A Competitive Wavelet Network for Signal Clustering

FAST LEARNING ALGORITHM OF WAVELET NETWORK BASED ON FAST WAVELET TRANSFORM

In this paper, a novel learning algorithm of wavelet networks based on the Fast Wavelet Transform (FWT) is proposed. It has many advantages compared to other algorithms, in which we solve the problem in previous works, when the weights of the hidden layer to the output layer are determined by applying the back propagation algorithm or by direct solution which requires to compute the matrix inversion, this may cause intensive computation when the learning data is too large. However, the new algorithm is realized by iterative application of FWT to compute the connection weights. Furthermore, we have extended the novel learning algorithm by using Levenberg–Marquardt method to optimize the learning functions. The experimental results have demonstrated that our model is remarkably more refreshing than some of the previously established models in terms of both speed and efficiency.

Efficient object recognition using boundary representation and wavelet neural network

Wavelet neural networks combine the functions of time-frequency localization from the wavelet transform and of self-studying from the neural network, which make them particularly suitable for the classification of complex patterns. In this paper, an efficient object recognition method using boundary representation and the wavelet neural network is proposed. The method employs a wavelet neural network (WNN) to characterize the singularities of the object curvature representation and to perform the object classification at the same time and in an automatic way. The local time-frequency attributes of the singularities on the object boundary are detected by making a preliminary wavelet analysis of the curvature representation. Then, the discriminative scale-translation features of the singularities are stored as the initial scale-translation parameters of the wavelet nodes in the WNN. These parameters are trained to their optimum status during the learning stage. With our approach, as opposed to matching features by convolving the signal with wavelet functions at a large number of scales, the computational burden is significantly reduced. Only a few convolutions are performed at the optimum scale-translation grids during the classification, which makes it suitable for real-time recognition tasks. Compared with the artificial-neural-network-based approaches preceded by wavelet filter banks with fixed scale-translation parameters, the support vector machine (SVM) using traditional Fourier descriptors and K-nearest-neighbor ( K-NN) classifier based on the state-of-the-art shape descriptors, our scheme demonstrates superior and stable discrimination performance under various noisy and affine conditions.

A probabilistic wavelet system for stochastic and incomplete data-based modeling

A probabilistic wavelet system (PWS) is proposed to model the unknown dynamic system with stochastic and incomplete data. When compared with the traditional wavelet system, the PWS uses a novel three-domain wavelet function to make a balance among the probability, time, and frequency domains, which achieves a robust modeling performance with poor data information. The definition, transformation, multiple-resolution analysis, and implementation of the PWS are presented to construct the whole theoretical framework. Simulation studies show that the performance of the proposed PWS is superior to the traditional one in a stochastic and incomplete data environment.

Pulse waveforms classification based on wavelet network

This paper proposes a new algorithm to classify pulse waveforms based on discrete wavelet network. This paper selects 4-order discrete Daubechies wavelet as the wavelet node of this wavelet network to classify six pulse patterns distinctive in shape. 600 pulse records are used to train this wavelet network and 300 pulse records are used to test the classifier's performance. The test results show that this approach has 83% agreement rate with the experienced experts. Compared with traditional classification methods, it needs not the experience in feature extraction.