def test_moving_avg_std():
a = np.array([1, 2, 3, 4, 5, 6])
mu, std = core.moving_avg_std(a, 3)
mu_desired = np.array([2., 3., 4., 5.])
std_desired = np.array([0.81649658, 0.81649658, 0.81649658, 0.81649658])
np.testing.assert_almost_equal(mu, mu_desired)
np.testing.assert_almost_equal(std, std_desired)
def stomp(ts, window_size, query=None, n_jobs=1):
"""
Computes matrix profiles for a single dimensional time series using the
parallelized STOMP algorithm (by default). Ray or Python's multiprocessing
library may be used. When you have initialized Ray on your machine,
it takes priority over using Python's multiprocessing.
Parameters
----------
ts : array_like
The time series to compute the matrix profile for.
window_size: int
The size of the window to compute the matrix profile over.
query : array_like
Optionally, a query can be provided to perform a similarity join.
n_jobs : int, Default = 1
Number of cpu cores to use.
Returns
-------
dict : profile
A MatrixProfile data structure.
>>> {
>>> 'mp': The matrix profile,
>>> 'pi': The matrix profile 1NN indices,
>>> 'rmp': The right matrix profile,
>>> 'rpi': The right matrix profile 1NN indices,
>>> 'lmp': The left matrix profile,
>>> 'lpi': The left matrix profile 1NN indices,
>>> 'metric': The distance metric computed for the mp,
>>> 'w': The window size used to compute the matrix profile,
>>> 'ez': The exclusion zone used,
>>> 'join': Flag indicating if a similarity join was computed,
>>> 'sample_pct': Percentage of samples used in computing the MP,
>>> 'data': {
>>> 'ts': Time series data,
>>> 'query': Query data if supplied
>>> }
>>> 'class': "MatrixProfile"
>>> 'algorithm': "stomp_parallel"
>>> }
Raises
------
ValueError
If window_size < 4.
If window_size > query length / 2.
If ts is not a list or np.array.
If query is not a list or np.array.
If ts or query is not one dimensional.
"""
is_join = core.is_similarity_join(ts, query)
if not is_join:
query = ts
# data conversion to np.array
ts = core.to_np_array(ts)
query = core.to_np_array(query)
if window_size < 4:
error = "window size must be at least 4."
raise ValueError(error)
if window_size > len(query) / 2:
error = "Time series is too short relative to desired window size"
raise ValueError(error)
# multiprocessing or single threaded approach
if n_jobs == 1:
pass
else:
n_jobs = core.valid_n_jobs(n_jobs)
# precompute some common values - profile length, query length etc.
profile_length = core.get_profile_length(ts, query, window_size)
data_length = len(ts)
query_length = len(query)
num_queries = query_length - window_size + 1
exclusion_zone = int(np.ceil(window_size / 2.0))
# do not use exclusion zone for join
if is_join:
exclusion_zone = 0
# find skip locations, clean up nan and inf in the ts and query
skip_locs = core.find_skip_locations(ts, profile_length, window_size)
ts = core.clean_nan_inf(ts)
query = core.clean_nan_inf(query)
# initialize matrices
matrix_profile = np.full(profile_length, np.inf)
profile_index = np.full(profile_length, 0)
# compute left and right matrix profile when similarity join does not happen
left_matrix_profile = None
right_matrix_profile = None
left_profile_index = None
right_profile_index = None
if not is_join:
left_matrix_profile = np.copy(matrix_profile)
right_matrix_profile = np.copy(matrix_profile)
left_profile_index = np.copy(profile_index)
right_profile_index = np.copy(profile_index)
# precompute some statistics on ts
data_mu, data_sig = core.moving_avg_std(ts, window_size)
first_window = query[0:window_size]
first_product = core.fft_convolve(ts, first_window)
batch_windows = []
results = []
# batch compute with multiprocessing
args = []
for start, end in core.generate_batch_jobs(num_queries, n_jobs):
args.append((start, end, ts, query, window_size, data_length,
profile_length, exclusion_zone, is_join, data_mu,
data_sig, first_product, skip_locs))
batch_windows.append((start, end))
