Hyvärinen, A., Hoyer, P. O., & Inki, M. (2001). Topographic Independent Component Analysis. Neural Computation, 13(7), 1527-1558. doi:10.1162/089976601750264992Salazar, A., Safont, G., & Vergara, L. (2011). Application of Independent Component Analysis for Evaluation of Ashlar Masonry Walls. Lecture Notes in Computer Science, 469-476. doi:10.1007/978-3-642-21498-1_5

Nuevas contribuciones a la teoría y aplicación del procesado de señal sobre grafos

[ES] El procesado de señal sobre grafos es un campo emergente de técnicas que combinan conceptos de dos áreas muy consolidadas: el procesado de señal y la teoría de grafos. Desde la perspectiva del procesado de señal puede obtenerse una definición de la señal mucho más general asignando cada valor de la misma a un vértice de un grafo. Las señales convencionales pueden considerarse casos particulares en los que los valores de cada muestra se asignan a una cuadrícula uniforme (temporal o espacial). Desde la perspectiva de la teoría de grafos, se pueden definir nuevas transformaciones del grafo de forma que se extiendan los conceptos clásicos del procesado de la señal como el filtrado, la predicción y el análisis espectral. Además, el procesado de señales sobre grafos está encontrando nuevas aplicaciones en las áreas de detección y clasificación debido a su flexibilidad para modelar dependencias generales entre variables. En esta tesis se realizan nuevas contribuciones al procesado de señales sobre grafos. En primer lugar, se plantea el problema de estimación de la matriz Laplaciana asociada a un grafo, que determina la relación entre nodos. Los métodos convencionales se basan en la matriz de precisión, donde se asume implícitamente Gaussianidad. En esta tesis se proponen nuevos métodos para estimar la matriz Laplaciana a partir de las correlaciones parciales asumiendo respectivamente dos modelos no Gaussianos diferentes en el espacio de las observaciones: mezclas gaussianas y análisis de componentes independientes. Los métodos propuestos han sido probados con datos simulados y con datos reales en algunas aplicaciones biomédicas seleccionadas. Se demuestra que pueden obtenerse mejores estimaciones de la matriz Laplaciana con los nuevos métodos propuestos en los casos en que la Gaussianidad no es una suposición correcta. También se ha considerado la generación de señales sintéticas en escenarios donde la escasez de señales reales puede ser un problema. Los modelos sobre grafos permiten modelos de dependencia por pares más generales entre muestras de señal. Así, se propone un nuevo método basado en la Transformada de Fourier Compleja sobre Grafos y en el concepto de subrogación. Se ha aplicado en el desafiante problema del reconocimiento de gestos con las manos. Se ha demostrado que la extensión del conjunto de entrenamiento original con réplicas sustitutas generadas con los métodos sobre grafos, mejora significativamente la precisión del clasificador de gestos con las manos.[CAT] El processament de senyal sobre grafs és un camp emergent de tècniques que combinen conceptes de dues àrees molt consolidades: el processament de senyal i la teoria de grafs. Des de la perspectiva del processament de senyal pot obtindre's una definició del senyal molt més general assignant cada valor de la mateixa a un vèrtex d'un graf. Els senyals convencionals poden considerar-se casos particulars en els quals els valors de la mostra s'assignen a una quadrícula uniforme (temporal o espacial). Des de la perspectiva de la teoria de grafs, es poden definir noves transformacions del graf de manera que s'estenguen els conceptes clàssics del processament del senyal com el filtrat, la predicció i l'anàlisi espectral. A més, el processament de senyals sobre grafs està trobant noves aplicacions en les àrees de detecció i classificació a causa de la seua flexibilitat per a modelar dependències generals entre variables. En aquesta tesi es donen noves contribucions al processament de senyals sobre grafs. En primer lloc, es planteja el problema d'estimació de la matriu Laplaciana associada a un graf, que determina la relació entre nodes. Els mètodes convencionals es basen en la matriu de precisió, on s'assumeix implícitament la gaussianitat. En aquesta tesi es proposen nous mètodes per a estimar la matriu Laplaciana a partir de les correlacions parcials assumint respectivament dos models no gaussians diferents en l'espai d'observació: mescles gaussianes i anàlisis de components independents. Els mètodes proposats han sigut provats amb dades simulades i amb dades reals en algunes aplicacions biomèdiques seleccionades. Es demostra que poden obtindre's millors estimacions de la matriu Laplaciana amb els nous mètodes proposats en els casos en què la gaussianitat no és una suposició correcta. També s'ha considerat el problema de generar senyals sintètics en escenaris on l'escassetat de senyals reals pot ser un problema. Els models sobre grafs permeten models de dependència per parells més generals entre mostres de senyal. Així, es proposa un nou mètode basat en la Transformada de Fourier Complexa sobre Grafs i en el concepte de subrogació. S'ha aplicat en el desafiador problema del reconeixement de gestos amb les mans. S'ha demostrat que l'extensió del conjunt d'entrenament original amb rèpliques substitutes generades amb mètodes sobre grafs, millora significativament la precisió del classificador de gestos amb les mans.[EN] Graph signal processing appears as an emerging field of techniques that combine concepts from two highly consolidated areas: signal processing and graph theory. From the perspective of signal processing, it is possible to achieve a more general signal definition by assigning each value of the signal to a vertex of a graph. Conventional signals can be considered particular cases where the sample values are assigned to a uniform (temporal or spatial) grid. From the perspective of graph theory, new transformations of the graph can be defined in such a way that they extend the classical concepts of signal processing such as filtering, prediction and spectral analysis. Furthermore, graph signal processing is finding new applications in detection and classification areas due to its flexibility to model general dependencies between variables. In this thesis, new contributions are given to graph signal processing. Firstly, it is considered the problem of estimating the Laplacian matrix associated with a graph, which determines the relationship between nodes. Conventional methods are based on the precision matrix, where Gaussianity is implicitly assumed. In this thesis, new methods to estimate the Laplacian matrix from the partial correlations are proposed respectively assuming two different non-Gaussian models in the observation space: Gaussian Mixtures and Independent Component Analysis. The proposed methods have been tested with simulated data and with real data in some selected biomedical applications. It is demonstrate that better estimates of the Laplacian matrix can be obtained with the new proposed methods in cases where Gaussianity is not a correct assumption. The problem of generating synthetic signal in scenarios where real signals scarcity can be an issue has also been considered. Graph models allow more general pairwise dependence models between signal samples. Thus a new method based on the Complex Graph Fourier Transform and on the concept of subrogation is proposed. It has been applied in the challenging problem of hand gesture recognition. It has been demonstrated that extending the original training set with graph surrogate replicas, significantly improves the accuracy of the hand gesture classifier.Belda Valls, J. (2022). Nuevas contribuciones a la teoría y aplicación del procesado de señal sobre grafos [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/19133

