def _perform_linkage(obs, max_cluster, distmat=None,
alpha=0.5, penup_z=10.0,
algorithm='complete',
verbose=False):
n = len(obs)
if max_cluster == 1:
return (np.ones(len(obs),dtype=np.int), None)
if algorithm not in ('average','single','complete'):
raise ValueError('algorithm must be either average, single, '
'or complte.')
# calculate distance matrix
if distmat is None:
if verbose: print "calculating distmat"
distmat = np.zeros((n,n))
for i in range(n):
for j in range(i+1,n):
distmat[i,j] = compute_dtw_distance(obs[i],
obs[j],
alpha=alpha,
penup_z=penup_z)
distmat[j,i] = distmat[i,j]
z_avg = sp_cluster.hierarchy.linkage(distance.squareform(distmat),
method=algorithm)
fc = sp_cluster.hierarchy.fcluster(z_avg,t=max_cluster,
criterion='maxclust')
return (np.asarray(fc), distmat)
def test_simple(self):
self.assertAlmostEqual(
compute_dtw_distance(self.ink1,
self.ink1,
alpha=0.5,
penup_z=10),
0.000, delta=1e-3)
self.assertAlmostEqual(
compute_dtw_distance(self.ink1,
self.ink2,
alpha=0.5,
penup_z=10),
0.100, delta=1e-3)
self.assertAlmostEqual(
compute_dtw_distance(self.ink1,
self.ink3,
alpha=0.5,
penup_z=10),
0.053, delta=1e-3)
def score(self, obs):
"""Calculates the score of an observation.
The score is defined as negative of the DTW distance
normalized by the expected value.
Returns
-------
(score, None)
"""
dist = compute_dtw_distance(self.model, obs, alpha=self.alpha)
return -dist / self.avg_dist
def train(self, obs, obs_weights=None, center_type="centroid", state_reduction=False, ignore_outliers=True):
"""Estimates the prototype from a set of observations."""
def _find_medoid(obs, obs_weights, distmat):
n = len(obs)
weighted_distmat = distmat * np.tile(obs_weights, (n, 1)).T
avg_distmat = weighted_distmat.sum(axis=0) / obs_weights.sum()
return avg_distmat.argmin()
def _find_centroid(obs, obs_weights, medoid_idx, distmat):
n_features = obs[0].shape[1]
medoid = obs[medoid_idx]
# Ignore outliers by setting their weights to 0
if ignore_outliers:
dist_mean = distmat[medoid_idx, :].mean()
dist_std = distmat[medoid_idx, :].std()
# only remove outliers when std is not too small
if dist_std > 1e-3:
for i in xrange(len(obs)):
if (distmat[medoid_idx, i] - dist_mean) / dist_std > 3.0:
obs_weights[i] = 0.0
# Ignore examples that doesn't have the same number of strokes
medoid_n_strokes = medoid[:, _PU_IDX].sum()
for i, o in enumerate(obs):
if o[:, _PU_IDX].sum() != medoid_n_strokes:
obs_weights[i] = 0.0
f = [compute_dtw_vector(medoid, ink) for ink in obs]
feature_mat = np.vstack(f)
feature_mat = np.nan_to_num(feature_mat)
weighted_feature_mat = feature_mat * np.tile(obs_weights, (feature_mat.shape[1], 1)).T
# reconstruct weighted-average ink
mean_ink = weighted_feature_mat.sum(axis=0) / obs_weights.sum()
mean_ink = mean_ink.reshape((-1, n_features), order="C")
mean_ink = mean_ink + medoid
# make sure pen-up is binary
mean_ink[:, _PU_IDX] = mean_ink[:, _PU_IDX].round()
# number of penups is off, fallback to medoid
if mean_ink[:, _PU_IDX].sum() != medoid_n_strokes:
return medoid
# It seems like not updating the direction yeilds
# a better result.
# return update_directions(mean_ink)
return mean_ink
n = len(obs)
self.num_obs = n
if obs_weights is None:
obs_weights = np.ones(n)
else:
obs_weights = np.asarray(obs_weights)
if not center_type in ["medoid", "centroid"]:
raise ValueError("center_type should be either medoid or centroid.")
# calculate distance matrix
distMat = np.zeros((n, n))
for i in xrange(n):
for j in xrange(i + 1, n):
distMat[i, j] = compute_dtw_distance(obs[i], obs[j], alpha=self.alpha)
distMat[j, i] = distMat[i, j]
# compute the center
if center_type == "centroid":
medoid_idx = _find_medoid(obs, obs_weights, distMat)
self.model = _find_centroid(obs, obs_weights, medoid_idx, distMat)
else:
medoid_idx = _find_medoid(obs, obs_weights, distMat)
self.model = obs[medoid_idx].copy()
if state_reduction:
self.model = _state_reduction(self.model, obs)
self.avg_dist = _compute_avg_dist(self.model, obs, obs_weights, self.alpha)
self.total_weight = obs_weights.sum()
return -self.avg_dist