# we are running single threaded stomp - no need to initialize any
# parallel environments.
if n_jobs == 1 or len(args) == 1:
results.append(_batch_compute(args[0]))
else:
# parallelize
with core.mp_pool()(n_jobs) as pool:
results = pool.map(_batch_compute, args)
# now we combine the batch results
if len(results) == 1:
result = results[0]
matrix_profile = result['mp']
profile_index = result['pi']
left_matrix_profile = result['lmp']
left_profile_index = result['lpi']
right_matrix_profile = result['rmp']
right_profile_index = result['rpi']
else:
for index, result in enumerate(results):
start = batch_windows[index][0]
end = batch_windows[index][1]
# update the matrix profile
indices = result['mp'] < matrix_profile
matrix_profile[indices] = result['mp'][indices]
profile_index[indices] = result['pi'][indices]
# update the left and right matrix profiles
if not is_join:
indices = result['lmp'] < left_matrix_profile
left_matrix_profile[indices] = result['lmp'][indices]
left_profile_index[indices] = result['lpi'][indices]
indices = result['rmp'] < right_matrix_profile
right_matrix_profile[indices] = result['rmp'][indices]
right_profile_index[indices] = result['rpi'][indices]
return {
'mp': matrix_profile,
'pi': profile_index,
'rmp': right_matrix_profile,
'rpi': right_profile_index,
'lmp': left_matrix_profile,
'lpi': left_profile_index,
'metric': 'euclidean',
'w': window_size,
'ez': exclusion_zone,
'join': is_join,
'sample_pct': 1,
'data': {
'ts': ts,
'query': query
},
'class': "MatrixProfile",
'algorithm': "stomp"
}
def mstomp(ts, window_size, return_dimension=False, n_jobs=1):
"""
Computes multidimensional matrix profile with mSTAMP (stomp based). Ray or Python's multiprocessing library may be used. When you have initialized Ray on your machine, it takes priority over using Python's multiprocessing.
Parameters
----------
ts : array_like, shape (n_dim, seq_len)
The multidimensional time series to compute the multidimensional matrix profile for.
window_size: int
The size of the window to compute the matrix profile over.
return_dimension : bool
if True, also return the matrix profile dimension. It takses O(d^2 n)
to store and O(d^2 n^2) to compute. (default is False)
n_jobs : int, Default = 1
Number of cpu cores to use.
Returns
-------
dict : profile
A MatrixProfile data structure.
>>> {
>>> 'mp': The matrix profile,
>>> 'pi': The matrix profile 1NN indices,
>>> 'rmp': The right matrix profile,
>>> 'rpi': The right matrix profile 1NN indices,
>>> 'lmp': The left matrix profile,
>>> 'lpi': The left matrix profile 1NN indices,
>>> 'metric': The distance metric computed for the mp,
>>> 'w': The window size used to compute the matrix profile,
>>> 'ez': The exclusion zone used,
>>> 'sample_pct': Percentage of samples used in computing the MP,
>>> 'data': {
>>> 'ts': Time series data,
>>> 'query': Query data if supplied
>>> }
>>> 'class': "MatrixProfile"
>>> 'algorithm': "stomp_based_mstamp"
>>> }
Raises
------
ValueError
If window_size < 4.
If window_size > time series length / 2.
If ts is not a list or np.array.
"""
query = ts
# data conversion to np.array
ts = core.to_np_array(ts)
query = core.to_np_array(query)
if window_size < 4:
error = "window size must be at least 4."
raise ValueError(error)
if ts.ndim == 1:
ts = np.expand_dims(ts, axis=0)
query = np.expand_dims(query, axis=0)
if window_size > query.shape[1] / 2:
error = "Time series is too short relative to desired window size"
raise ValueError(error)
# multiprocessing or single threaded approach
if n_jobs == 1:
pass
else:
n_jobs = core.valid_n_jobs(n_jobs)
# precompute some common values - profile length, query length etc.
profile_length = core.get_profile_length(ts, query, window_size)
data_length = ts.shape[1]
query_length = query.shape[1]
num_queries = query_length - window_size + 1
exclusion_zone = int(np.ceil(window_size / 2.0))
num_dim = ts.shape[0]
# find skip locations, clean up nan and inf in the ts and query
skip_locs = core.find_multid_skip_locations(ts, profile_length, window_size)
ts = core.clean_nan_inf(ts)
query = core.clean_nan_inf(query)
# initialize matrices
matrix_profile = np.full((num_dim, profile_length), np.inf)
profile_index = np.full((num_dim, profile_length), 0)
# profile_index = np.full((num_dim, profile_length), -1)
# compute left and right matrix profile when similarity join does not happen
left_matrix_profile = np.copy(matrix_profile)
right_matrix_profile = np.copy(matrix_profile)
left_profile_index = np.copy(profile_index)
right_profile_index = np.copy(profile_index)
profile_dimension = []
if return_dimension:
n_jobs = 1
for i in range(num_dim):
profile_dimension.append(np.empty((i + 1, profile_length), dtype=int))
# precompute some statistics on ts
data_mu, data_sig, first_product = np.empty((num_dim, profile_length)), np.empty(
(num_dim, profile_length)), np.empty((num_dim, profile_length))
for i in range(num_dim):
data_mu[i, :], data_sig[i, :] = core.moving_avg_std(ts[i, :], window_size)
first_window = query[i, 0:window_size]
first_product[i, :] = core.fft_convolve(ts[i, :], first_window)
batch_windows = []
results = []
# batch compute with multiprocessing
args = []
for start, end in core.generate_batch_jobs(num_queries, n_jobs):
args.append((num_dim, start, end, ts, query, window_size, data_length, profile_length, exclusion_zone, data_mu,
data_sig, first_product, skip_locs, profile_dimension, return_dimension))
batch_windows.append((start, end))
