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Comparison of prototype selection algorithms used in construction of neural networks learned by SVD

Jankowski N.

International Journal of Applied Mathematics and Computer Science

2018

Vol. 28, no. 4

719--733

Radial basis function networks (RBFNs) or extreme learning machines (ELMs) can be seen as linear combinations of kernel functions (hidden neurons). Kernels can be constructed in random processes like in ELMs, or the positions of kernels can be initialized by a random subset of training vectors, or kernels can be constructed in a (sub-)learning process (sometimes by k-means, for example). We found that kernels constructed using prototype selection algorithms provide very accurate and stable solutions. What is more, prototype selection algorithms automatically choose not only the placement of prototypes, but also their number. Thanks to this advantage, it is no longer necessary to estimate the number of kernels with time-consuming multiple train-test procedures. The best results of learning can be obtained by pseudo-inverse learning with a singular value decomposition (SVD) algorithm. The article presents a comparison of several prototype selection algorithms co-working with singular value decomposition-based learning. The presented comparison clearly shows that the combination of prototype selection and SVD learning of a neural network is significantly better than a random selection of kernels for the RBFN or the ELM, the support vector machine or the kNN. Moreover, the presented learning scheme requires no parameters except for the width of the Gaussian kernel.

Kernel Ho-Kashyap classifier with generalization control

Łęski J.

International Journal of Applied Mathematics and Computer Science

2004

Vol. 14, no 1

53-61

This paper introduces a new classifier design method based on a kernel extension of the classical Ho-Kashyap procedure. The proposed method uses an approximation of the absolute error rather than the squared error to design a classifier, which leads to robustness against outliers and a better approximation of the misclassification error. Additionally, easy control of the generalization ability is obtained using the structural risk minimization induction principle from statistical learning theory. Finally, examples are given to demonstrate the validity of the introduced method.