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By H V Geramb

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Extra info for Medium energy nucleon and antinucleon scattering : proceedings of the international symposium ; Bad Honnef, June 18-21, 1985

Example text

60 by the accuracy while the performance to partially matched data is evaluated by the robustness. Therefore, the classifier with high robustness would perform well in the accuracy. On the other hand, the relation between the number of induced rules and the robustness can be understood from the fact that the classifier with the more independent rules will perform better against data with missing values because some other rule could be fired even if a rule could not be fired by the missing value.

Execute S TEP 2 of Algorithm 1. S TEP 3. Update di,k as di,k = (ek − Wi )T Kβ (ek − Wi ). S TEP 4. If di,k < 0, update Δ β , di,k , β , and Kβ as: (19) Δ β = max{−di,k / ek − Wi 22 }, (20) (21) di,k ← di,k + Δ β ek − Wi 2 , β ← β + Δβ, (22) Kβ ← Kβ + Δ β E. (23) S TEP 5. Execute S TEP 4 of Algorithm 1. S TEP 6. If the stopping criterion is satisfied, terminate this algorithm. Otherwise, return to S TEP 2. Another option for handling indefinite kernel data is to apply K-FCM to a positive semi-definite matrix K , which is modified from K in the following two ways.

Here, R is a matrix whose (k, j)-th element is Rk, j . Let C denote the cluster number. The goal of RFCM and NERFCM is obtaining the membership by which the datum xk belongs to the i-th cluster, denoted by ui,k , from R. u ∈ RC×N is referred to as the partition matrix. RFCM is obtained by solving the optimization problem C minimizeu ∑ m ∑Nk=1 ∑Nj=1 um i,k u j,k Rk, j N 2 ∑t=1 um i,t i=1 C subject to (1) , ∑ ui,k = 1, (2) i=1 where m > 1 is a fuzzifier parameter. The RFCM procedure is as follows.

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