# we are running single threaded stomp - no need to initialize any
# parallel environments.
if n_jobs == 1 or len(args) == 1:
results.append(_batch_compute(args[0]))
else:
# parallelize
with core.mp_pool()(n_jobs) as pool:
results = pool.map(_batch_compute, args)
# now we combine the batch results
if len(results) == 1:
result = results[0]
matrix_profile = result['mp']
profile_index = result['pi']
profile_dimension = result['pd']
left_matrix_profile = result['lmp']
left_profile_index = result['lpi']
right_matrix_profile = result['rmp']
right_profile_index = result['rpi']
else:
for index, result in enumerate(results):
start = batch_windows[index][0]
end = batch_windows[index][1]
# update the matrix profile
indices = result['mp'] < matrix_profile
matrix_profile[indices] = result['mp'][indices]
profile_index[indices] = result['pi'][indices]
# update the left and right matrix profiles
indices = result['lmp'] < left_matrix_profile
left_matrix_profile[indices] = result['lmp'][indices]
left_profile_index[indices] = result['lpi'][indices]
indices = result['rmp'] < right_matrix_profile
right_matrix_profile[indices] = result['rmp'][indices]
right_profile_index[indices] = result['rpi'][indices]
return {
'mp': matrix_profile,
'pi': profile_index,
'pd': profile_dimension,
'rmp': right_matrix_profile,
'rpi': right_profile_index,
'lmp': left_matrix_profile,
'lpi': left_profile_index,
'metric': 'euclidean',
'w': window_size,
'ez': exclusion_zone,
'sample_pct': 1,
'data': {
'ts': ts,
'query': query
},
'class': "MatrixProfile",
'algorithm': "stomp_based_mstamp"
}
def _batch_compute(args):
"""
Internal function to compute a batch of the time series in parallel.
Parameters
----------
args : tuple
Various attributes used for computing the batch.
(
batch_start : int
The starting index for this batch.
batch_end : int
The ending index for this batch.
ts : array_like
The time series to compute the matrix profile for.
query : array_like
The query.
window_size : int
The size of the window to compute the profile over.
data_length : int
The number of elements in the time series.
profile_length : int
The number of elements that will be in the final matrix
profile.
exclusion_zone : int
Used to exclude trivial matches.
is_join : bool
Flag to indicate if an AB join or self join is occuring.
data_mu : array_like
The moving average over the time series for the given window
size.
data_sig : array_like
The moving standard deviation over the time series for the
given window size.
first_product : array_like
The first sliding dot product for the time series over index
0 to window_size.
skip_locs : array_like
Indices that should be skipped for distance profile calculation
due to a nan or inf.
)
Returns
-------
dict : profile
The matrix profile, left and right matrix profiles and their respective
profile indices.
>>> {
>>> 'mp': The matrix profile,
>>> 'pi': The matrix profile 1NN indices,
>>> 'rmp': The right matrix profile,
>>> 'rpi': The right matrix profile 1NN indices,
>>> 'lmp': The left matrix profile,
>>> 'lpi': The left matrix profile 1NN indices,
>>> }
"""
batch_start, batch_end, ts, query, window_size, data_length, \
profile_length, exclusion_zone, is_join, data_mu, data_sig, \
first_product, skip_locs = args
# initialize matrices
matrix_profile = np.full(profile_length, np.inf)
profile_index = np.full(profile_length, 0)
left_matrix_profile = None
right_matrix_profile = None
left_profile_index = None
right_profile_index = None
if not is_join:
left_matrix_profile = np.copy(matrix_profile)
right_matrix_profile = np.copy(matrix_profile)
left_profile_index = np.copy(profile_index)
right_profile_index = np.copy(profile_index)
# with batch 0 we do not need to recompute the dot product
# however with other batch windows, we need the previous iterations sliding
# dot product
last_product = None
if batch_start is 0:
first_window = query[batch_start:batch_start + window_size]
last_product = np.copy(first_product)
else:
