def mass_distance_matrix(ts, query, w):
"""
Computes a distance matrix using mass that is used in mpdist_vector
algorithm.
Parameters
----------
ts : array_like
The time series to compute the matrix for.
query : array_like
The time series to compare against.
w : int
The window size.
Returns
-------
array_like : dist_matrix
The MASS distance matrix.
"""
subseq_num = len(query) - w + 1
distances = []
for i in range(subseq_num):
distances.append(np.real(mass2(ts, query[i:i + w])))
return np.array(distances)
def test_mass2():
ts = np.array([1, 1, 1, 2, 1, 1, 4, 5])
query = np.array([2, 1, 1, 4])
actual = mass2(ts, query)
desired = np.array([
0.67640791 - 1.37044402e-16j, 3.43092352 + 0.00000000e+00j,
3.43092352 + 1.02889035e-17j, 0. + 0.00000000e+00j,
1.85113597 + 1.21452707e-17j
])
np.testing.assert_almost_equal(actual, desired)
def mp_top_k_motifs(profile,
exclusion_zone=None,
k=3,
max_neighbors=10,
radius=3):
"""
Find the top K number of motifs (patterns) given a matrix profile. By
default the algorithm will find up to 3 motifs (k) and up to 10 of their
neighbors with a radius of 3 * min_dist.
Parameters
----------
profile : dict
The output from one of the matrix profile algorithms.
exclusion_zone : int, Default to algorithm ez
Desired number of values to exclude on both sides of the motif. This
avoids trivial matches. It defaults to half of the computed window
size. Setting the exclusion zone to 0 makes it not apply.
k : int, Default = 3
Desired number of motifs to find.
neighbor_count : int, Default = 10
The maximum number of neighbors to include for a given motif.
radius : int, Default = 3
The radius is used to associate a neighbor by checking if the
neighbor's distance is less than or equal to dist * radius
Returns
-------
The original input obj with the addition of the "motifs" key. The motifs
key consists of the following structure.
A list of dicts containing motif indices and their corresponding neighbor
indices.
[
{
'motifs': [first_index, second_index],
'neighbors': [index, index, index ...max_neighbors]
}
]
"""
if not core.is_mp_obj(profile):
raise ValueError('Expecting MP data structure!')
window_size = profile['w']
data = profile.get('data', None)
if data:
ts = data.get('ts', None)
data_len = len(ts)
motifs = []
mp = np.copy(profile['mp'])
mpi = profile['pi']
# TODO: this is based on STOMP standards when this motif finding algorithm
# originally came out. Should we default this to 4.0 instead? That seems
# to be the common value now per new research.
if exclusion_zone is None:
exclusion_zone = profile.get('ez', None)
for i in range(k):
min_idx = np.argmin(mp)
min_dist = mp[min_idx]
# we no longer have any motifs to find as all values are nan/inf
if core.is_nan_inf(min_dist):
break
# create a motif pair corresponding to the first appearance and
# second appearance
first_idx = np.min([min_idx, mpi[min_idx]])
second_idx = np.max([min_idx, mpi[min_idx]])
# compute distance profile using mass2 for first appearance
query = ts[first_idx:first_idx + window_size]
distance_profile = mass2(ts, query)
# exclude already picked motifs and neighbors
mask = core.nan_inf_indices(mp)
distance_profile[mask] = np.inf
# apply exclusion zone for motif pair
for j in (first_idx, second_idx):
distance_profile = core.apply_exclusion_zone(
exclusion_zone, False, window_size, data_len, j,
distance_profile)
mp = core.apply_exclusion_zone(exclusion_zone, False, window_size,
data_len, j, mp)
# find up to max_neighbors
neighbors = []
for j in range(max_neighbors):
neighbor_idx = np.argmin(distance_profile)
neighbor_dist = distance_profile[neighbor_idx]
not_in_radius = not ((radius * min_dist) >= neighbor_dist)
# no more neighbors exist based on radius
if core.is_nan_inf(neighbor_dist) or not_in_radius:
break
# add neighbor and apply exclusion zone
neighbors.append(neighbor_idx)
distance_profile = core.apply_exclusion_zone(
exclusion_zone, False, window_size, data_len, neighbor_idx,
distance_profile)
mp = core.apply_exclusion_zone(exclusion_zone, False, window_size,
data_len, neighbor_idx, mp)
# add motifs and neighbors to results
motifs.append({
'motifs': [first_idx, second_idx],
'neighbors': neighbors
})
profile['motifs'] = motifs
return profile
def pmp_top_k_motifs(profile,
exclusion_zone=None,
k=3,
max_neighbors=10,
radius=3):
"""
Find the top K number of motifs (patterns) given a pan matrix profile. By
default the algorithm will find up to 3 motifs (k) and up to 10 of their
neighbors with a radius of 3 * min_dist.
