使用自定义距离度量的最长公共子序列

这个例子展示了如何使用用户定义的距离矩阵上的对齐路径的LCSS计算，通过dtw_path_from_metric()。

该示例是使用单位圆上的弧长作为距离度量的两个角度时间序列的LCSS [2]。

图像表示成本矩阵，即单位圆上每对角度之间的弧长。相应的时间序列表示在每个成本矩阵的左侧和顶部。

对齐路径，即在预定义阈值内两个时间序列之间匹配发生的路径，在图像中以白色表示。

[1]

M. Vlachos, D. Gunopoulos, 和 G. Kollios. 2002. “发现相似的多维轨迹”，在第十八届国际数据工程会议（ICDE '02）的会议录中。IEEE计算机协会，美国，673页。

[2]

弧长定义在Wikipedia上。

/home/docs/checkouts/readthedocs.org/user_builds/tslearn/checkouts/stable/docs/examples/metrics/plot_lcss_custom_metric.py:119: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.
  plt.tight_layout()

# Author: Daniela Duarte
# License: BSD 3 clause
# sphinx_gallery_thumbnail_number = 2

import numpy as np
from numpy import pi
from sklearn.metrics import pairwise_distances
import matplotlib.pyplot as plt
from matplotlib.colors import LinearSegmentedColormap

from tslearn.generators import random_walks
from tslearn import metrics
from tslearn.preprocessing import TimeSeriesScalerMeanVariance


np.random.seed(0)
n_ts, sz = 2, 100


# Example : Length of the arc between two angles on a circle
def arc_length(angle_1, angle_2, r=1.):
    """Length of the arc between two angles (in rad) on a circle of
    radius r.
    """
    # Compute the angle between the two inputs between 0 and 2*pi.
    theta = np.mod(angle_2 - angle_1, 2*pi)
    if theta > pi:
        theta = theta - 2 * pi
    # Return the length of the arc
    L = r * np.abs(theta)
    return(L)


dataset_1 = random_walks(n_ts=n_ts, sz=sz, d=1)
scaler = TimeSeriesScalerMeanVariance(mu=0., std=pi)  # Rescale the time series
dataset_scaled_1 = scaler.fit_transform(dataset_1)

# LCSS using a function as the metric argument
path_1, sim_1 = metrics.lcss_path_from_metric(
    dataset_scaled_1[0], dataset_scaled_1[1], metric=arc_length
)

# Plots
# Compute the distance matrices for the plot
distances_1 = pairwise_distances(
    dataset_scaled_1[0], dataset_scaled_1[1], metric=arc_length
)

# Definitions for the axes
left, bottom = 0.01, 0.1
w_ts = h_ts = 0.2
left_h = left + w_ts + 0.02
width = height = 0.65
bottom_h = bottom + height + 0.02

rect_s_y = [left, bottom, w_ts, height]
rect_dist = [left_h, bottom, width, height]
rect_s_x = [left_h, bottom_h, width, h_ts]

# Plot example
plt.figure(1, figsize=(6, 6))
ax_dist = plt.axes(rect_dist)
ax_s_x = plt.axes(rect_s_x)
ax_s_y = plt.axes(rect_s_y)

ax_dist.imshow(distances_1, origin='lower')
ax_dist.axis("off")
ax_dist.autoscale(False)
ax_dist.plot(*zip(*path_1), "w-", linewidth=3.)

ticks_location = [-pi, 0, pi]
ticks_labels = [r"$\bf-\pi$", r"$\bf0$", r"$\bf\pi$"]

ax_s_x.plot([0, sz - 1], [ticks_location]*2, "k--", alpha=.2)
ax_s_x.plot(np.arange(sz), dataset_scaled_1[1], "b-", linewidth=3.)
ax_s_x.set_xlim((0, sz - 1))
ax_s_x.axis("off")

ax_s_y.plot([ticks_location]*2, [0, sz - 1], "k--", alpha=.2)
ax_s_y.plot(-dataset_scaled_1[0], np.arange(sz), "b-", linewidth=3.)
ax_s_y.set_ylim((0, sz - 1))
ax_s_y.axis("off")

for loc, s in zip(ticks_location, ticks_labels):
    ax_s_x.text(0, loc, s, fontsize="large", color="grey",
                horizontalalignment="right", verticalalignment="center")
    ax_s_y.text(-loc, 0, s, fontsize="large", color="grey",
                horizontalalignment="center", verticalalignment="top")

plt.tight_layout()
plt.show()