Dynamic Time Warping

Dynamic time warping can be defined as an algorithm for gauging resemblance in amongst two sequences that might fluctuate in both speed and time. For example, similarities in the walking patterns may get be detected, no matter the media, for example video, a person appears to be just walking leisurely. Moreover, another person appears to be walking more hurriedly, despite decelerations and accelerations during the progression of one’s observation. This algorithm has got an application in several audios, graphics and video, any type of data having the ability to be turned to linear illustration can safely be analyzed by DTW. On key application is in the automatic speech recognition, to put up/ to handle dissimilar speaking speeds. In addition, to the above mentioned, applications include online signature recognition and speaker recognition can be abbreviated as DTW.

Generally speaking, DTW allows the computer to discovery an ideal match in between the two given sequences, such as in time series with some specific restrictions. The sequences get rather "warped" non-linearly during the time dimension in order to determine the measure of their resemblance independent of some specific non-linear variations in the time dimension. The sequence alignment method is mostly applied in this example, since it gives an illustration of an implementation of a DTW when the two sequences are strings of discrete symbols. Such as d(a, b), space in between the symbols, such as x(a, b) = | a - b |.

Dynamic Time Warping

The problem in recognizing words in a rather continuous human speech appears in order to include most of the significant features of pattern detection some time series.  Word recognition is commonly based on the matching of word templates alongside the waveform of an endless speech, and get converted to a discrete time series. Fruitful recognition approaches are always based on the ability to give an approximation matching of words in spite of wide disparities in pronunciation, timing and pronunciation. Lately, speech recognition researchers have applied the dynamic programming, just as the basis for isolation and connection and word recognition.

The technique of DTW applies a dynamic programming approach

In order to align time series and some specific word template, furthermore for some distance measure to get minimized. Because the time axis is getting stretched or rather compressed in order to achieve a sensible fit, template might match a more wide diversity of an actual time series. Precisely, the pattern detection task encompasses searching a time series, S, for example, of the template, T.

S =  si,s2 ,...,,~,...s n,                                                                                       (1)

T= t1 ,t2,...,tJ,...t m,                                                                                         (2)

These sequences in S and T can get arranged to form the n-by-m plane (see figure 1), in which each grid points, (i, j). Parallels the alignment in between elements si and tj. Warping

Path, W, aligns elements of S and T, in a way that the "distance" in between them is minimized.

W = wl, w2,...,wk

Meaning that W is a sequence of the grid points, in which each wk corresponds to the point (i, j)k.

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