first_window = query[batch_start - 1:batch_start + window_size - 1]
last_product = core.fft_convolve(ts, first_window)
query_sum = np.sum(first_window)
query_2sum = np.sum(first_window**2)
query_mu, query_sig = core.moving_avg_std(first_window, window_size)
drop_value = first_window[0]
# only compute the distance profile for index 0 and update
if batch_start is 0:
distance_profile = core.distance_profile(last_product, window_size,
data_mu, data_sig, query_mu,
query_sig)
# apply exclusion zone
distance_profile = core.apply_exclusion_zone(exclusion_zone, is_join,
window_size, data_length,
0, distance_profile)
# update the matrix profile
indices = (distance_profile < matrix_profile)
matrix_profile[indices] = distance_profile[indices]
profile_index[indices] = 0
batch_start += 1
# make sure to compute inclusively from batch start to batch end
# otherwise there are gaps in the profile
if batch_end < profile_length:
batch_end += 1
# iteratively compute distance profile and update with element-wise mins
for i in range(batch_start, batch_end):
# check for nan or inf and skip
if skip_locs[i]:
continue
query_window = query[i:i + window_size]
query_sum = query_sum - drop_value + query_window[-1]
query_2sum = query_2sum - drop_value**2 + query_window[-1]**2
query_mu = query_sum / window_size
query_sig2 = query_2sum / window_size - query_mu**2
query_sig = np.sqrt(query_sig2)
last_product[1:] = last_product[0:data_length - window_size] \
- ts[0:data_length - window_size] * drop_value \
+ ts[window_size:] * query_window[-1]
last_product[0] = first_product[i]
drop_value = query_window[0]
distance_profile = core.distance_profile(last_product, window_size,
data_mu, data_sig, query_mu,
query_sig)
# apply the exclusion zone
distance_profile = core.apply_exclusion_zone(exclusion_zone, is_join,
window_size, data_length,
i, distance_profile)
# update the matrix profile
indices = (distance_profile < matrix_profile)
matrix_profile[indices] = distance_profile[indices]
profile_index[indices] = i
# update the left and right matrix profiles
if not is_join:
# find differences, shift left and update
indices = distance_profile[i:] < left_matrix_profile[i:]
falses = np.zeros(i).astype('bool')
indices = np.append(falses, indices)
left_matrix_profile[indices] = distance_profile[indices]
left_profile_index[np.argwhere(indices)] = i
# find differences, shift right and update
indices = distance_profile[0:i] < right_matrix_profile[0:i]
falses = np.zeros(profile_length - i).astype('bool')
indices = np.append(indices, falses)
right_matrix_profile[indices] = distance_profile[indices]
right_profile_index[np.argwhere(indices)] = i
return {
'mp': matrix_profile,
'pi': profile_index,
'rmp': right_matrix_profile,
'rpi': right_profile_index,
'lmp': left_matrix_profile,
'lpi': left_profile_index,
}
def _batch_compute(args):
"""
Internal function to compute a batch of the time series in parallel.
Parameters
----------
args : tuple
Various attributes used for computing the batch.
(
batch_start : int
The starting index for this batch.
batch_end : int
The ending index for this batch.
ts : array_like
The time series to compute the matrix profile for.
query : array_like
The query.
window_size : int
The size of the window to compute the profile over.
data_length : int
The number of elements in the time series.
profile_length : int
The number of elements that will be in the final matrix
profile.
exclusion_zone : int
Used to exclude trivial matches.
data_mu : array_like
The moving average over the time series for the given window
size.
data_sig : array_like
The moving standard deviation over the time series for the
given window size.
first_product : array_like
The first sliding dot product for the time series over index
0 to window_size.
skip_locs : array_like
Indices that should be skipped for distance profile calculation
due to a nan or inf.
)
Returns
-------
dict : profile
The matrix profile, left and right matrix profiles and their respective
profile indices.
