- -

A New Surrogating Algorithm by the Complex Graph Fourier Transform (CGFT)

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

A New Surrogating Algorithm by the Complex Graph Fourier Transform (CGFT)

Mostrar el registro sencillo del ítem

Ficheros en el ítem

Thumbnail
Nombre: Belda;Vergara;Safont ...
Tamaño: 645.8Kb
Formato: PDF
Descripción: Versión editorial
Abrir
dc.contributor.author Belda, Jordi es_ES
dc.contributor.author Vergara Domínguez, Luís es_ES
dc.contributor.author Safont Armero, Gonzalo es_ES
dc.contributor.author Salazar Afanador, Addisson es_ES
dc.contributor.author Parcheta, Zuzanna es_ES
dc.date.accessioned 2020-12-01T04:33:05Z
dc.date.available 2020-12-01T04:33:05Z
dc.date.issued 2019-08 es_ES
dc.identifier.issn 1099-4300 es_ES
dc.identifier.uri http://hdl.handle.net/10251/156117
dc.description.abstract [EN] The essential step of surrogating algorithms is phase randomizing the Fourier transform while preserving the original spectrum amplitude before computing the inverse Fourier transform. In this paper, we propose a new method which considers the graph Fourier transform. In this manner, much more flexibility is gained to define properties of the original graph signal which are to be preserved in the surrogates. The complex case is considered to allow unconstrained phase randomization in the transformed domain, hence we define a Hermitian Laplacian matrix that models the graph topology, whose eigenvectors form the basis of a complex graph Fourier transform. We have shown that the Hermitian Laplacian matrix may have negative eigenvalues. We also show in the paper that preserving the graph spectrum amplitude implies several invariances that can be controlled by the selected Hermitian Laplacian matrix. The interest of surrogating graph signals has been illustrated in the context of scarcity of instances in classifier training. es_ES
dc.description.sponsorship This research was funded by the Spanish Administration and the European Union under grant TEC2017-84743-P. es_ES
dc.language Inglés es_ES
dc.publisher MDPI AG es_ES
dc.relation.ispartof Entropy es_ES
dc.rights Reconocimiento (by) es_ES
dc.subject Surrogates es_ES
dc.subject Graph Fourier transform es_ES
dc.subject Hermitian Laplacian matrix es_ES
dc.subject.classification TEORIA DE LA SEÑAL Y COMUNICACIONES es_ES
dc.title A New Surrogating Algorithm by the Complex Graph Fourier Transform (CGFT) es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.3390/e21080759 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/TEC2017-84743-P/ES/METODOS INFORMADOS PARA LA SINTESIS DE SEÑALES/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Instituto Universitario de Telecomunicación y Aplicaciones Multimedia - Institut Universitari de Telecomunicacions i Aplicacions Multimèdia es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Comunicaciones - Departament de Comunicacions es_ES
dc.description.bibliographicCitation Belda, J.; Vergara Domínguez, L.; Safont Armero, G.; Salazar Afanador, A.; Parcheta, Z. (2019). A New Surrogating Algorithm by the Complex Graph Fourier Transform (CGFT). Entropy. 21(8):1-18. https://doi.org/10.3390/e21080759 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.3390/e21080759 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 18 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 21 es_ES
dc.description.issue 8 es_ES
dc.relation.pasarela S\408015 es_ES
dc.contributor.funder Agencia Estatal de Investigación es_ES
dc.description.references Schreiber, T., & Schmitz, A. (2000). Surrogate time series. Physica D: Nonlinear Phenomena, 142(3-4), 346-382. doi:10.1016/s0167-2789(00)00043-9 es_ES
dc.description.references Miralles, R., Vergara, L., Salazar, A., & Igual, J. (2008). Blind detection of nonlinearities in multiple-echo ultrasonic signals. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 55(3), 637-647. doi:10.1109/tuffc.2008.688 es_ES
