W. Duch, R. Adamczak, K. Grabczewski, and G. Zal, "Hybrid neural-global minimization method of logical rule extraction," Int. J. Adv. Comput. Intell., vol. 3, pp. 348--356, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....are described by 4 measurements (petal and sepal width and length) Two classes, Iris virginica and Iris versicolor, overlap, and therefore a perfect partition of the input space into separate classes is not possible. An optimal solution (from the point of view of generalization) contains 3 errors [10] and may be obtained using only two of the four input features (x 3 and x 4 ) therefore it is easy to display and only those two features have been left in simulations described below. A standard MLP solution is obtained with 4 hidden neurons and 3 output neurons. One discriminating plane per ....

Duch W, Adamczak R, Grzbczewski K, ral G, Hybrid neural-global minimization method of logical rule extraction, Journal of Advanced Computational

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W. Duch, R. Adamczak, K. Grabczewski, and G. Zal, "Hybrid neural-global minimization method of logical rule extraction," Int. J. Adv. Comput. Intell., vol. 3, pp. 348--356, 1999.

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W. Duch, R. Adamczak, K. Grabczewski, and G. Zal, "Hybrid neural-global minimization method of logical rule extraction," Int. J. Adv. Comput. Intell., vol. 3, pp. 348--356, 1999.

....[80] PVM 99.79 99.33 [80] SSV rules 99.79 99.33 our result FSM 10 rules 99.60 98.90 our result Cascade correl. 100.00 98.5 [89] MLP backprop 99.60 98.5 [89] 3 NN, 3 features used 98.7 97.9 our result Bayes 97.0 96.1 [80] k NN 95.3 [80] The C MLP2LN solution seems to be close to optimal [77]) Similar rules were obtained from the SSV separability criterion: R 1 : TSH 6.05# FTI 64.72# thyroid surgery=no R 2 : TSH 6.05# FTI 64.72# TT4 150.5 # thyroid surgery =no # on thyroxine=no These rules match our best results and have been found with fully automatic rule extraction ....

W. Duch, R. Adamczak, K. Grabczewski, G. Zal, Hybrid neural-global minimization method of logical rule extraction, Int. Journal of Advanced Computational Intelligence (in print)

....maximizes between class distances. Such functions allow to minimize in class and maximize between class distances (as it is done in the Fisher discrimnant analysis, cf. 1] and may be used in classification models that provide sharp, hyperrectangular decision borders, similar to logical systems [10], 11] Feature selection and weighting methods. S IMILARITY based algorithms faced with many features that are not necessary for predicting the desired output may perform quite poorly. We have developed several methods for feature selection and weighting, based on variants of the best first ....

W. Duch, R. Adamczak, K. Grabczewski, G. al, Hybrid neural-global minimization method of logical rule extraction. Journal of Advanced Computational Intelligence (in print)

....certainly worth using. Extraction of logical rules from data may be done using statistical, pattern recognition and machine learning methods, as well as neural network methods [3] Recently we have presented a complete methodology for extraction, optimization and application of logical rules [2] [4]. The last two steps are largely neglected in the literature, with current emphasis being still on the extraction methods. Logical rules require linguistic variables. Selection of linguistic variables for symbolic attributes is simple but for real valued attributes may be difficult. In such cases ....

W. Duch, R. Adamczak, K. Grabczewski, G. Zal, Hybrid neural-global minimization method of logical rule extraction, Int. Journal of Advanced Computational Intelligence (in print)

....are described by 4 measurements (petal and sepal width and length) Two classes, Iris virginica and Iris versicolor, overlap, and therefore a perfect partition of the input space into separate classes is not possible. An optimal solution (from the point of view of generalization) contains 3 errors [18] and may be obtained using only two of the four input features (x 3 and x 4 ) therefore results are easy to display and only those two features have been left in simulations described below. The data has been standardized and rescaled to fit inside a square with 1 corners. A standard MLP ....

Duch W, Adamczak R, Grabczewski K, Zal G, Hybrid neural-global minimization method of logical rule extraction, Journal of Advanced Computational Intelligence (in print, 1999)

....hypothyroid and normal (no hypothyroid) It has already been quite thoroughly examined with different systems. It seems impossible to find a better solution than the already known especially, that some of the results use global optimization strategies like ASA (adaptive simulated annealing [4]) Rules obtained from the separability criterion are: R 1 : TSH 6.05 # FTI 64.72 # thyroid surgery = 0# class 1 R 2 : TSH 6.05 # FTI 64.72 # thyroid surgery = 0 # on thyroxine = 0 # TT4 150.5 # class 2 R 3 : ELSE# class 3 These rules give very high accuracy, ....

