Exact Mean Computation in Dynamic Time Warping Spaces

Dynamic time warping constitutes a major tool for analyzing time series. In particular, computing a mean series of a given sample of series in dynamic time warping spaces (by minimizing the Fr\'echet function) is a challenging computational problem, so far solved by several heuristic and inexact strategies. We spot some inaccuracies in the literature on exact mean computation in dynamic time warping spaces. Our contributions comprise an exact dynamic program computing a mean (useful for benchmarking and evaluating known heuristics). Based on this dynamic program, we empirically study properties like uniqueness and length of a mean. Moreover, experimental evaluations reveal substantial deficits of state-of-the-art heuristics in terms of their output quality. We also give an exact polynomial-time algorithm for the special case of binary time series

Online and Offline Character Recognition Using Alignment to Prototypes

Nearest neighbor classifiers are simple to implement, yet they can model complex non-parametric distributions, and provide state-of-the-art recognition accuracy in OCR databases. At the same time, they may be too slow for practical character recognition, especially when they rely on similarity measures that require computationally expensive pairwise alignments between characters. This paper proposes an efficient method for computing an approximate similarity score between two characters based on their exact alignment to a small number of prototypes. The proposed method is applied to both online and offline character recognition, where similarity is based on widely used and computationally expensive alignment methods, i.e., Dynamic Time Warping and the Hungarian method respectively. In both cases significant recognition speedup is obtained at the expense of only a minor increase in recognition error.Office of Naval Research (N00014-03-1-0108); National Science Foundation (IIS-0308213, EIA-0202067