Parameters
----------
profile : dict
The output from one of the pan matrix profile algorithms.
exclusion_zone : int, Default to algorithm ez
Desired number of values to exclude on both sides of the motif. This
avoids trivial matches. It defaults to half of the computed window
size. Setting the exclusion zone to 0 makes it not apply.
k : int, Default = 3
Desired number of motifs to find.
neighbor_count : int, Default = 10
The maximum number of neighbors to include for a given motif.
radius : int, Default = 3
The radius is used to associate a neighbor by checking if the
neighbor's distance is less than or equal to dist * radius
Returns
-------
The original input obj with the addition of the "motifs" key. The motifs
key consists of the following structure.
A list of dicts containing motif indices and their corresponding neighbor
indices. Note that each index is a (row, col) index corresponding to the
pan matrix profile.
[
{
'motifs': [first_index, second_index],
'neighbors': [index, index, index ...max_neighbors]
}
]
"""
if not core.is_pmp_obj(profile):
raise ValueError('Expecting PMP data structure!')
data = profile.get('data', None)
ts = data.get('ts', None)
data_len = len(ts)
pmp = profile.get('pmp', None)
profile_len = pmp.shape[1]
pmpi = profile.get('pmpi', None)
windows = profile.get('windows', None)
# make sure we are working with Euclidean distances
tmp = None
if core.is_pearson_array(pmp):
tmp = core.pearson_to_euclidean(pmp, windows)
else:
tmp = np.copy(pmp).astype('d')
# replace nan and infs with infinity
tmp[core.nan_inf_indices(tmp)] = np.inf
motifs = []
for _ in range(k):
min_idx = np.unravel_index(np.argmin(tmp), tmp.shape)
min_dist = tmp[min_idx]
# nothing else to find...
if core.is_nan_inf(min_dist):
break
# create the motif pair
min_row_idx = min_idx[0]
min_col_idx = min_idx[1]
# motif pairs are respective to the column of the matching row
first_idx = np.min([min_col_idx, pmpi[min_row_idx][min_col_idx]])
second_idx = np.max([min_col_idx, pmpi[min_row_idx][min_col_idx]])
# compute distance profile for first appearance
window_size = windows[min_row_idx]
query = ts[first_idx:first_idx + window_size]
distance_profile = mass2(ts, query)
# extend the distance profile to be as long as the original
infs = np.full(profile_len - len(distance_profile), np.inf)
distance_profile = np.append(distance_profile, infs)
# exclude already picked motifs and neighbors
mask = core.nan_inf_indices(pmp[min_row_idx])
distance_profile[mask] = np.inf
# determine the exclusion zone if not set
if not exclusion_zone:
exclusion_zone = int(np.floor(window_size / 2))
# apply exclusion zone for motif pair
for j in (first_idx, second_idx):
distance_profile = core.apply_exclusion_zone(
exclusion_zone, False, window_size, data_len, j,
distance_profile)
tmp2 = core.apply_exclusion_zone(exclusion_zone, False,
window_size, data_len, j,
tmp[min_row_idx])
tmp[min_row_idx] = tmp2
# find up to max_neighbors
neighbors = []
for j in range(max_neighbors):
neighbor_idx = np.argmin(distance_profile)
neighbor_dist = np.real(distance_profile[neighbor_idx])
not_in_radius = not ((radius * min_dist) >= neighbor_dist)
# no more neighbors exist based on radius
if core.is_nan_inf(neighbor_dist) or not_in_radius:
break
# add neighbor and apply exclusion zone
neighbors.append((min_row_idx, neighbor_idx))
distance_profile = core.apply_exclusion_zone(
exclusion_zone, False, window_size, data_len, neighbor_idx,
distance_profile)
tmp2 = core.apply_exclusion_zone(exclusion_zone, False,
window_size, data_len,
neighbor_idx, tmp[min_row_idx])
tmp[min_row_idx] = tmp2
# add the motifs and neighbors
# note that they are (row, col) indices
motifs.append({
'motifs': [(min_row_idx, first_idx), (min_row_idx, second_idx)],
'neighbors':
neighbors
})
profile['motifs'] = motifs
return profile