Learning Algorithms for a Neural network with Laterally Inhibited Receptive Fields By IEEE Neural Networks Council
Neural networks have been established as a general tool for approximation and classification by fitting inputloutput data effectively into nonlinear models. The multilayer perceptron, in which a neuron receives inputs from all the neurons in the adjacent pre-layer, is widely used for function approximation and signal classification. On most occasions it performs quite satisfactorily. However, when the network input is characterized by time-frequency localized features, the generally used multilayer perceptron with unconstrained global connections between the adjacent layers does not work well. In the human visual system there exist example models for dealing with this problem [l]. That is the conception of receptive field, the shape of which can be adapted with the visual input under certain constraints. In the human visual system there are various receptive fields of different shapes. For example, there are Gauss function shaped receptive fields for local smoothing, and Gabor function shaped receptive fields for combining local smoothing and sharpening which provides the function of lateral inhibition. We find that this kind of receptive fields can not be formed automatically by learning without any constraints on the weights in a multilayer perceptron.
Wavelet transform is a good model for the receptive fields in the human visual system [2]. Because a wavelet function satisfies the admissibility condition [3], it must be oscillatory across its zero points. Hence, wavelet hctions provide natural models for laterally inhibited receptive fields, which are good at extracting time-frequency localized features. Actually, Gabor function has been widely used in theoretical studies of the primary visual information processing such as lateral inhibition and it can be regarded as a mother wavelet of good time-frequency localization properties. Through dilation and translation a wavelet filter bank can be formed as a group of receptive fields which approximately perform wavelet transforms. Hence, in the design of receptive fields we can benefit from the advanced theory of wavelet transforms.
There have been several pieces of work done on combining neural networks with wavelet transforms which perform as the receptive fields of hidden neurons. Szu [4] developed neural network adaptive wavelets for signal representation and classification, and tentatively applied them in phoneme recognition and image compression. Gan [5] proposed a wavelet neural network architecture and applied it to ECG signal classification. Dickhaus [6] and Akay [7] have also studied biomedical signal detection and classification using different wavelet network structures. The key issue in the design of this kind of neural networks is how to obtain optimal sets of dilation and translation parameters (or wavelet parameters). In all the networks mentioned above, continuous wavelet parameters are used and trained by the gradient-descent learning algorithm, or preset and fixed wavelets are applied. Because of the inherent oscillatory property of the wavelet function, learning wavelet parameters is easy to sink into local minima and it is difficult to get the optimal result. In this paper, we use Gabor function to constrain the receptive fields of the hidden neurons so that the lateral inhibition is introduced into the network. Furthermore, discrete wavelets are used and a method for calculating wavelet parameters is proposed to combat the problem of unconvergence in the learning process.
The remainder of this paper is organized as follows. The neural network formulation is put forward in section 2. Two learning algorithms are proposed in section 3. Simulation studies on ECG signal classification are carried out in section 4, followed by discussions and conclusions in section 5.
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