dc.description.references Mandic, D. ., Chen, M., Gautama, T., Van Hulle, M. ., & Constantinides, A. (2008). On the characterization of the deterministic/stochastic and linear/nonlinear nature of time series. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 464(2093), 1141-1160. doi:10.1098/rspa.2007.0154 es_ES
dc.description.references Rios, R. A., Small, M., & de Mello, R. F. (2015). Testing for Linear and Nonlinear Gaussian Processes in Nonstationary Time Series. International Journal of Bifurcation and Chaos, 25(01), 1550013. doi:10.1142/s0218127415500133 es_ES
dc.description.references Borgnat, P., Flandrin, P., Honeine, P., Richard, C., & Xiao, J. (2010). Testing Stationarity With Surrogates: A Time-Frequency Approach. IEEE Transactions on Signal Processing, 58(7), 3459-3470. doi:10.1109/tsp.2010.2043971 es_ES
dc.description.references Shuman, D. I., Narang, S. K., Frossard, P., Ortega, A., & Vandergheynst, P. (2013). The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains. IEEE Signal Processing Magazine, 30(3), 83-98. doi:10.1109/msp.2012.2235192 es_ES
dc.description.references Sandryhaila, A., & Moura, J. M. F. (2013). Discrete Signal Processing on Graphs. IEEE Transactions on Signal Processing, 61(7), 1644-1656. doi:10.1109/tsp.2013.2238935 es_ES
dc.description.references Sandryhaila, A., & Moura, J. M. F. (2014). Big Data Analysis with Signal Processing on Graphs: Representation and processing of massive data sets with irregular structure. IEEE Signal Processing Magazine, 31(5), 80-90. doi:10.1109/msp.2014.2329213 es_ES
dc.description.references Pirondini, E., Vybornova, A., Coscia, M., & Van De Ville, D. (2016). A Spectral Method for Generating Surrogate Graph Signals. IEEE Signal Processing Letters, 23(9), 1275-1278. doi:10.1109/lsp.2016.2594072 es_ES
dc.description.references Sandryhaila, A., & Moura, J. M. F. (2014). Discrete Signal Processing on Graphs: Frequency Analysis. IEEE Transactions on Signal Processing, 62(12), 3042-3054. doi:10.1109/tsp.2014.2321121 es_ES
dc.description.references Shuman, D. I., Ricaud, B., & Vandergheynst, P. (2016). Vertex-frequency analysis on graphs. Applied and Computational Harmonic Analysis, 40(2), 260-291. doi:10.1016/j.acha.2015.02.005 es_ES
dc.description.references Dong, X., Thanou, D., Frossard, P., & Vandergheynst, P. (2016). Learning Laplacian Matrix in Smooth Graph Signal Representations. IEEE Transactions on Signal Processing, 64(23), 6160-6173. doi:10.1109/tsp.2016.2602809 es_ES
dc.description.references Perraudin, N., & Vandergheynst, P. (2017). Stationary Signal Processing on Graphs. IEEE Transactions on Signal Processing, 65(13), 3462-3477. doi:10.1109/tsp.2017.2690388 es_ES
dc.description.references Yu, G., & Qu, H. (2015). Hermitian Laplacian matrix and positive of mixed graphs. Applied Mathematics and Computation, 269, 70-76. doi:10.1016/j.amc.2015.07.045 es_ES
dc.description.references Gilbert, G. T. (1991). Positive Definite Matrices and Sylvester’s Criterion. The American Mathematical Monthly, 98(1), 44-46. doi:10.1080/00029890.1991.11995702 es_ES
dc.description.references Merris, R. (1994). Laplacian matrices of graphs: a survey. Linear Algebra and its Applications, 197-198, 143-176. doi:10.1016/0024-3795(94)90486-3 es_ES
dc.description.references Shapiro, H. (1991). A survey of canonical forms and invariants for unitary similarity. Linear Algebra and its Applications, 147, 101-167. doi:10.1016/0024-3795(91)90232-l es_ES
dc.description.references Futorny, V., Horn, R. A., & Sergeichuk, V. V. (2017). Specht’s criterion for systems of linear mappings. Linear Algebra and its Applications, 519, 278-295. doi:10.1016/j.laa.2017.01.006 es_ES
dc.description.references Mazumder, R., & Hastie, T. (2012). The graphical lasso: New insights and alternatives. Electronic Journal of Statistics, 6(0), 2125-2149. doi:10.1214/12-ejs740 es_ES
