Author:  Pang, Takhing William 
Title:  Speaker verification using optimized radial basis function networks 
Degree:  M.Sc. 
Year:  1998 
Subject:  Speech processing systems Automatic speech recognition Neural networks (Computer science) Hong Kong Polytechnic University  Dissertations 
Department:  Multidisciplinary Studies Dept. of Electronic Engineering 
Pages:  v, 56 leaves : ill. ; 30 cm 
Language:  English 
InnoPac Record:  http://library.polyu.edu.hk/record=b1425843 
URI:  http://theses.lib.polyu.edu.hk/handle/200/3177 
Abstract:  Radial Basis Function (RBF) networks provide an alternative approach to pattern classification. The Radial basis function (RBF) networks were introduced by Broomhead and Lowe (in 1988) and were known to be a universal approximator. These networks approximate an unknown function by overlapping localized regions formed by radially symmetric kernel functions to create complex decision boundaries over the sample data of the input space. Due to the localized nature of the network training vectors, standard clustering algorithm such as the Kmeans clustering is often used to determine the centers of the kernel functions. The widths of the RBF units are usually determined by the Knearest neighbor algorithm. The output weights can be obtained using the technique of singular value decomposition. The elliptical basis function (EBF) networks, whose kernel functions have an elliptical form, can be considered as an extension of the RBF networks. The EBF networks use full covariance matrices instead of diagonal ones in the basis functions. It is believed that the elliptical kernel functions can provide a better representation of the input vectors and therefore a higher classification accuracy is achievable. In this thesis, a learning algorithm for constructing and optimizing radial basis function networks is proposed. The algorithm takes the advantage of an EBF network by extending the diagonal covariance matrices of an RBF network to full covariance matrices. The algorithm improves the network performance through refining the clustering geometry of the basis functions. The results of the proposed algorithm were demonstrated through a noisy XOR problem. We have also implemented a node insertion algorithm to determine the optimal number of hidden nodes of an RBF network. The total mean squared error (MSE) and the recognition accuracy of a general classifier were used to determine when a new hidden node should be inserted. The result shows that the proposed learning algorithm was able to generate a network with appropriate elliptical kernel functions and improve the performance in terms of MSE and recognition accuracy. The learning algorithm has also been applied to speaker verification where the algorithm is generalized to a twelvedimensional problem. The hidden node insertion algorithm has been applied to speaker verification to determine the optimal number of hidden nodes for the network of each speaker. The optimal network topology was selected based on the error performance of the speaker verification system. The resulting networks save computation time and have a higher generalization capability. We compare the false rejection rate (FRR) and the false acceptance rate (FAR) of optimized RBF networks with that of the standard RBF networks. The results show that inserting extra nodes in the networks do not significantly improve the verification performance despite the extra computation effort. 
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