# PAA transform (and inverse transform) of the data
n_paa_segments = 10
paa = PiecewiseAggregateApproximation(n_segments=n_paa_segments)
paa_dataset_inv = paa.inverse_transform(paa.fit_transform(dataset))
# SAX transform
n_sax_symbols = 8
sax = SymbolicAggregateApproximation(n_segments=n_paa_segments,
alphabet_size_avg=n_sax_symbols)
sax_dataset_inv = sax.inverse_transform(sax.fit_transform(dataset))
# 1d-SAX transform
n_sax_symbols_avg = 8
n_sax_symbols_slope = 8
one_d_sax = OneD_SymbolicAggregateApproximation(
n_segments=n_paa_segments,
alphabet_size_avg=n_sax_symbols_avg,
alphabet_size_slope=n_sax_symbols_slope)
transformed_data = one_d_sax.fit_transform(dataset)
one_d_sax_dataset_inv = one_d_sax.inverse_transform(transformed_data)
plt.figure()
plt.subplot(2, 2, 1) # First, raw time series
plt.plot(dataset[0].ravel(), "b-")
plt.title("Raw time series")
plt.subplot(2, 2, 2) # Second, PAA
plt.plot(dataset[0].ravel(), "b-", alpha=0.4)
plt.plot(paa_dataset_inv[0].ravel(), "b-")
plt.title("PAA")
plt.subplot(2, 2, 3) # Then SAX
# Generate a random walk
ts = np.random.normal(size=700)
ts = np.cumsum(ts)
ts = ts - np.mean(ts)
ts /= np.std(ts, ddof=1)
print('length of ts', len(ts))
n_sax_symbols_avg = 8
n_sax_symbols_slope = 8
n_paa_segments = 10
# 1d-SAX transform
one_d_sax = OneD_SymbolicAggregateApproximation(
n_segments=n_paa_segments,
alphabet_size_avg=n_sax_symbols_avg,
alphabet_size_slope=n_sax_symbols_slope,
sigma_l=np.sqrt(0.03 / (np.floor(len(ts) / n_paa_segments))))
one_d_sax_dataset_inv = one_d_sax.inverse_transform(
one_d_sax.fit_transform(ts))
# Our oneD_SAX
width = len(ts) // n_paa_segments
onedsax = compress(ts, width)
onedsax = digitize(onedsax, width, n_sax_symbols_slope, n_sax_symbols_avg)
onedsax_ts = reverse_digitize(onedsax, width, n_sax_symbols_slope,
n_sax_symbols_avg)
onedsax_ts = reconstruct(onedsax_ts, width=width)
# plot
plt.figure()