>>> {
>>> 'mp': The matrix profile,
>>> 'pi': The matrix profile 1NN indices,
>>> 'rmp': The right matrix profile,
>>> 'rpi': The right matrix profile 1NN indices,
>>> 'lmp': The left matrix profile,
>>> 'lpi': The left matrix profile 1NN indices,
>>> }
"""
num_dim, batch_start, batch_end, ts, query, window_size, data_length, \
profile_length, exclusion_zone, data_mu, data_sig, \
first_product, skip_locs, profile_dimension, return_dimension = args
# initialize matrices
matrix_profile = np.full((num_dim, profile_length), np.inf)
profile_index = np.full((num_dim, profile_length), 0)
left_matrix_profile = None
right_matrix_profile = None
left_profile_index = None
right_profile_index = None
left_matrix_profile = np.copy(matrix_profile)
right_matrix_profile = np.copy(matrix_profile)
left_profile_index = np.copy(profile_index)
right_profile_index = np.copy(profile_index)
# with batch 0 we do not need to recompute the dot product
# however with other batch windows, we need the previous iterations sliding
# dot product
last_product = np.copy(first_product)
if batch_start is 0:
first_window = query[:, batch_start:batch_start + window_size]
else:
first_window = query[:, batch_start - 1:batch_start + window_size - 1]
for i in range(num_dim):
last_product[i, :] = core.fft_convolve(ts[i, :], first_window[i, :])
query_sum = np.sum(first_window, axis=1)
query_2sum = np.sum(first_window**2, axis=1)
query_mu, query_sig = np.empty(num_dim), np.empty(num_dim)
for i in range(num_dim):
query_mu[i], query_sig[i] = core.moving_avg_std(first_window[i, :], window_size)
drop_value = np.empty(num_dim)
for i in range(num_dim):
drop_value[i] = first_window[i, 0]
distance_profile = np.empty((num_dim, profile_length))
# make sure to compute inclusively from batch start to batch end
# otherwise there are gaps in the profile
if batch_end < profile_length:
batch_end += 1
# iteratively compute distance profile and update with element-wise mins
for i in range(batch_start, batch_end):
# check for nan or inf and skip
if skip_locs[i]:
continue
for j in range(num_dim):
if i == 0:
query_window = query[j, i:i + window_size]
distance_profile[j, :] = core.distance_profile(last_product[j, :], window_size, data_mu[j, :],
data_sig[j, :], query_mu[j], query_sig[j])
# apply exclusion zone
distance_profile[j, :] = core.apply_exclusion_zone(exclusion_zone, 0, window_size, data_length, 0,
distance_profile[j, :])
else:
query_window = query[j, i:i + window_size]
query_sum[j] = query_sum[j] - drop_value[j] + query_window[-1]
query_2sum[j] = query_2sum[j] - drop_value[j]**2 + query_window[-1]**2
query_mu[j] = query_sum[j] / window_size
query_sig2 = query_2sum[j] / window_size - query_mu[j]**2
if query_sig2 < _EPS:
query_sig2 = _EPS
query_sig[j] = np.sqrt(query_sig2)
last_product[j, 1:] = last_product[j, 0:data_length - window_size] \
- ts[j, 0:data_length - window_size] * drop_value[j] \
+ ts[j, window_size:] * query_window[-1]
last_product[j, 0] = first_product[j, i]
distance_profile[j, :] = core.distance_profile(last_product[j, :], window_size, data_mu[j, :],
data_sig[j, :], query_mu[j], query_sig[j])
# apply the exclusion zone
distance_profile[j, :] = core.apply_exclusion_zone(exclusion_zone, 0, window_size, data_length, i,
distance_profile[j, :])
distance_profile[j, distance_profile[j, :] < _EPS] = 0
drop_value[j] = query_window[0]
if np.any(query_sig < _EPS):
continue
distance_profile[:, skip_locs] = np.inf
distance_profile[data_sig < np.sqrt(_EPS)] = np.inf
distance_profile_dim = np.argsort(distance_profile, axis=0)
distance_profile_sort = np.sort(distance_profile, axis=0)
distance_profile_cumsum = np.zeros(profile_length)
for j in range(num_dim):
distance_profile_cumsum += distance_profile_sort[j, :]
distance_profile_mean = distance_profile_cumsum / (j + 1)
# update the matrix profile
indices = (distance_profile_mean < matrix_profile[j, :])
matrix_profile[j, indices] = distance_profile_mean[indices]
profile_index[j, indices] = i
if return_dimension:
profile_dimension[j][:, indices] = distance_profile_dim[:j + 1, indices]
# update the left and right matrix profiles
# find differences, shift left and update
indices = distance_profile_mean[i:] < left_matrix_profile[j, i:]
falses = np.zeros(i).astype('bool')
indices = np.append(falses, indices)
left_matrix_profile[j, indices] = distance_profile_mean[indices]
left_profile_index[j, np.argwhere(indices)] = i
# find differences, shift right and update
indices = distance_profile_mean[0:i] < right_matrix_profile[j, 0:i]
falses = np.zeros(profile_length - i).astype('bool')
indices = np.append(indices, falses)
right_matrix_profile[j, indices] = distance_profile_mean[indices]
right_profile_index[j, np.argwhere(indices)] = i
return {
'mp': matrix_profile,
'pi': profile_index,
'pd': profile_dimension,
'rmp': right_matrix_profile,
'rpi': right_profile_index,
'lmp': left_matrix_profile,
'lpi': left_profile_index,
}
def statistics(ts, window_size):
"""
Compute global and moving statistics for the provided 1D time
series. The statistics computed include the min, max, mean, std. and median
over the window specified and globally.
Parameters
----------
ts : array_like
The time series.
window_size: int
The size of the window to compute moving statistics over.
Returns
-------
dict :
{
ts: the original time series,
min: the global minimum,
max: the global maximum,
mean: the global mean,
std: the global standard deviation,
median: the global standard deviation,
moving_min: the moving minimum,
moving_max: the moving maximum,
moving_mean: the moving mean,
moving_std: the moving standard deviation,
moving_median: the moving median,
window_size: the window size provided,
class: Statistics
}
Raises
------
ValueError
If window_size is not an int.
