Dynamic Time Warping (DTW)

Standard DTW

mlpy.dtw_std(x, y, dist_only=True)

Standard DTW as described in [Muller07], using the Manhattan distance (absolute value of the difference) as local cost measure.

Parameters :

x : 1d array_like object (N)

first sequence

y : 1d array_like object (M)

second sequence

dist_only : bool

compute only the distance

Returns :

dist : float

unnormalized minimum-distance warp path between sequences

cost : 2d numpy array (N,M) [if dist_only=False]

accumulated cost matrix

path : tuple of two 1d numpy array (path_x, path_y) [if dist_only=False]

warp path

[Muller07]

(1, 2) M Muller. Information Retrieval for Music and Motion. Springer, 2007.

Example

Reproducing the Fig. 2 example in [Salvador04].

>>> import mlpy
>>> import matplotlib.pyplot as plt
>>> import matplotlib.cm as cm
>>> x = [0,0,0,0,1,1,2,2,3,2,1,1,0,0,0,0]
>>> y = [0,0,1,1,2,2,3,3,3,3,2,2,1,1,0,0]
>>> dist, cost, path = mlpy.dtw_std(x, y, dist_only=False)
>>> dist
0.0
>>> fig = plt.figure(1)
>>> ax = fig.add_subplot(111)
>>> plot1 = plt.imshow(cost.T, origin='lower', cmap=cm.gray, interpolation='nearest')
>>> plot2 = plt.plot(path[0], path[1], 'w')
>>> xlim = ax.set_xlim((-0.5, cost.shape[0]-0.5))
>>> ylim = ax.set_ylim((-0.5, cost.shape[1]-0.5))
>>> plt.show()

[Salvador04]

S Salvador and P Chan. FastDTW: Toward Accurate Dynamic Time Warping in Linear Time and Space. 3rd Wkshp. on Mining Temporal and Sequential Data, ACM KDD ‘04, 2004.

Subsequence DTW

mlpy.dtw_subsequence(x, y)

Subsequence DTW as described in [Muller07], assuming that the length of y is much larger than the length of x and using the Manhattan distance (absolute value of the difference) as local cost measure.

Returns the subsequence of y that are close to x with respect to the minimum DTW distance.

Parameters :

x : 1d array_like object (N)

first sequence

y : 1d array_like object (M)

second sequence

Returns :

dist : float

unnormalized minimum-distance warp path between x and the subsequence of y

cost : 2d numpy array (N,M) [if dist_only=False]

complete accumulated cost matrix

path : tuple of two 1d numpy array (path_x, path_y)

warp path