dc.description.references Baba, K., Shibata, R., & Sibuya, M. (2004). PARTIAL CORRELATION AND CONDITIONAL CORRELATION AS MEASURES OF CONDITIONAL INDEPENDENCE. Australian <html_ent glyph=«@amp;» ascii=«&amp;»/> New Zealand Journal of Statistics, 46(4), 657-664. doi:10.1111/j.1467-842x.2004.00360.x es_ES
dc.description.references Chen, X., Xu, M., & Wu, W. B. (2013). Covariance and precision matrix estimation for high-dimensional time series. The Annals of Statistics, 41(6), 2994-3021. doi:10.1214/13-aos1182 es_ES
dc.description.references Theiler, J., Eubank, S., Longtin, A., Galdrikian, B., & Doyne Farmer, J. (1992). Testing for nonlinearity in time series: the method of surrogate data. Physica D: Nonlinear Phenomena, 58(1-4), 77-94. doi:10.1016/0167-2789(92)90102-s es_ES
dc.description.references Schreiber, T., & Schmitz, A. (1996). Improved Surrogate Data for Nonlinearity Tests. Physical Review Letters, 77(4), 635-638. doi:10.1103/physrevlett.77.635 es_ES
dc.description.references MAMMEN, E., NANDI, S., MAIWALD, T., & TIMMER, J. (2009). EFFECT OF JUMP DISCONTINUITY FOR PHASE-RANDOMIZED SURROGATE DATA TESTING. International Journal of Bifurcation and Chaos, 19(01), 403-408. doi:10.1142/s0218127409022968 es_ES
dc.description.references Lucio, J. H., Valdés, R., & Rodríguez, L. R. (2012). Improvements to surrogate data methods for nonstationary time series. Physical Review E, 85(5). doi:10.1103/physreve.85.056202 es_ES
dc.description.references Schreiber, T. (1998). Constrained Randomization of Time Series Data. Physical Review Letters, 80(10), 2105-2108. doi:10.1103/physrevlett.80.2105 es_ES
dc.description.references Prichard, D., & Theiler, J. (1994). Generating surrogate data for time series with several simultaneously measured variables. Physical Review Letters, 73(7), 951-954. doi:10.1103/physrevlett.73.951 es_ES
dc.description.references Belda, J., Vergara, L., Salazar, A., & Safont, G. (2018). Estimating the Laplacian matrix of Gaussian mixtures for signal processing on graphs. Signal Processing, 148, 241-249. doi:10.1016/j.sigpro.2018.02.017 es_ES
dc.description.references Belda, J., Vergara, L., Safont, G., & Salazar, A. (2018). Computing the Partial Correlation of ICA Models for Non-Gaussian Graph Signal Processing. Entropy, 21(1), 22. doi:10.3390/e21010022 es_ES
dc.description.references Liao, T. W. (2008). Classification of weld flaws with imbalanced class data. Expert Systems with Applications, 35(3), 1041-1052. doi:10.1016/j.eswa.2007.08.044 es_ES
dc.description.references Song, S.-J., & Shin, Y.-K. (2000). Eddy current flaw characterization in tubes by neural networks and finite element modeling. NDT & E International, 33(4), 233-243. doi:10.1016/s0963-8695(99)00046-8 es_ES
dc.description.references Bhattacharyya, S., Jha, S., Tharakunnel, K., & Westland, J. C. (2011). Data mining for credit card fraud: A comparative study. Decision Support Systems, 50(3), 602-613. doi:10.1016/j.dss.2010.08.008 es_ES
dc.description.references Mitra, S., & Acharya, T. (2007). Gesture Recognition: A Survey. IEEE Transactions on Systems, Man and Cybernetics, Part C (Applications and Reviews), 37(3), 311-324. doi:10.1109/tsmcc.2007.893280 es_ES
dc.description.references Dardas, N. H., & Georganas, N. D. (2011). Real-Time Hand Gesture Detection and Recognition Using Bag-of-Features and Support Vector Machine Techniques. IEEE Transactions on Instrumentation and Measurement, 60(11), 3592-3607. doi:10.1109/tim.2011.2161140 es_ES
dc.description.references Boashash, B. (1992). Estimating and interpreting the instantaneous frequency of a signal. I. Fundamentals. Proceedings of the IEEE, 80(4), 520-538. doi:10.1109/5.135376 es_ES
dc.description.references Horn, A. (1954). Doubly Stochastic Matrices and the Diagonal of a Rotation Matrix. American Journal of Mathematics, 76(3), 620. doi:10.2307/2372705 es_ES


Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro sencillo del ítem