If window_size > len(ts)
If ts is not a list or np.array.
If ts is not 1D.
"""
if not core.is_array_like(ts):
raise ValueError('ts must be array like')
if not core.is_one_dimensional(ts):
raise ValueError('The time series must be 1D')
if not isinstance(window_size, int):
raise ValueError('Expecting int for window_size')
if window_size > len(ts):
raise ValueError('Window size cannot be greater than len(ts)')
if window_size < 3:
raise ValueError('Window size cannot be less than 3')
moving_mu, moving_sigma = core.moving_avg_std(ts, window_size)
rolling_ts = core.rolling_window(ts, window_size)
return {
'ts': ts,
'min': np.min(ts),
'max': np.max(ts),
'mean': np.mean(ts),
'std': np.std(ts),
'median': np.median(ts),
'moving_min': np.min(rolling_ts, axis=1),
'moving_max': np.max(rolling_ts, axis=1),
'moving_mean': moving_mu,
'moving_std': moving_sigma,
'moving_median': np.median(rolling_ts, axis=1),
'window_size': window_size,
'class': 'Statistics'
}
def scrimp_plus_plus(ts, window_size, query=None, step_size=0.25, sample_pct=0.1,
random_state=None, n_jobs=1):
"""SCRIMP++ is an anytime algorithm that computes the matrix profile for a
given time series (ts) over a given window size (m). Essentially, it allows
for an approximate solution to be provided for quicker analysis. In the
case of this implementation, sample percentage is used. An approximate
solution is given based a sample percentage from 0 to 1. The default sample
percentage is currently 10%.
This algorithm was created at the University of California Riverside. For
further academic understanding, please review this paper:
Matrix Profile XI: SCRIMP++: Time Series Motif Discovery at Interactive
Speed. Yan Zhu, Chin-Chia Michael Yeh, Zachary Zimmerman, Kaveh Kamgar
Eamonn Keogh, ICDM 2018.
https://www.cs.ucr.edu/~eamonn/SCRIMP_ICDM_camera_ready_updated.pdf
Parameters
----------
ts : np.ndarray
The time series to compute the matrix profile for.
window_size : int
The window size.
query : array_like
Optionally, a query can be provided to perform a similarity join.
step_size : float, default 0.25
The sampling interval for the window. The paper suggest 0.25 is the
most practical. It should be a float value between 0 and 1.
sample_pct : float, default = 0.1 (10%)
Number of samples to compute distances for in the MP.
random_state : int, default None
Set the random seed generator for reproducible results.
n_jobs : int, Default = 1
Number of cpu cores to use.
Returns
-------
dict : profile
A MatrixProfile data structure.
>>> {
>>> 'mp': The matrix profile,
>>> 'pi': The matrix profile 1NN indices,
>>> 'rmp': The right matrix profile,
>>> 'rpi': The right matrix profile 1NN indices,
>>> 'lmp': The left matrix profile,
>>> 'lpi': The left matrix profile 1NN indices,
>>> 'metric': The distance metric computed for the mp,
>>> 'w': The window size used to compute the matrix profile,
>>> 'ez': The exclusion zone used,
>>> 'join': Flag indicating if a similarity join was computed,
>>> 'sample_pct': Percentage of samples used in computing the MP,
>>> 'data': {
>>> 'ts': Time series data,
>>> 'query': Query data if supplied
>>> }
>>> 'class': "MatrixProfile"
>>> 'algorithm': "scrimp++"
>>> }
Raises
------
ValueError
If window_size < 4.
If window_size > query length / 2.
If ts is not a list or np.array.
If query is not a list or np.array.
If ts or query is not one dimensional.
If sample_pct is not between 0 and 1.
"""
# validate random_state
if random_state is not None:
try:
np.random.seed(random_state)
except:
raise ValueError('Invalid random_state value given.')
###########################
# PreSCRIMP
###########################
profile = prescrimp(ts, window_size, query=query, step_size=step_size,
sample_pct=sample_pct, random_state=random_state, n_jobs=n_jobs)
# data conversion to np.array
ts = profile['data']['ts']
query = profile['data']['query']
if isinstance(query, type(None)):
