Rule Extraction from Support Vector Machines: A Geometric Approach

Subject: T

References
(154)
7.1 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
7.2 Limitations and Future Work . . . . . . . . . . . . . . . . . . . . . 146 A Rule Sets 157
A.0.1 Monk's Problem . . . . . . . . . . . . . . . . . . . . . . . . . 157
A.0.2 Iris Plant Problem . . . . . . . . . . . . . . . . . . . . . . . 161
A.0.3 Breast Cancer Problem . . . . . . . . . . . . . . . . . . . . . 162
2.1 Boundary of two dichotomies . . . . . . . . . . . . . . . . . . . . . 12 2.2 The example of VC dimension . . . . . . . . . . . . . . . . . . . . . 16 2.3 The bound of risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4 Twoclass linear separable problem . . . . . . . . . . . . . . . . . . 20 2.5 Twoclass linear nonseparable problem . . . . . . . . . . . . . . . . 24 2.6 Mapping from original to feature space . . . . . . . . . . . . . . . . 26 2.7 The hyperplane of XOR problem in feature space. . . . . . . . . . . 30 2.8 Relations of two Lagrange multipliers ®1 and ®2 [40] . . . . . . . . 32 2.9 Using Rooted Binary DAG to decide the best class within four
classes [39]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.10 Hierarchical Clustering . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.11 The mean of di®erent N samples converges to the integral. . . . . 41 3.1 Two classes classi¯cation . . . . . . . . . . . . . . . . . . . . . . . . 46 3.2 Rules extracted from data groups . . . . . . . . . . . . . . . . . . . 46 3.3 Rule extraction system . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.4 A unit of ANN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.5 Rules extracted from a unit in Figure 3.4 . . . . . . . . . . . . . . . 51 3.6 Simple example of VIA algorithm in forward phase . . . . . . . . . 55 3.7 Rules extracted from a unit(Fig 3.6) . . . . . . . . . . . . . . . . . 55 3.8 a) Equationrule b) Interval rule [59] . . . . . . . . . . . . . . . . . 62
3.10 A twodimension example to get the cross points for the initial phase
of RulExSVM [58] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.17 RULE PRUNING function . . . . . . . . . . . . . . . . . . . . . . . 98 5.1 The accuracy of Monk1 under di®erent data size comparing with
that of SVM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.2 The accuracy of Monk2 under di®erent data size comparing with

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