Impact of the Sakoe-Chiba Band on the DTW Time Series Distance Measure for kNN Classification

For classification of time series, the simple 1-nearest neighbor (1NN) classifier in combination with an elastic distance measure such as Dynamic Time Warping (DTW) distance is considered superior in terms of classification accuracy to many other more elaborate methods, including k-nearest neighbor (kNN) with neighborhood size k > 1. In this paper we revisit this apparently peculiar relationship and investigate the differences between 1NN and kNN classifiers in the context of time-series data and constrained DTW distance. By varying neighborhood size k, constraint width r, and evaluating 1NN and kNN with and without distance-based weighting in different schemes of cross-validation, we show that the first nearest neighbor indeed has special significance in labeled time-series data, but also that weighting can drastically improve the accuracy of kNN. This improvement is manifested by better accuracy of weighted kNN than 1NN for small values of k (3–4), better accuracy of weighted kNN than unweighted kNN in general, and reduced need to use large values of constraint r with weighted kNN.