query = ts
# precompute some common values - profile length, query length etc.
step_size = int(math.floor(window_size * step_size))
profile_length = core.get_profile_length(ts, query, window_size)
data_length = len(ts)
exclusion_zone = profile['ez']
window_size = profile['w']
# precompute some statistics on ts
data_mu, data_sig = core.moving_avg_std(ts, window_size)
###########################
# SCRIMP
###########################
# randomly sort indices for compute order
orig_index = np.arange(profile_length)
compute_order = np.copy(orig_index[orig_index > exclusion_zone])
#np.random.shuffle(compute_order)
# Only refine to provided sample_pct
sample_size = int(np.ceil(len(compute_order) * sample_pct))
compute_order = np.random.choice(compute_order, size=sample_size,
replace=False)
# initialize some values
curlastz = np.zeros(profile_length)
curdistance = np.zeros(profile_length)
dist1 = np.full(profile_length, np.inf)
dist2 = np.full(profile_length, np.inf)
for idx in compute_order:
# compute last z
curlastz[idx] = np.sum(ts[0:window_size] * ts[idx:idx + window_size])
curlastz[idx+1:] = curlastz[idx] + np.cumsum(
(ts[window_size:data_length - idx] * ts[idx + window_size:data_length]) -\
(ts[0:profile_length - idx - 1] * ts[idx:profile_length - 1])
)
# compute distances
curdistance[idx:] = np.sqrt(np.abs(
2 * (window_size - (curlastz[idx:profile_length + 1] -\
window_size * (data_mu[idx:] * data_mu[0:profile_length - idx])) /\
(data_sig[idx:] * data_sig[0:profile_length - idx]))
))
dist1[0:idx - 1] = np.inf
dist1[idx:] = curdistance[idx:]
dist2[0:profile_length - idx] = curdistance[idx:]
dist2[profile_length - idx + 2:] = np.inf
loc1 = dist1 < profile['mp']
if loc1.any():
profile['mp'][loc1] = dist1[loc1]
profile['pi'][loc1] = orig_index[loc1] - idx
loc2 = dist2 < profile['mp']
if loc2.any():
profile['mp'][loc2] = dist2[loc2]
profile['pi'][loc2] = orig_index[loc2] + idx
profile['algorithm'] = 'scrimp++'
profile['sample_pct'] = sample_pct
return profile
def prescrimp(ts, window_size, query=None, step_size=0.25, sample_pct=0.1,
random_state=None, n_jobs=1):
"""
This is the PreScrimp algorithm from the SCRIMP++ paper. It is primarly
used to compute the approximate matrix profile. In this case we use
a sample percentage to mock "the anytime/approximate nature".
Parameters
----------
ts : np.ndarray
The time series to compute the matrix profile for.
window_size : int
The window size.
query : array_like
Optionally, a query can be provided to perform a similarity join.
step_size : float, default 0.25
The sampling interval for the window. The paper suggest 0.25 is the
most practical. It should be a float value between 0 and 1.
sample_pct : float, default = 0.1 (10%)
Number of samples to compute distances for in the MP.
random_state : int, default None
Set the random seed generator for reproducible results.
n_jobs : int, Default = 1
Number of cpu cores to use.
Note
----
The matrix profiles computed from prescrimp will always be the approximate
solution.
Returns
-------
dict : profile
A MatrixProfile data structure.
>>> {
>>> 'mp': The matrix profile,
>>> 'pi': The matrix profile 1NN indices,
>>> 'rmp': The right matrix profile,
>>> 'rpi': The right matrix profile 1NN indices,
>>> 'lmp': The left matrix profile,
>>> 'lpi': The left matrix profile 1NN indices,
>>> 'metric': The distance metric computed for the mp,
>>> 'w': The window size used to compute the matrix profile,
>>> 'ez': The exclusion zone used,
>>> 'join': Flag indicating if a similarity join was computed,
>>> 'sample_pct': Percentage of samples used in computing the MP,
>>> 'data': {
>>> 'ts': Time series data,
>>> 'query': Query data if supplied
>>> }
>>> 'class': "MatrixProfile"
>>> 'algorithm': "prescrimp"
>>>}
Raises
------
ValueError
If window_size < 4.
If window_size > query length / 2.
If ts is not a list or np.array.
If query is not a list or np.array.
If ts or query is not one dimensional.
If sample_pct is not between 0 and 1.
"""
is_join = core.is_similarity_join(ts, query)
if not is_join:
query = ts
# data conversion to np.array
ts = core.to_np_array(ts)
query = core.to_np_array(query)
# validate step_size
if not isinstance(step_size, float) or step_size > 1 or step_size < 0:
raise ValueError('step_size should be a float between 0 and 1.')
# validate sample_pct
if not isinstance(sample_pct, float) or sample_pct > 1 or sample_pct < 0:
raise ValueError('sample_pct should be a float between 0 and 1.')
