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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

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2018

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Vol. 28, no. 4

719--733

EN

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.

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Graph-based generation of a meta-learning search space

Jankowski N.

International Journal of Applied Mathematics and Computer Science

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2012

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Vol. 22, no. 3

647-667

EN

Meta-learning is becoming more and more important in current and future research concentrated around broadly defined data mining or computational intelligence. It can solve problems that cannot be solved by any single, specialized algorithm. The overall characteristic of each meta-learning algorithm mainly depends on two elements: the learning machine space and the supervisory procedure. The former restricts the space of all possible learning machines to a subspace to be browsed by a meta-learning algorithm. The latter determines the order of selected learning machines with a module responsible for machine complexity evaluation, organizes tests and performs analysis of results. In this article we present a framework for meta-learning search that can be seen as a method of sophisticated description and evaluation of functional search spaces of learning machine configurations used in meta-learning. Machine spaces will be defined by specially defined graphs where vertices are specialized machine configuration generators. By using such graphs the learning machine space may be modeled in a much more flexible way, depending on the characteristics of the problem considered and a priori knowledge. The presented method of search space description is used together with an advanced algorithm which orders test tasks according to their complexities.

3

Neural methods of knowledge extraction

Duch W., Adamczak R., Grąbczewski K., Jankowski N.

Control and Cybernetics

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2000

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Vol. 29, no 4

997-1017

EN

Contrary to the common opinion, neural networks may be used for knowledge extraction. Recently, a new methodology of logical rule extraction, optimization and application of rule-based systems has been described. C-MLP2LN algorithm, based on constrained multilayer perceptron network, is described here in details and the dynamics of a transition from neural to logical system illustrated. The algorithm handles real-valued features, determining appropriate linguistic variables or membership functions as a part of the rule extraction process. Initial rules are optimized by exploring the accuracy/simplicity tradeoff at the rule extraction stage and the one between reliability of rules and rejection rate at the optimization stage. Gaussian uncertainties of measurements are assumed during application of crisp logical rules, leading to "soft trapezoidal" membership functions and allowing to optimize the linguistic variables using gradient procedures. Comments are made on application of neural networks to knowledge discovery in the benchmark and real life problems.