def ts_to_string(series, cuts):
"""A straightforward num-to-string conversion.
>>> ts_to_string([-1, 0, 1], cuts_for_asize(3))
'abc'
>>> ts_to_string([1, -1, 1], cuts_for_asize(3))
'cac'
"""
series = np.array(series)
a_size = len(cuts)
sax = list()
for i in range(series.shape[0]):
num = series[i]
# If the number is below 0, start from the bottom, otherwise from the top
if num >= 0:
j = a_size - 1
while j > 0 and cuts[j] >= num:
j = j - 1
sax.append(idx2letter(j))
else:
j = 1
while j < a_size and cuts[j] <= num:
j = j + 1
sax.append(idx2letter(j-1))
return ''.join(sax)
def ts_to_string(series, cuts):
"""A straightforward num-to-string conversion."""
a_size = len(cuts)
sax = list()
for i in range(0, len(series)):
num = series[i]
# if teh number below 0, start from the bottom, or else from the top
if (num >= 0):
j = a_size - 1
while ((j > 0) and (cuts[j] >= num)):
j = j - 1
sax.append(idx2letter(j))
else:
j = 1
while (j < a_size and cuts[j] <= num):
j = j + 1
sax.append(idx2letter(j - 1))
return ''.join(sax)
def test_sizing():
"""Test idx to char."""
assert 'a' == idx2letter(0)
assert 'h' == idx2letter(7)
assert 't' == idx2letter(19)
with pytest.raises(ValueError, match=r'.* idx'):
idx2letter(-1)
with pytest.raises(ValueError, match=r'.* idx .*'):
idx2letter(20)
def ts_to_string(series, cuts):
"""A straightforward num-to-string conversion."""
# - series中的一个时刻的数值 num, 在alphabet cuts中找对应的位置, 根据其位置转化为字母
a_size = len(cuts)
sax = list()
for i in range(0, len(series)):
num = series[i]
# num >= 0 从后往前找对应字母 j = a_size - 1
if (num >= 0):
j = a_size - 1
while ((j > 0) and (cuts[j] >= num)):
j = j - 1
sax.append(idx2letter(j))
# num < 0 从前往后找对应字母 j = 1
else:
j = 1
while (j < a_size and cuts[j] <= num):
j = j + 1
sax.append(idx2letter(j - 1))
return ''.join(sax)
def sax_via_window(series, win_size, paa_size, alphabet_size=3,
nr_strategy='exact', znorm_threshold=0.01, sax_type='unidim'):
"""Simple via window conversion implementation.
# SAX-ENERGY
>>> sax_via_window([[1, 2, 3], [4, 5, 6]], win_size=1, paa_size=3, sax_type='energy', nr_strategy=None)['abc']
[0, 1]
>>> sax_via_window([[1, 2, 3, 4], [4, 5, 6, 7]], win_size=1, paa_size=4, sax_type='energy', nr_strategy=None)['aacc']
[0, 1]
>>> sax_via_window([[1, 2, 3, 4], [4, 5, 6, 7]], win_size=2, paa_size=4, sax_type='energy', nr_strategy=None)['aaccaacc']
[0]
# SAX-REPEAT
>>> sax_via_window([[1, 2, 3], [4, 5, 6], [7, 8, 9]], win_size=2, paa_size=2, sax_type='repeat', nr_strategy=None)['ab']
[0, 1]
>>> sax_via_window([[1, 2, 3], [4, 5, 6], [7, 8, 9]], win_size=1, paa_size=1, sax_type='repeat', nr_strategy=None)['a']
[0, 1, 2]
# SAX-INDEPENDENT
>>> sax_via_window([[1, 2, 3, 4], [4, 5, 6, 7]], win_size=2, paa_size=2, sax_type='independent', nr_strategy=None)['acacacac']
[0]
>>> sax_via_window([[1, 2], [4, 5], [7, 8]], win_size=2, paa_size=2, sax_type='independent', nr_strategy=None)['acac']
[0, 1]
>>> sax_via_window([[1, 2], [4, 8], [7, 5]], win_size=2, paa_size=2, sax_type='independent', nr_strategy=None)['acac']
[0]
>>> sax_via_window([[1, 2], [4, 8], [7, 5]], win_size=2, paa_size=2, sax_type='independent', nr_strategy=None)['acca']
[1]
"""
# Convert to numpy array.
series = np.array(series)
# Check on dimensions.
if len(series.shape) > 2:
raise ValueError('Please reshape time-series to stack dimensions along the 2nd dimension, so that the array shape is a 2-tuple.')
# PAA size is the length of the PAA sequence.
if sax_type != 'energy' and paa_size > win_size:
raise ValueError('PAA size cannot be greater than the window size.')
if sax_type == 'energy' and len(series.shape) == 1:
raise ValueError('Must pass a multidimensional time-series to SAX-ENERGY.')
# Breakpoints.
cuts = cuts_for_asize(alphabet_size)
# Dictionary mapping SAX words to indices.
sax = defaultdict(list)
if sax_type == 'repeat':
# Maps indices to multi-dimensional SAX words.
multidim_sax_dict = []
# List of all the multi-dimensional SAX words.
multidim_sax_list = []
# Sliding window across time dimension.
for i in range(series.shape[0] - win_size + 1):
# Subsection starting at this index.
sub_section = series[i: i + win_size]
# Z-normalized subsection.
if win_size == 1:
zn = sub_section
else:
zn = znorm(sub_section, znorm_threshold)
# PAA representation of subsection.
paa_rep = paa(zn, paa_size, 'repeat')
# SAX representation of subsection, but in terms of multi-dimensional vectors.
multidim_sax = get_sax_list(paa_rep, cuts)
# Update data-structures.
multidim_sax_dict.append(multidim_sax)
multidim_sax_list.extend(multidim_sax)
# Cluster with k-means++.
kmeans = KMeans(n_clusters=alphabet_size, random_state=0).fit(multidim_sax_list)
# Cluster indices in sorted order.
order = np.lexsort(np.rot90(kmeans.cluster_centers_))
# Sliding window across time dimension.
prev_word = ''
for i in range(series.shape[0] - win_size + 1):
# Map cluster indices to new SAX letters.
curr_word_list = map(lambda cluster_index: idx2letter(order[cluster_index]), kmeans.predict(multidim_sax_dict[i]))
curr_word = ''.join(curr_word_list)
if '' != prev_word:
if 'exact' == nr_strategy and prev_word == curr_word:
continue
elif 'mindist' == nr_strategy and is_mindist_zero(prev_word, curr_word):
continue
prev_word = curr_word
sax[curr_word].append(i)
else:
# Sliding window across time dimension.
prev_word = ''
for i in range(series.shape[0] - win_size + 1):
# Subsection starting at this index.
sub_section = series[i: i + win_size]
if sax_type == 'energy':
curr_word = ''
for energy_dist in sub_section:
# Normalize energy distribution.
energy_zn = znorm(energy_dist, znorm_threshold)
# PAA representation of energy distribution.
paa_rep = paa(energy_zn, paa_size, 'unidim')
# paa_rep = energy_zn
# SAX representation of the energy distribution.
energy_word = ts_to_string(paa_rep, cuts)
# Add to current word.
curr_word += energy_word
elif sax_type == 'independent':
curr_word = ''
for dim in range(sub_section.shape[1]):
# Obtain the subsequence restricted to one dimension.
one_dimension_sub_section = sub_section[:, dim]
# Z-normalized subsection.
zn = znorm(one_dimension_sub_section, znorm_threshold)
# PAA representation of subsection.
paa_rep = paa(zn, paa_size, 'unidim')
# Get the SAX word - just a unidimensional SAX.
one_dim_word = ts_to_string(paa_rep, cuts)
# Add this dimensions' representation to the overall SAX word.
curr_word += one_dim_word
else:
# Z-normalized subsection.
zn = znorm(sub_section, znorm_threshold)
# PAA representation of subsection.
paa_rep = paa(zn, paa_size, sax_type)
# SAX representation of subsection.
curr_word = ts_to_string(paa_rep, cuts)
if '' != prev_word:
if 'exact' == nr_strategy and prev_word == curr_word:
continue
elif 'mindist' == nr_strategy and is_mindist_zero(prev_word, curr_word):
continue
prev_word = curr_word
sax[curr_word].append(i)
return sax