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5  Parameter Estimation                                      21 1




                                                                              (5.89)


                   Substituting  (5.82)-(5.89) into (5.70), v of  (5.71) becomes

                                                                              (5.90)


                   where






















                   Since  ,f,(X,w) is  a  linear  combination  of  xf. (k I2), v,- can  be  theoretically
                   computed for Data I-I, resulting  in

                                                                              (5.92)



                        Equation  (5.92)  was  experimentally  verified  in  the  same  manner  as
                   (5.81).  The results are shown in Table 5-7.
                        Experiment 5: Error of  the linear classifier
                             Data: 1-1 (Normal, MTM = 2.562, E  = 10%)
                             Dimensionality:  n  = 4, 8, 16, 32, 64
                             Classifier:  Linear classifier of  (5.55)
                             Design samples:  YI = y.2  = kn, k  = 3, 5, 10, 20,  40
                             Tcst:  Theoretical  using the normal error table
                             No. of  trials:  z = 10
                             Results: Table 5-7 [4]
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