....classifiers is still twice as large (1.5 ) as the error made by these simple rules. TABLE II Results for the hypothyroid dataset Method Train. error Test error k NN 4.73 Bayes 2.97 3.94 MLP backprop 0.40 1.55 Cascade correl. 0.00 1.52 C MLP2LN 0.32 0. 93 C MLP2LN rules ASA [4] 0.11 0.64 PVM 0.21 0.67 CART 0.21 0.64 SSV rules 0.21 0.67 C. Other datasets We have also tested our method on some other datasets such as Wisconsin breast cancer, Cleveland heart and mushrooms data. For the Wisconsin breast cancer data we have obtained a very simple (compared to ....

W. Duch, R. Adamczak, K. Gr abczewski and G. Zal, Hybrid neural-global minimization method of logical rule extraction, Int. Journal of Advanced Computational Intelligence (in print, 1999)

....classification system. Extraction of logical rules from data may be done using statistical, pattern recognition and machine learning methods, as well as neural network methods [3] Recently we have presented a complete methodology for extraction, optimization and application of logical rules [2] [4]. The last two steps are largely neglected in the literature, with current emphasis being still on the extraction methods. Previously we have used global minimization methods for optimization of linguistic variables for real valued attributes. Although such method work well they are ....

....Results on benchmark and real world datasets are presented in the fourth section and in the last section conclusions are given. Neural rule extraction methodology N EURAL methodology of crisp logical rule extraction developed by our group has been described in a series of papers [1] 2] [4], 10] 13] therefore only a very brief summary is given here. Selection of linguistic variables. Linguistic variables used by us are context dependent, i.e. they may be different in each rule (more on the linguistic variables [14] For realvalued attributes intervals defining linguistic ....

W. Duch, R. Adamczak, K. Grabczewski, G. Zal, Hybrid neuralglobal minimization method of logical rule extraction, Int. Journal of Advanced Computational Intelligence (in print)

....only one parameter s was optimized [12] Optimization of the positions of the reference centers R j leads to the LVQ method [13] in which the training set is used to define the initial prototypes and the minimal distance rule to assign the classes. The Restricted Coulomb Energy (RCE) classifier [14] 5 uses a hard sphere weighting functions. The Feature Space Mapping model (FSM) is based on separable, rather than radial weighting functions [15] All these models are special cases of general SBM framework. An important problem with localized description of the data by RBF and similar methods ....

....Kanal, eds, Handbook of statistics 2: classification, pattern recognition and reduction of dimensionality. North Holland, Amsterdam, 1982. 12] P.D. Wasserman, Advanced methods in neural networks. Van Nostrand Reinhold, 1993. 13] T. Kohonen, Self organizing maps. Berlin, Springer Verlag, 1995. [14] D.L. Reilly, L.N. Cooper, C. Elbaum, A neural model for category learning, Biological Cybernetics 45 (1982) 35 41 [15] W. Duch, G.H.F. Diercksen, Feature Space Mapping as a universal adaptive system. Comp. Phys. Communic 87 (1995) 341 371 [16] R.P. Lippmann, An introduction to computing with ....

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Duch W, Adamczak R, Grabczewski K, Zal G, Hybrid neural-global minimization method of logical rule extraction, Journal of Advanced Computational Intelligence (in print)

....are described by 4 measurements (petal and sepal width and length) Two classes, Iris virginica and Iris versicolor, overlap, and therefore a perfect partition of the input space into separate classes is not possible. An optimal solution (from the point of view of generalization) contains 3 errors [14] and may be obtained using only two of the four input features (x 3 and x 4 ) therefore results are easy to display and only those two features have been left in simulations described below. A standard MLP solution is obtained with 4 hidden neurons and 3 output neurons. One discriminating plane ....

Duch W, Adamczak R, Grabczewski K, Zal G, Hybrid neural-global minimization method of logical rule extraction, Journal of Advanced Computational Intelligence (in print)

....gradient based methods it is often easier to obtain good results with larger networks than with small ones. Global minimization should be especially useful for smaller networks. The use of global methods should also improve the quality of logical rules extracted with the help of neural networks [22]. Only a few global optimization methods have been applied so far to neural networks. Many methods are buried in the literature on engineering, financial, physical or chemical optimization problems and are virtually unknown to neural networks experts. The problem of unconstrained global ....

.... Alopex algorithm has been tested so far only on a few problems with very good results, for example it has learned to solve quite large parity problems, it also solved all the standard machine learning benchmark, i.e. the 3 Monk s problems [40] with 100 accuracy (except for our MLP2LN approach [22, 41] this is the only network that was able to do it) but no results on the real world noisy data have been reported so far. 4 REACTIVE TABU SEARCH The reactive tabu search (both spellings, tabu and taboo are in use) is based on a very simple idea [42, 43] The search is started at a random ....

W. Duch, R. Adamczak, K. Grabczewski and G. Zal, Hybrid neural-global minimization method of logical rule extraction. Journal of Advanced Computational Intelligence, 1998 (in print).

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W. Duch, R. Adamczak, K. Grabczewski, and G. Zal. Hybrid neural-global minimization method of logical rule extraction. J. Advanced Computational Intelligence, 3:348-356, 1999.

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