Foundations of Wavelet Networks and Applications

Traditionally, neural networks and wavelet theory have been two separate disciplines, taught separately and practiced separately. In recent years the offspring of wavelet theory and neural networks-wavelet networks-have emerged and grown vigorously both in research and applications. Yet the material needed to learn or teach wavelet networks has remained scattered in various research monographs.Foundations of Wavelet Networks and Applications unites these two fields in a comprehensive, integrated presentation of wavelets and neural networks. It begins by building a foundation, including the necessary mathematics. A transitional chapter on recurrent learning then leads to an in-depth look at wavelet networks in practice, examining important applications that include using wavelets as stock market trading advisors, as classifiers in electroencephalographic drug detection, and as predictors of chaotic time series. The final chapter explores concept learning and approximation by wavelet networks.The potential of wavelet networks in engineering, economics, and social science applications is rich and still growing. Foundations of Wavelet Networks and Applications prepares and inspires its readers not only to help ensure that potential is achieved, but also to open new frontiers in research and applications.

PART AMATHEMATICAL PRELIMINARIESSetsFunctionsSequences and SeriesComplex NumbersLinear SpacesMatricesHilbert SpacesTopologyMeasure and IntegralFourier SeriesExercisesWAVELETSIntroductionDilation and TranslationInner ProductHaar WaveletMultiresolution AnalysisContinuous Wavelet TransformDiscrete Wavelet TransformFourier TransformDiscrete Fourier TransformDiscrete Fourier Transform of Finite SequencesConvolutionExercisesNEURAL NETWORKSIntroductionMultilayer PerceptronsHebbian LearningCompetitive and Kohonen NetworksRecurrent Neural NetworksWAVELET NETWORKSIntroductionWhat Are Wavelet NetworksDyadic Wavelet NetworkTheory of Wavelet NetworksWavelet Network StructureMultidimensional WaveletsLearning in Wavelet NetworksInitialization of Wavelet NetworksProperties of Wavelet NetworksScaling at Higher DimensionsExercisesPART BRECURRENT LEARNINGIntroductionRecurrent Neural NetworksRecurrent WavenetsNumerical ExperimentsConcluding RemarksExercisesSEPARATING ORDER FROM DISORDEROrder Within DisorderWavelet Networks: Trading AdvisorsComparison ResultsConclusionsExercisesRADIAL WAVELET NEURAL NETWORKSIntroductionData Description and PreparationClassification SystemsResultsConclusionsExercisesPREDICTING CHAOTIC TIME SERIESIntroductionNonlinear PredictionWavelet NetworksShort-Term PredictionParameter-Varying SystemsLong-Term PredictionConclusionsAcknowledgementsAppendixExercisesCONCEPT LEARNINGAn OverviewAn Illustrative Example of LearningIntroductionPreliminariesLearning AlgorithmsSummaryExercisesBIBLIOGRAPHYINDEX