System Evaluation To evaluate the error probability of the designed Pattern Recognition System Resubstitution Method – Apparent Error Overoptimistic Holdout.

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System Evaluation To evaluate the error probability of the designed Pattern Recognition System Resubstitution Method – Apparent Error Overoptimistic Holdout Method - Unreliable Leave-one-out Method – Time Consuming Cross-Validation (Jack-Knife) Bootstrap Method – Biased, Smaller Variance but Time Consuming

Problem 10.2 on Page 480 In a two-class problem, the classifier to be used in the minimum Euclidean distance. Assume N i samples from class ω i for i=1,2. Show that the leave-one-out method estimate can be obtained from the resubstitution method if the distance of x from the class means d i (x), i=1,2, are modified as e i (x)=[N i /(N i -1)] 2 d i (x), if x belongs to ω i. Show that in this case, the leave-one-out method always results in larger error estimates than the resubstitution method.