def k_means_clust(self, data, num_iter, progress=False, w=100, euclidean=True):
'''
k-means clustering algorithm for time series data. dynamic time warping Euclidean distance
used as default similarity measure.
'''
self.centroids = random.sample(data,self.num_clust)
for n in range(num_iter):
if progress:
print 'iteration ' + str(n + 1)
# assign data points to clusters
self.assignments = {}
# assignments has the following structure:
# {
# centroid_idx: [idxs of time series that are nearest the centroid]
# }
for ind, i in enumerate(data):
# ind is the data series number, i is the data series
# define the minimum distance for the data series
min_dist = float('inf')
# define the index of the closest centroid
closest_clust = None
for c_ind, j in enumerate(self.centroids):
# c_ind is the index of the centroid, j is the centroid
if dtw.lb_keogh_onQuery(i, j, w, euclidean) < min_dist:
print('lb less than min dist -- calculating full dtw')
# could use windowed dtw here instead to speed things up
cur_dist = dtw.dist_dtw(i, j, euclidean)
if cur_dist < min_dist:
min_dist = cur_dist
closest_clust = c_ind
# add the index of the current data series to a cluster
if closest_clust in self.assignments:
self.assignments[closest_clust].append(ind)
else:
self.assignments[closest_clust] = []
# now that we've updated the clusters that each series is part of,
# we recalculate the centroids of the clusters
for key in self.assignments:
# key is the index of a centroid in the centroids list
clust_sum = 0
for k in self.assignments[key]:
# k is the index of a time series in the current cluster
# add the time series to the cluster sum
clust_sum = clust_sum + data[k]
# update each point in the centroid with the average of all points in the cluster of time
# series around the centroid
self.centroids[key] = [m / len(self.assignments[key]) for m in clust_sum]
def dtw(query, subject, squared=True):
"""unconstrained Euclidean-flavoured DTW """
return ldtw.dist_dtw(ldtw.TimeSeries(query), ldtw.TimeSeries(subject), squared)
# do for Euclidean and Manhatten mode
for mode, name in [(True, 'Euclidean'), (False, 'Manhatten')]:
# calculate naive L_p-norm
print dtw.dist_euclidean(query, subject) \
if mode == True else \
dtw.dist_manhatten(query, subject)
# calculate a bunch of windowed DTWs (error should decrease monotonically)
for window in range(0, max(len(subject), len(query)), 32):
gamma = dtw.WarpingPath()
print dtw.dist_cdtw_backtrace(query, subject, window, gamma, mode)
pl.plot(*zip(*[node[::-1] for node in gamma]))
# calculate full DTW
print dtw.dist_dtw(query, subject, mode)
# plot objective function H(i,j) := |query(i)-subject(j)|
pl.imshow([[abs(query[i]-subject[j]) for j in range(len(subject))]
for i in range(len(query))], aspect="auto")
pl.title(name)
pl.show()
# draw explicit alignment for full dtw
pl.plot(query)
pl.plot(subject)
for i, j in gamma[0:len(gamma):4]:
pl.plot([i, j], [query[i], subject[j]], c="grey")
pl.show()
# do for Euclidean and Manhatten mode
for mode, name in [(True, 'Euclidean'), (False, 'Manhatten')]:
# calculate naive L_p-norm
print dtw.dist_euclidean(query, subject) \
if mode == True else \
dtw.dist_manhatten(query, subject)
# calculate a bunch of windowed DTWs (error should decrease monotonically)
for window in range(0, max(len(subject), len(query)), 32):
gamma = dtw.WarpingPath()
print dtw.dist_cdtw_backtrace(query, subject, window, gamma, mode)
pl.plot(*zip(*[node[::-1] for node in gamma]))
# calculate full DTW
print dtw.dist_dtw(query, subject, mode)
# plot objective function H(i,j) := |query(i)-subject(j)|
pl.imshow([[abs(query[i] - subject[j]) for j in range(len(subject))]
for i in range(len(query))],
aspect="auto")
pl.title(name)
pl.show()
# draw explicit alignment for full dtw
pl.plot(query)
pl.plot(subject)
for i, j in gamma[0:len(gamma):4]:
pl.plot([i, j], [query[i], subject[j]], c="grey")
def dtw(query, subject, squared=True):
"""unconstrained Euclidean-flavoured DTW """
return ldtw.dist_dtw(ldtw.TimeSeries(query), ldtw.TimeSeries(subject),
squared)
