Asymmetric learning vector quantization for efficient nearest neighbor classification in dynamic time warping spaces

The nearest neighbor method together with the dynamic time warping (DTW) distance is one of the most popular approaches in time series classification. This method suffers from high storage and computation requirements for large training sets. As a solution to both drawbacks, this article extends learning vector quantization (LVQ) from Euclidean spaces to DTW spaces. The proposed generic LVQ scheme uses asymmetric weighted averaging as update rule. We theoretically justify the asymmetric LVQ scheme via subgradient techniques and by the margin-growth principle. In addition, we show that the decision boundary of two prototypes from different classes is piecewise quadratic. Empirical results exhibited superior performance of asymmetric generalized LVQ (GLVQ) over other state-of-the-art prototype generation methods for nearest neighbor classification.