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k-Nearest Neighbor Method

k-nearest neighbor (kNN) classifiers, as described in Section 1.7.1 (p. [*]) were implemented using the Matlab M-files in Section 5.6 (p. [*]). Features were grouped by class and then a fixed number of instances from each class were randomly assigned to the training (40 instances from each class), pick (20 instances from each class), and test (remaining 13 to 38 instances from each class) sets. The mean and standard deviation of each feature were calculated using the instances assigned to the training set. These values were then used to normalize the training data to have a mean of 0 and a variance of 1. The mean and standard deviation of the training data were also used to normalize the pick and test sets. This normalization step was included so that all features contributed equally to the Euclidean distance metric used to define nearest neighbors.

To find the best value of k for each of the ten classifiers, the pick data were classified using the training data and a range of k values from one to ten. The best value of k was defined to be the one that resulted in the largest average correct classification rate. This value of k and the training data were then used to classify the test data. This procedure was repeated ten times for each set of features evaluated, resulting in ten kNN classifiers for a given set of features. The classification for a particular test instance was defined by the class from which a plurality of its k nearest neighbors were derived. In the case of a tie (i.e., two or more classes were equally common in the list of the k nearest neighbors), the test instance was assigned to the `unknown' class.

The results from each of the 10 kNN classifiers were summarized with a confusion matrix. The entries in the 10 confusion matrices were summed across all classifiers in the trial and converted to percentages. A second number was generated for each diagonal element which was the percentage of the classification attempts (number of instances in the test set minus those that were classified as unknowns) that were successful. Overall performance of all 10 classifiers used with each feature set was summarized by calculating the mean and variance of the classification rates from each individual classifier. Each of these classification rates was calculated as the mean of the diagonal elements (correct classifications) from a confusion matrix generated from one of the 10 trials.


next up previous contents
Next: Results Up: Materials and Methods Previous: Back-Propagation Neural Network
Copyright ©1999 Michael V. Boland
1999-09-18