# validate random_state
if random_state is not None:
try:
np.random.seed(random_state)
except:
raise ValueError('Invalid random_state value given.')
if window_size < 4:
error = "window size must be at least 4."
raise ValueError(error)
if window_size > len(query) / 2:
error = "Time series is too short relative to desired window size"
raise ValueError(error)
# precompute some common values - profile length, query length etc.
step_size = int(math.floor(window_size * step_size))
profile_length = core.get_profile_length(ts, query, window_size)
data_length = len(ts)
exclusion_zone = int(np.ceil(window_size / 4.0))
matrix_profile = np.zeros(profile_length)
mp_index = np.zeros(profile_length, dtype='int')
X = np.fft.fft(ts)
mux, sigx = core.moving_avg_std(ts, window_size)
dotproduct = np.zeros(profile_length)
refine_distance = np.full(profile_length, np.inf)
orig_index = np.arange(profile_length)
# iterate over sampled indices and update the matrix profile
# compute_order = compute_indices(profile_length, step_size, sample_pct)
compute_order = np.arange(0, profile_length, step=step_size)
for iteration, idx in enumerate(compute_order):
subsequence = ts[idx:idx + window_size]
# compute distance profile
distance_profile = calc_distance_profile(X, subsequence, data_length,
window_size, mux, sigx)
# apply exclusion zone
distance_profile = core.apply_exclusion_zone(exclusion_zone, is_join,
window_size, data_length, idx, distance_profile)
# find and store nearest neighbor
if iteration == 0:
matrix_profile = distance_profile
mp_index[:] = idx
else:
update_pos = distance_profile < matrix_profile
mp_index[update_pos] = idx
matrix_profile[update_pos] = distance_profile[update_pos]
idx_min = np.argmin(distance_profile)
matrix_profile[idx] = distance_profile[idx_min]
mp_index[idx] = idx_min
idx_nn = mp_index[idx]
# compute the target indices
idx_diff = idx_nn - idx
endidx = np.min([
profile_length - 1,
idx + step_size - 1,
profile_length - idx_diff - 1
])
beginidx = np.max([0, idx - step_size + 1, 2 - idx_diff])
# compute dot product and refine distance for the idx, begin idx
# and end idx
dotproduct = calc_dotproduct_idx(dotproduct, window_size,
matrix_profile, idx, sigx, idx_nn, mux)
dotproduct = calc_dotproduct_end_idx(ts, dotproduct, idx, window_size,
endidx, idx_nn, idx_diff)
refine_distance = calc_refine_distance_end_idx(
refine_distance, dotproduct, idx, endidx, mux, sigx, idx_nn,
idx_diff, window_size)
dotproduct = calc_dotproduct_begin_idx(
ts, dotproduct, beginidx, idx, idx_diff, window_size, idx_nn)
refine_distance = calc_refine_distance_begin_idx(
refine_distance, dotproduct, beginidx, idx, idx_diff, idx_nn,
sigx, mux, window_size)
matrix_profile, mp_index = apply_update_positions(matrix_profile,
mp_index,
refine_distance,
beginidx,
endidx,
orig_index, idx_diff)
return {
'mp': matrix_profile,
'pi': mp_index,
'rmp': None,
'rpi': None,
'lmp': None,
'lpi': None,
'w': window_size,
'ez': exclusion_zone,
'join': is_join,
'sample_pct': sample_pct,
'metric': 'euclidean',
'data': {
'ts': ts,
'query': query if is_join else None
},
'class': 'MatrixProfile',
'algorithm': 'prescrimp',
}
def mass2(ts, query, extras=False):
"""
Compute the distance profile for the given query over the given time
series.
Parameters
----------
ts : array_like
The time series to search.
query : array_like
The query.
extras : boolean, default False
Optionally return additional data used to compute the matrix profile.
Returns
-------
An array of distances np.array() or dict with extras.
Extras:
{
'distance_profile': The distance profile,
'product': The FFT product between ts and query,
'data_mean': The moving average of the ts over len(query),
'query_mean': The mean of the query,
'data_std': The moving std. of the ts over len(query),
'query_std': The std. of the query
}
Raises
------
ValueError
If ts is not a list or np.array.
If query is not a list or np.array.
If ts or query is not one dimensional.
"""
ts, query = core.precheck_series_and_query_1d(ts, query)
n = len(ts)
m = len(query)
x = ts
y = query
meany = np.mean(y)
sigmay = np.std(y)
meanx, sigmax = core.moving_avg_std(x, m)
meanx = np.append(np.ones([1, len(x) - len(meanx)]), meanx)
sigmax = np.append(np.zeros([1, len(x) - len(sigmax)]), sigmax)
y = np.append(np.flip(y), np.zeros([1, n - m]))
X = np.fft.fft(x)
Y = np.fft.fft(y)
Y.resize(X.shape)
Z = X * Y
z = np.fft.ifft(Z)
dist = 2 * (m - (z[m - 1:n] - m * meanx[m - 1:n] * meany) /
(sigmax[m - 1:n] * sigmay))
dist = np.sqrt(dist)
if extras:
return {
'distance_profile': dist,
'product': z,
'data_mean': meanx,
'query_mean': meany,
'data_std': sigmax,
'query_std': sigmay
}
return dist
