def test_sax():
"""Testing 'sax'"""
# Test 1
X = np.tile(np.arange(3), 5)
str_actual = sax(X, n_bins=3, quantiles='empirical', alphabet='abc')
str_desired = ''.join(["a", "b", "c"] * 5)
np.testing.assert_string_equal(str_actual, str_desired)
# Test 2
X = np.repeat(np.arange(-0.75, 1, 0.5), 3)
str_actual = sax(X, n_bins=4, quantiles='gaussian', alphabet='abcd')
str_desired = ''.join([a for a in "abcd" for _ in range(3)])
np.testing.assert_string_equal(str_actual, str_desired)
def plot_sax(ts, n_bins, quantiles='gaussian', output_file=None, **kwargs):
"""Plot the time series before and after SAX transformation.
Parameters
----------
ts : np.array, shape = [n_features]
time series to plot
n_bins : int (default = 8)
number of bins (also known as the size of the alphabet)
quantiles : str (default = 'gaussian')
the way to compute quantiles. Possible values:
- 'gaussian' : quantiles from a gaussian distribution N(0,1)
- 'empirical' : empirical quantiles
output_file : str or None (default = None)
if str, save the figure.
kwargs : keyword arguments
kwargs for matplotlib.pyplot.plot
"""
# Check input data
if not (isinstance(ts, np.ndarray) and ts.ndim == 1):
raise ValueError("'ts' must be a 1-dimensional np.ndarray.")
# Check parameters
if not isinstance(n_bins, int):
raise TypeError("'n_bins' must be an integer.")
if n_bins < 2:
raise ValueError("'n_bins' must be greater or equal than 2.")
if n_bins > 52:
raise ValueError("'n_bins' must be lower or equal than 52.")
if quantiles not in ['gaussian', 'empirical']:
raise ValueError(
"'quantiles' must be either 'gaussian' or 'empirical'.")
# Alphabet
alphabet = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"
# Compute gaussian quantiles if quantiles == 'gaussian'
if quantiles == 'gaussian':
quantiles = scipy.stats.norm.ppf(np.linspace(0, 1, num=n_bins + 1)[1:])
ts_sax = sax(ts, n_bins, quantiles, alphabet, plot=True)
else:
quantiles, ts_sax = sax(ts, n_bins, quantiles, alphabet, plot=True)
fig = plt.figure()
ax = fig.add_subplot(111)
plt.plot(ts, color='r', **kwargs)
for i in range(n_bins - 1):
plt.axhline(y=quantiles[i], ls='--', lw=1, color='g')
if 1:
x_lim = ax.get_xlim()
y_lim = ax.get_ylim()
for i in range(len(ts_sax)):
x_pos = (i - x_lim[0]) / (x_lim[1] - x_lim[0])
y_pos = (ts[i] - y_lim[0]) / (y_lim[1] - y_lim[0])
ax.text(x_pos,
y_pos,
ts_sax[i],
horizontalalignment='center',
verticalalignment='bottom',
transform=ax.transAxes,
color='m',
fontsize=25)
if output_file is not None:
plt.savefig(output_file)
# Show plot
plt.show()
def plot_paa_sax(ts,
window_size=None,
output_size=None,
overlapping=True,
n_bins=8,
quantiles='gaussian',
output_file=None,
**kwargs):
"""Plot the original time series, the time series after PAA
transformation and the time series after PAA and SAX transformations.
Parameters
----------
ts : np.array, shape = [n_features]
time series to plot
window_size : int or None (default = None)
size of the sliding window
output_size : int or None (default = None)
size of the returned time series
overlapping : bool (default = True)
when output_size is specified, the window_size is fixed
if overlapping is True and may vary if overlapping is False.
Ignored if window_size is specified.
n_bins : int (default = 8)
number of bins (also known as the size of the alphabet)
quantiles : str (default = 'gaussian')
the way to compute quantiles. Possible values:
- 'gaussian' : quantiles from a gaussian distribution N(0,1)
- 'empirical' : empirical quantiles
output_file : str or None (default = None)
if str, save the figure.
kwargs : keyword arguments
kwargs for matplotlib.pyplot.plot
"""
# Check input data
if not (isinstance(ts, np.ndarray) and ts.ndim == 1):
raise ValueError("'ts' must be a 1-dimensional np.ndarray.")
