Entropy Based k Nearest Neighbor Pattern Classification (EbkNN): En-route to Achieving a High Accuracy in Breast Cancer Diagnosis

Abstract

Entropy based k-Nearest Neighbor pattern classification (EbkNN) is a variation of the conventional k-Nearest Neighbor rule of pattern classification, which exclusively optimizes the value of k-neighbors for each test data based on the calculations of entropy. The formula for entropy used in EbkNN is the one that has been defined popularly in information theory for a set of n different types of information (class) attached to a total of m objects (data points) with each object defined by f features. In EbkNN that value of k is chosen for discrimination of given test data for which the entropy is the least non-zero value. Other rules of conventional kNN are retained in EbkNN. It is concluded that EbkNN works best for binary classification. It is computationally prohibitive to use EbkNN for discriminating the data points of the test dataset into number of classes greater than two. The biggest advantage of EbkNN vis-à-vis the conventional kNN is that in one single run of EbkNN algorithm we get optimum classification of test data. But conventional kNN algorithm has to be run separately for each of the selected range of values of k, and then the optimum k to be chosen from amongst them. We also tested our EbkNN method on WDBC (Wisconsin Diagnostic Breast Cancer) dataset. There are 569 instances in this dataset and we made a random choice of first 290 instances as training dataset and the rest 279 instances as test dataset. We got an exceptionally remarkable result with EbkNN method- accuracy close to 100% and better than the ones got by most of the other researchers who worked on WDBC dataset.