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A standard, currently popular solution to the matching of patterns requiring time warping is the use of dynamic programming, for example, for recognizing discrete utterances, as disclosed by F. Itakura .
English (United States)
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Fast, Accurate Metric in Time Warping, Dynamic Programming Recognizers
A standard, currently popular solution to the matching of patterns requiring
time warping is the use of dynamic programming, for example, for recognizing
discrete utterances, as disclosed by F. Itakura .
The optimum distance metric for normally distributed data with zero
covariance terms is described by N. J. Nilsson  and is as follows:
The proposed metric is an approximation of the above metric which retains
both mean and variance terms:
This metric has been found to be both fast and accurate for matching
patterns requiring time warping in dynamic programming recognition procedures.
The metric is accurate due to its retention of a measure of both the mean and
standard deviation at each time point. A fast metric results from a reduction in
the number of multiplications represented in the optimal metric.
The data consists of a time sequence of subpatterns. During a training
procedure, mu(ijk) and delta(ijk) are computed and stored for each prototype 1,
parameter j and time point k.
The distance metric between time point k of prototype i and time point l of the
As shown in the figure, the dynamic programming algorithm computes an
optimal path and corresponding overall metric between the candidate time
sequence and each of the prototype time sequences. The overall metric for
prototype i is: