距离和矩阵轮廓

这个例子说明了如何计算矩阵轮廓。对于时间序列中每个指定长度的片段，计算每个子序列与该片段之间的距离。返回最小的距离，除了从提取片段的位置上的平凡匹配，该距离等于零。

# Author: Gilles Vandewiele
# License: BSD 3 clause

import numpy
import matplotlib.patches as patches
from mpl_toolkits.axes_grid1.inset_locator import inset_axes
import matplotlib.pyplot as plt

from tslearn.datasets import CachedDatasets
from tslearn.preprocessing import TimeSeriesScalerMeanVariance
from tslearn.matrix_profile import MatrixProfile

import warnings
warnings.filterwarnings('ignore')

# Set a seed to ensure determinism
numpy.random.seed(42)

# Load the Trace dataset
X_train, y_train, _, _ = CachedDatasets().load_dataset("Trace")

# Normalize the time series
scaler = TimeSeriesScalerMeanVariance()
X_train = scaler.fit_transform(X_train)

# Take the first time series
ts = X_train[0, :, :]

# We will take the spike as a segment
subseq_len = 20
start = 45
segment = ts[start:start + subseq_len]

# Create our matrix profile
matrix_profiler = MatrixProfile(subsequence_length=subseq_len, scale=True)
mp = matrix_profiler.fit_transform([ts]).flatten()

# Create a grid for our plots
fig, (ax1, ax2, ax3) = plt.subplots(3, 1, sharex=True)

# Plot our timeseries
ax1.plot(ts, c='b', label='time series')
ax1.add_patch(patches.Rectangle((start, numpy.min(ts) - 0.1), subseq_len,
                                numpy.max(ts) - numpy.min(ts) + 0.2,
                                facecolor='b', alpha=0.25,
                                label='segment'))
ax1.axvline(start, c='b', linestyle='--', lw=2, alpha=0.5,
            label='segment start')
ax1.legend(loc='lower right', ncol=4, fontsize=8,
           handletextpad=0.1, columnspacing=0.5)
ax1.set_title('The time series')

# Inset plot with our segment
fig_ax_in = ax1.inset_axes([0.5, 0.55, 0.2, 0.4])
fig_ax_in.plot(scaler.fit_transform(segment.reshape(1, -1, 1))[0], c='b')
ax1.indicate_inset(inset_ax=fig_ax_in, transform=ax1.transData,
                   bounds=[start, numpy.min(ts) - 0.1, subseq_len,
                           numpy.max(ts) - numpy.min(ts) + 0.2],
                   linestyle='--', alpha=0.75)
fig_ax_in.tick_params(labelleft=False, labelbottom=False)
fig_ax_in.xaxis.set_visible(False)
fig_ax_in.yaxis.set_visible(False)

# Calculate a distance profile, which represents the distance from each
# subsequence of the time series and the segment
distances = []
for i in range(len(ts) - subseq_len):
    scaled_ts = scaler.fit_transform(ts[i:i+subseq_len].reshape(1, -1, 1))
    scaled_segment = scaler.fit_transform(segment.reshape(1, -1, 1))
    distances.append(numpy.linalg.norm(scaled_ts - scaled_segment))

# Mask out the distances in the trivial match zone, get the nearest
# neighbor and put the old distances back in place so we can plot them.
distances = numpy.array(distances)
mask = list(range(start - subseq_len // 4, start + subseq_len // 4))
old_distances = distances[mask]
distances[mask] = numpy.inf
nearest_neighbor = numpy.argmin(distances)
dist_nn = distances[nearest_neighbor]
distances[mask] = old_distances

# Plot our distance profile
ax2.plot(distances, c='b')
ax2.set_title('Segment distance profile')
dist_diff = numpy.max(distances) - numpy.min(distances)
ax2.add_patch(patches.Rectangle((start - subseq_len // 4,
                                 numpy.min(distances) - 0.1),
                                subseq_len // 2,
                                dist_diff + 0.2,
                                facecolor='r', alpha=0.5,
                                label='exclusion zone'))
ax2.scatter(nearest_neighbor, dist_nn, c='r', marker='x', s=50,
            label='neighbor dist = {}'.format(numpy.around(dist_nn, 3)))
ax2.axvline(start, c='b', linestyle='--', lw=2, alpha=0.5,
            label='segment start')
ax2.legend(loc='lower right', fontsize=8, ncol=3,
           handletextpad=0.1, columnspacing=0.5)

# Plot our matrix profile
ax3.plot(mp, c='b')
ax3.set_title('Matrix profile')
ax3.scatter(start, mp[start],
            c='r', marker='x', s=75,
            label='MP segment = {}'.format(numpy.around(mp[start], 3)))
ax3.axvline(start, c='b', linestyle='--', lw=2, alpha=0.5,
            label='segment start')
ax3.legend(loc='lower right', fontsize=8,
           handletextpad=0.1, columnspacing=0.25)

plt.tight_layout()
plt.show()