BI-DIRECTIONAL FUNCTION LEARNING METHOD FOR TIME SERIES PREDICTION
Hiroki Tamura, Koichi Tanno, Hisasi Tanaka, Zongmei Zhang · 2008
Abstract. The local linear wavelet neural network is an improvement of wavelet net-work and commonly used learning algorithm is gradient descent method. In this paper, weattempt to predict sunspots, Mackey-Glass time series and Box-Jenkins data using a locallinear wavelet neural network. Furthermore, we propose a technique using bi-directionalfunction learning method. The simulation results show the effectiveness of the proposedmethod.Keywords: Local linear wavelet neural network, Local search, Bi-directional function,Sunspots data, Mackey-glass time series, Box-Jenkins data 1. Introduction. The wavelet theory whichoffers efficient algorithms for numericalanal-ysis, signal processing and other applications, are usually limited to applications of smalldimension wavelets because of the dimension problems. Artificial neural networks whichare powerful tool for handling problems of large dimension suffer from the lack of efficientconstructive methods. The wavelet neural networks (abbr. WNN), first mentioned byZhang [1, 2], overcame the disadvantages of both wavelet theory applications and neuralnetworks. The local linear wavelet neural network (abbr. LLWNN) [3, 4] is an improve-ment of the WNN, in which the connection weights between the hidden layer neurons andoutput neurons are replaced by a local linear model.One of the most frequently used learning algorithm for WNN is the gradient descentmethod. Weight Perturbation [5] is a neural network training technique based on gradientdescent. The gradient of the Mean Square Error (MSE) with respect to a weight isapproximated by applying a small perturbation. Local Search Method (abbr. LS) is aheuristic algorithm like the gradient descent method. However, many models and learningalgorithm for time series prediction have the over-learning problem.In this paper, we attempt to predict sunspots, Mackey-Glass time series and Box-Jenkins data using LLWNN and LS. Furthermore, we propose a technique using bi-directional function learning method. The over-learning problem can be eased by usingbi-directional function learning method. The simulation results show that the propsedmethod using bi-directional function learning method improves from original LLWNN.2. Local Linear Wavelet Neural Network. According to wavelet transformation the-ory, wavelets are a family of functions generated from one function ψ(x) (called the motherwavelet) by the operation of dilation and translation as follows:Ψ=½Ψ