# Size of ts
ts_size = ts.size
# Check parameters for PAA and compute window_size if output_size is given
if (window_size is None and output_size is None):
raise ValueError("'window_size' xor 'output_size' must be specified.")
elif (window_size is not None and output_size is not None):
raise ValueError("'window_size' xor 'output_size' must be specified.")
elif (window_size is not None and output_size is None):
if not isinstance(overlapping, (float, int)):
raise TypeError("'overlapping' must be a boolean.")
if not isinstance(window_size, int):
raise TypeError("'window_size' must be an integer.")
if window_size < 1:
raise ValueError("'window_size' must be greater or equal than 1.")
if window_size > ts_size:
raise ValueError(
"'window_size' must be lower or equal than the size 'ts'.")
else:
if not isinstance(overlapping, (float, int)):
raise TypeError("'overlapping' must be a boolean.")
if not isinstance(output_size, int):
raise TypeError("'output_size' must be an integer.")
if output_size < 1:
raise ValueError("'output_size' must be greater or equal than 1.")
if output_size > ts_size:
raise ValueError(
"'output_size' must be lower or equal than the size of 'ts'.")
window_size = ts_size // output_size
window_size += 0 if ts_size % output_size == 0 else 1
# Check parameters for SAX
if not isinstance(n_bins, int):
raise TypeError("'n_bins' must be an integer")
if n_bins < 2:
raise ValueError("'n_bins' must be greater or equal than 2")
if n_bins > 52:
raise ValueError("'n_bins' must be lower or equal than 52")
if quantiles not in ['gaussian', 'empirical']:
raise ValueError(
"'quantiles' must be either 'gaussian' or 'empirical'")
indices, ts_paa = paa(ts,
ts.size,
window_size,
overlapping,
output_size,
plot=True)
indices_len = len(indices)
fig = plt.figure()
ax = fig.add_subplot(111)
plt.plot(ts, color='#1f77b4', **kwargs)
for i in range(indices_len):
plt.plot(indices[i], np.repeat(ts_paa[i], indices[i].size), 'r-')
plt.axvline(x=indices[0][0], ls='--', linewidth=1, color='k')
for i in range(indices_len - 1):
plt.axvline(x=(indices[i][-1] + indices[i + 1][0]) / 2,
ls='--',
linewidth=1,
color='k')
plt.axvline(x=indices[indices_len - 1][-1],
ls='--',
linewidth=1,
color='k')
# Alphabet
alphabet = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"
# Compute gaussian quantiles if quantiles == 'gaussian'
if quantiles == 'gaussian':
quantiles = scipy.stats.norm.ppf(np.linspace(0, 1, num=n_bins + 1)[1:])
ts_sax = sax(ts_paa, n_bins, quantiles, alphabet, plot=True)
else:
quantiles, ts_sax = sax(ts_paa, n_bins, quantiles, alphabet, plot=True)
for i in range(n_bins - 1):
plt.axhline(y=quantiles[i], ls='--', lw=1, color='g')
x_lim = ax.get_xlim()
y_lim = ax.get_ylim()
for i in range(indices_len):
x_pos = (np.percentile(indices[i], [50]) - x_lim[0]) / (x_lim[1] -
x_lim[0])
y_pos = (ts_paa[i] - y_lim[0]) / (y_lim[1] - y_lim[0])
ax.text(x_pos,
y_pos,
ts_sax[i],
horizontalalignment='center',
verticalalignment='bottom',
transform=ax.transAxes,
color='m',
fontsize=25)
if output_file is not None:
plt.savefig(output_file)
# Show plot
plt.show()
# Putting breakpoints to PAA and SAX visualization.
n_bins = 8
tss = [Digi_PAA_n8[0], Maxis_PAA_n8[0]]
colors = ["y", "r", "b", "c", "m"]
labels = ["Digi", "Maxis"]
alphabet = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"
fig = plt.figure(figsize=(20, 18))
for ts, color, label, e in zip(tss, colors, labels, range(5)):
ax = fig.add_subplot(3, 2, 1 + e)
#for the break point formula
quantiles = scipy.stats.norm.ppf(np.linspace(0, 1, num=n_bins + 1)[1:])
ts_sax = sax(ts, n_bins, quantiles, alphabet, plot=True)
plt.plot(ts, color=color, label=label)
plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
plt.legend(bbox_to_anchor=(1.05, 1), loc=5, borderaxespad=0.)
#for the break point visualization
for i in range(n_bins - 1):
plt.axhline(y=quantiles[i], ls='--', lw=1, color='g')
if 1:
x_lim = ax.get_xlim()
y_lim = ax.get_ylim()
for i in range(len(ts_sax)):
x_pos = (i - x_lim[0]) / (x_lim[1] - x_lim[0])
y_pos = (ts[i] - y_lim[0]) / (y_lim[1] - y_lim[0])
ax.text(x_pos,