Selection of RBF Neural Network Parameters Based on Normalized Cut Clustering

Masoumeh Mohseni1, Reza Ghaderi2, Alireza Asvadi3,and Mehdi Ezoji4
1,3,4 Babol University of Technology,
Shahid Beheshti University

Abstract:

Nearly 25 years ago, Radial Basis Function Network (RBFN) which adopts the radial basis functions as its activation function of hidden neurons was introduced into the neural network literature by Broomhead and Lowe. Since then, RBFNs have been applied to a variety of applications namely, interpolation and classification. The increasing popularity of RBF networks in many fields is mainly due to their ability to learn the complex nonlinear mapping between the input-output data and generalize them. An important question is: how to construct an RBFN classifier with the fewest number of hidden units and with the highest generalization ability. 
This paper presents a two-phase learning method for constructing RBFNs. The proposed approach reduces the complexity of RBFNs by reducing the number of hidden units in comparison with conventional RBFN generated by k-means method. One of the limitations of k-means clustering is its trend to fall into the local minimum that depends on the initial selection of cluster centers. Another drawback to k-means is that it cannot separate clusters that are non-linearly separable in input space. Therefore, the result can produce a large RBFN which is not optimum. Spectral clustering has emerged recently as a popular clustering method that can separate non-linearly separable clusters in the input space. Spectral clustering uses the eigenvectors of an affinity matrix derived from the data to obtain a clustering of the data. Here normalized cut as a special case of spectral clustering is used for constructing an RBF network classifier. Normalized cut clustering is used for determining center and width of Radial Basis Functions. It leads to constructing an RBF network classifier with reduced number of hidden layer neurons in comparison with conventional RBF network obtained by k-means method. The well-known pseudo inverse method is used to adjust the weights of the output layer of RBF network. Quantitative and qualitative evaluations show that the proposed method reduces the number of hidden units and preserves classification accuracy in comparison with conventional RBF network generated by k-means method.

Paper:
M. Mohseni, R. Ghaderi, A. Asvadi, and M. Ezoji, “Selection of RBF Neural Network Parameters Based on Normalized Cut Clustering,” Journal of Soft Computing and Information Technology (JSCIT) , vol. 3, no. 4, pp. 48-54, 2015.
[link to pdf]

Code:

The code runs on Windows XP with MATLAB R2010a.
[Code]

Data:

Crab gender dataset, breast cancer data set and glass chemical dataset from the Neural Network toolbox and Haberman’s Survival Data Set, Parkinsons DataSet and Liver Disorders Data Set available online at UCI Machine Learning Repository.

Result:

The first to the fourth rows demonstrate some of the results from the k-means method where k varies between 2 and 5 and the last row shows the results of normalized cut method for k = 2. Column (a) shows the obtained clusters and their center and width for determining center and width of hidden layer neurons of RBF network. Column (b) shows the output of RBF network. By choosing threshold (0.5) from the output of RBF network (that is between 0 to 1), the results of classifying obtained and is shown in column (c). Bias of RBF network in both cases is withdrawn for simplicity.

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