The Research And The Application Of The Wavelet Neural Network

Wavelet transformation has the property of time-frequency localization and focusvariation, while the neural network has the property of self-study, self-adaptation,high stabilization, and error acceptability as well as popularization ability. So how tocombine the advantages of two techniques is the ever concern of people. Waveletnetwork is advanced to achieve the combination goal, which not only carries thecharacteristics of paralleling architecture, paralleling processing, distributedinformation storage, error acceptability, self-organization, self-adaptation andnon-linear and so on, but also has the faster speed and more precise of convergence,and has more perfect basic wavelet theory than any normal neural network. It iswidely used to treat signal, simulate function, forecast data, discriminate system,diagnostic ate fault, auto control, simulate the thinking of human etc.Traditional wavelet network is basically divided into three types, which is basedon continuous wavelet transformation, wavelet frame and orthogonal wavelettransformation separately. As for the wavelet neural network based on wavelet frame ,there is no problem of local extreme value because of the linear relationship betweenthe weight coefficients of the net and the output, and the choice of basis functions isflexible, so that the neural network based on wavelet frame has more useful value.However, because this kind of wavelet network uses the wavelet basis functions of thewavelet frame as the hidden layer nodes which are regularly cut out fromtime-frequency plane, the way usually causes the born network has the tremendousredundancy. The redundancy results in the network resources waste, usually causesdata's over match, and affects the network's turn ability. Moreover with the incrementof the input dimensions of network, the hidden layer nodes increase abruptly, thusobstructing it's application in high dimensional problems. So the optimization of thestructure of the neural network based on wavelet frame has great significance.