DTW simple example



In [1]:

    
%pylab inline









    



Populating the interactive namespace from numpy and matplotlib

The dtw module contains a single function named dtw as well.



In [2]:

    
from dtw import dtw

Let's define two sequences:



In [3]:

    
x = array([0, 0, 1, 1, 2, 4, 2, 1, 2, 0]).reshape(-1, 1)
y = array([1, 1, 1, 2, 2, 2, 2, 3, 2, 0]).reshape(-1, 1)



In [4]:

    
plot(x)
plot(y)









    Out[4]:





[<matplotlib.lines.Line2D at 0x10572df10>]

Compute DTW



In [5]:

    
dist, cost, acc, path = dtw(x, y, dist=lambda x, y: norm(x - y, ord=1))



In [6]:

    
print 'Minimum distance found:', dist









    



Minimum distance found: 0.2

You can plot the accumulated cost matrix and the "shortest" wrap path.



In [7]:

    
imshow(acc.T, origin='lower', cmap=cm.gray, interpolation='nearest')
plot(path[0], path[1], 'w')
xlim((-0.5, acc.shape[0]-0.5))
ylim((-0.5, acc.shape[1]-0.5))









    Out[7]:





(-0.5, 9.5)

Using another distance

You can specify your own distance used as the cost measure by the DTW. By default the L1 norm is used.



In [8]:

    
def my_custom_norm(x, y):
    return (x * x) + (y * y)

dist, cost, acc, path = dtw(x, y, dist=my_custom_norm)

Obviously you can also directly use those defined in numpy.



In [9]:

    
from numpy.linalg import norm

dist, cost, acc, path = dtw(x, y, dist=norm)









    



/Users/pierrerouanet/.pyenv/versions/anaconda-2.4.0/lib/python2.7/site-packages/numpy/linalg/linalg.py:2119: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison
  (ord in ('f', 'fro') and ndim == 2) or

Using subsequences

The sequences used can be of different length. DTW can also be useful to detect subsequences.



In [10]:

    
x = range(10)
y = [0] * 5 + x

x = array(x).reshape(-1, 1)
y = array(y).reshape(-1, 1)



In [11]:

    
dist, cost, acc, path = dtw(x, y, dist=lambda x, y: norm(x - y, ord=1))



In [12]:

    
imshow(acc.T, origin='lower', cmap=cm.gray, interpolation='nearest')
plot(path[0], path[1], 'w')
xlim((-0.5, acc.shape[0]-0.5))
ylim((-0.5, acc.shape[1]-0.5))









    Out[12]:





(-0.5, 14.5)



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