Revisiting a Nearest Neighbor Method for Shape Classification

Abstract

The nearest neighbor method is a simple and flexible scheme for the classification of data points in a vector space. It predicts a class label of an unseen data point using a majority rule for the labels of known data points inside a neighborhood of the unseen data point. Because it sometimes achieves good performance even for complicated problems, several derivatives of it have been studied. Among them, the discriminant adaptive nearest neighbor method is particularly worth revisiting to demonstrate its application. The main idea of this method is to adjust the neighbor metric of an unseen data point to the set of known data points before label prediction. It often improves the prediction, provided the neighbor metric is adjusted well. For statistical shape analysis, shape classification attracts attention because it is a vital topic in shape analysis. However, because a shape is generally expressed as a matrix, it is non-trivial to apply the discriminant adaptive nearest neighbor method to shape classification. Thus, in this study, we develop the discriminant adaptive nearest neighbor method to make it slightly more useful in shape classification. To achieve this development, a mixture model and optimization algorithm for shape clustering are incorporated into the method. Furthermore, we describe several helpful techniques for the initial guess of the model parameters in the optimization algorithm. Using several shape datasets, we demonstrated that our method is successful for shape classification.