def get_periodic_stat(a):
'''
Given a sequence, find its periodicity statistics
Returns
-------
stat: dictionary
pmin
pmax
eps
length
'''
assert_vector(a)
assert_monotonic(a)
stat = {}
diff = []
for i in range(len(a) - 1):
diff.append(a[i + 1] - a[i])
stat['pmin'] = min(diff)
stat['pmax'] = max(diff)
stat['eps'] = stat['pmax'] / stat['pmin'] - 1
stat['start'] = epoch_to_datetime(a[0])
stat['end'] = epoch_to_datetime(a[-1])
stat['length'] = len(a)
return stat
def periodic_subsequence(peaksIndex,
peaksTime,
min_length=5,
max_length=100,
eps=0.15,
alpha=0.1,
low=500,
high=1000):
'''
Find periodic subsequences from an array of timestamp, and values
Parameters
----------
peaksIndex: list of peak index
peaks_time: list of timestamps
min_length: minimum length of the subsequence
max_length: maximum length of the subsequence
eps: periodicity attribute
alpha: error bound percentage of upper margin
low: lower bound for series of p_min
high: upper bound for series of p_max
Returns
-------
subsequences: a list of numpy vector
each vector is one subsequence
contains the index of periodic peaks
'''
assert_vector(peaksTime)
assert_monotonic(peaksTime)
subsIndex = relative_error_periodic_subsequence(peaksTime, eps, alpha, low,
high, min_length,
max_length)
subsequences = []
for s in subsIndex:
tmp = [peaksIndex[i] for i in s]
subsequences.append(np.array(tmp))
return subsequences
def periodic_subsequence(peaks_index,
peaks_time,
min_length=5,
max_length=100,
eps=0.15,
alpha=0.1,
low=500,
high=1000):
'''
Find periodic subsequences from an array of timestamp, and values
Parameters
----------
time: list of timestamps
value: list of sensor value
peak_neighbor: size of the neighborhood
min_length: minimum length of the subsequence
eps: periodicity
low: lower bound for p_min
high: upper bound for p_max
Returns
-------
subsequences: a list of numpy vector
each vector is one subsequence
contains the index of periodic peaks
'''
assert_vector(peaks_time)
assert_monotonic(peaks_time)
subs_index = relative_error_periodic_subsequence(peaks_time, eps, alpha,
low, high, min_length,
max_length)
subsequences = []
for s in subs_index:
tmp = [peaks_index[i] for i in s]
subsequences.append(np.array(tmp))
return subsequences
def relative_error_periodic_subsequence(a, eps, alpha, low, high, min_length,
max_length):
'''
Approximation algorithm that find eps-periodic subsequences
'''
assert_vector(a)
assert_monotonic(a)
subsequences = []
n_steps = np.ceil(np.log(high / low) / np.log(1 + eps)).astype(int)
for i in range(n_steps):
pmin = low * np.power((1 + eps), i)
pmax = pmin * (1 + eps) * (1 + alpha)
if pmax > high:
break
logger.info("pmin {:0.2f} and pmax {:0.2f}".format(pmin, pmax))
seqs = absolute_error_periodic_subsequence(a, pmin, pmax)
seqs = [
np.array(s) for s in seqs
if len(s) > min_length and len(s) < max_length
]
subsequences += seqs
# sort subsequences by its start time
start = [seq[0] for seq in subsequences]
subsequences = [
seq for _, seq in sorted(zip(start, subsequences),
key=lambda pair: pair[0])
]
return subsequences
def absolute_error_periodic_subsequence(a, pmin, pmax):
'''
Return longest subsequences that is periodic
Dynamic programming approach
Parameters
----------
a: list of increasing numbers
'''
assert_vector(a)
assert_monotonic(a)
N = len(a)
traceback = {}
for i in range(N):
traceback[i] = []
for i in range(1, N):
valid = []
for j in range(i - 1, -1, -1):
if a[i] - a[j] > pmax:
break
if a[i] - a[j] >= pmin:
valid.append(j)
valid = list(reversed(valid))
# now find valid predecessor for i
for j in valid:
if not traceback[j]:
L = 2
else:
L = traceback[j][0]['L'] + 1
predecessor = {'prev': j, 'L': L}
tobe_kept = []
for k in range(len(traceback[i])):
if traceback[i][k]['L'] >= predecessor['L']:
tobe_kept.append(k)
traceback[i] = [traceback[i][k] for k in tobe_kept]
traceback[i].append(predecessor)
# logger.debug(traceback[i])
subsequences = []
sequence = []
i = N - 1
while i >= 0:
if traceback[i]:
sequence.append(i)
i = traceback[i][0]['prev']
else:
if len(sequence) > 0:
sequence.append(i)
reverse = list(reversed(sequence))
subsequences.append(reverse)
sequence = []
i -= 1
return list(reversed(subsequences))