Fusión de datos estadísticamente dependientes en sistemas de detección

La presente tesis se centra en la problemática existente a la hora de implementar un sistema de detección o clasificación binaria cuando es necesario combinar, integrar o fusionar diversas fuentes de información que pueden ser dependientes y heterogéneas entre sí. Las técnicas de fusión de datos tratan de combinar múltiples fuentes de información para alcanzar la exactitud y precisión en la toma de decisiones que no sería posible conseguir con el uso de una sola fuente de información de forma aislada. En un sistema de detección se pueden encontrar diferentes etapas y niveles de fusión: en la etapa de pre-detección encontramos los niveles de fusión de sensores y de características, donde se combinan los diferentes flujos de muestras proporcionados por una serie de sensores o diferentes características obtenidas del procesado estos; en la etapa de post- detección, se realiza la combinación de diferentes detectores, a través de la fusión de valoraciones continuas o de decisiones individuales aportadas por cada uno de ellos. Atendiendo al tipo de datos a combinar encontramos dos grupos: fusión soft, donde se combinan datos modelados mediante variables aleatorias continuas, caracterizadas mediante sus funciones de densidad de probabilidad (PDFs), o fusión hard, asociada a la combinación de las decisiones individuales tomadas en la etapa de fusión de detectores, donde se combinan datos binarios modelados mediante variables aleatorias discretas, caracterizadas por funciones de masa de probabilidad. Se destaca la fusión de scores como un caso particular de fusión soft asociada a la fusión de diversos detectores, en donde los datos a combinar presentan buenas propiedades discriminatorias de forma aislada y se encuentran definidos en un mismo rango normalizado [0,1]. En el presente trabajo se ha realizado una completa revisión del estado del arte en cuanto a técnicas de fusión y combinación de datos aplicadas en problemas de detección donde los datos pueden ser heterogéneos y dependientes entre sí. Se realiza una revisión en mayor profundidad de la técnica de estimación de PDFs basada en la teoría de cópulas, la cual puede ser usada en la fusión óptima de datos soft. Se destaca de forma especial tanto por su novedad e incipiente uso en el campo del procesado de señal, como por su adecuación en problemas de detección, permitiéndonos modelar de forma aislada las funciones marginales de los datos y la estructura de dependencia presente entre ellos, simplificando el problema de modelado de PDFs de datos heterogéneos y dependientes. Se ha propuesto una nueva técnica de fusión soft denominada integración-a, basada en una función de media-a, la cual, sin elevar mucho la complejidad, aporta un mayor grado de flexibilidad y de adaptación, siendo capaz de mejorar las prestaciones que se pueden obtener con respecto al resto de técnicas subóptimas utilizadas comúnmente en problemas de fusión de scores heterogéneos y dependientes entre sí. Se ha derivado un novedoso método de entrenamiento basado en el criterio de maximización parcial del área bajo la curva ROC. Se han utilizado diversas bases de datos públicas para poder testear y comprobar el correcto funcionamiento de las técnicas de fusión propuestas en problemas de autentificación multibiométrica. También se han aplicado algunas de las técnicas de fusión en la mejora de un sistema de detección de eventos acústicos. Se ha propuesto un nuevo tipo de detector basado en la teoría de cópulas denominado COCD para lidiar con el problema de la detección de señal desconocida en presencia de ruido aleatorio dependiente y no Gaussiano, centrándonos en su utilización para una aplicación de detección de eventos sonoros desconocidos. También se realiza un estudio de fusión de más de un canal de audio (utilizando más de un micrófono para captar diferentes señales) como método para incrementar las prestaciones obtenidas.Soriano Tolosa, A. (2013). Fusión de datos estadísticamente dependientes en sistemas de detección [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/34780TESI