By T. Poggio, S. Smale (auth.), Professor Wesley Chu, Professor Tsau Young Lin (eds.)

With the growing to be use of knowledge expertise and the hot advances in internet structures, the volume of knowledge to be had to clients has elevated exponentially. therefore, there's a serious have to comprehend the content material of the information. therefore, data-mining has turn into a favored study subject in recent times for the therapy of the "data wealthy and data negative" syndrome. during this conscientiously edited quantity a theoretical beginning in addition to vital new instructions for data-mining study are offered. It brings jointly a collection of good revered information mining theoreticians and researchers with useful facts mining reviews. The provided theories will supply information mining practitioners a systematic viewpoint in information mining and hence offer extra perception into their difficulties, and the supplied new facts mining issues will be anticipated to stimulate additional study in those vital directions.

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Several rule extraction algorithms depend on training methods, that is, the rule extraction algorithms can extract rules only from the neural networks trained by a particular training method [5, 20]. The pedagogical algorithms basically do not depend on training methods. Computational complexity: Most algorithms are exponential in computational complexity. For example, in pedagogical algorithms, the total number of samples generated from a neural network is 2n , where n is the number of inputs to the neural network.

00 . x x . 01 10 11 Fig. 5. Approximation 32 H. Tsukimoto g(x, y) = g(0, 0)¯ xy¯ ∨ g(0, 1)¯ xy ∨ g(1, 0)x¯ y ∨ g(1, 1)xy g(x, y) = 0¯ xy¯ ∨ 1¯ xy ∨ 0x¯ y ∨ 1xy g(x, y) = x ¯y ∨ xy g(x, y) = y . Example 2. 4 . By approximating the function to a Boolean function g(x, y), g(0, 0) = 1, g(0, 1) = 0, g(1, 0) = 1, g(1, 1) = 0 . are obtained. The Boolean function g(x, y) is as follows: g(x, y) = g(0, 0)¯ xy¯ ∨ g(0, 1)¯ xy ∨ g(1, 0)x¯ y ∨ g(1, 1)xy g(x, y) = 1¯ xy¯ ∨ 0¯ xy ∨ 1x¯ y ∨ 0xy g(x, y) = x ¯y¯ ∨ x¯ y g(x, y) = y¯ .

The mathematical formulas are incomprehensible black boxes. A mathematical formula consisting of a few independent variables may be understandable. However, a mathematical formula consisting of a lot of independent variables cannot be understood. Moreover, in multivariate autoregression analysis, there are several mathematical formulas, and so the set of the mathematical formulas cannot be understood at all. Therefore, rule extraction from linear regression formulas is important. 3 Decision Trees When a class is continuous, the class is discretized into several intervals.