Python，如何对多变量时间序列进行聚类？

我有一个玩具时间序列数据帧，格式如下：

>>> df
                 dtime dev        sw1        sw2
0  2020-01-01 00:00:00  A1   5.496714   5.593792
1  2020-01-01 00:15:00  A1   5.417291   6.385936
2  2020-01-01 00:30:00  A1   6.758800   6.056747
3  2020-01-01 00:45:00  A1   8.189697   7.862034
4  2020-01-01 01:00:00  A1   6.988069   6.595961
5  2020-01-01 01:15:00  A1   7.543641   6.080126
6  2020-01-01 01:30:00  A1   9.912546  10.208666
7  2020-01-01 01:45:00  A1   9.656324   9.917379
8  2020-01-01 02:00:00  A1   8.974970   8.980084
9  2020-01-01 02:15:00  A1  10.542560  10.307973
0  2020-01-01 00:00:00  B1   4.536582   3.121212
1  2020-01-01 00:15:00  B1   5.089826   4.669180
2  2020-01-01 00:30:00  B1   6.353073   6.010359
3  2020-01-01 00:45:00  B1   4.753386   3.951109
4  2020-01-01 01:00:00  B1   5.497304   5.336019
..                 ...  ..        ...        ...
5  2020-01-01 01:15:00  H3   3.044125   3.456906
6  2020-01-01 01:30:00  H3   1.753714   2.575774
7  2020-01-01 01:45:00  H3   0.812104   2.708897
8  2020-01-01 02:00:00  H3   0.647316   0.401928
9  2020-01-01 02:15:00  H3  -1.987569  -2.741305
0  2020-01-01 00:00:00  I3   4.780328   3.890814
1  2020-01-01 00:15:00  I3   4.801557   3.985747
2  2020-01-01 00:30:00  I3   5.366783   5.289681
3  2020-01-01 00:45:00  I3   2.815063   3.156215
4  2020-01-01 01:00:00  I3   1.969284   2.245975
5  2020-01-01 01:15:00  I3   1.720465   2.547648
6  2020-01-01 01:30:00  I3   2.582069   2.595071
7  2020-01-01 01:45:00  I3   1.439862   2.893396
8  2020-01-01 02:00:00  I3   0.025795  -0.238861
9  2020-01-01 02:15:00  I3   0.513267   3.233437

[90 rows x 4 columns]

每行显示d（ate）时间、设备和设备两个开关的位置。 我必须根据开关的位置对时间序列进行聚类。 因此，类似的设置开关（最小距离）应该形成一个集群

数据帧的创建方式是：设备A1、B1和C1应形成集群1，设备D2、E2、F2应形成集群2，设备G3、H3、I3应形成集群3

如何构建时间序列的代码如下所示：

import pandas as pd
import numpy as np

nper = 10 # number of periods
dtime_fr = '2020-01-01' # datetime from
freq = '15T'
dtime_range = pd.date_range(dtime_fr, periods=nper, freq=freq) # timestamps creation

df = pd.DataFrame()

# reising baseline
baseline_start = 5
baseline_stop = 10
baseline_linspace = np.linspace(baseline_start, baseline_stop, nper)
ts = baseline_linspace + np.random.normal(size=nper)
df = pd.concat([df, pd.DataFrame({'dtime' : dtime_range, 'dev': 'A1', 'sw1': ts, 'city':'C1'})], sort=False)
ts = baseline_linspace + np.random.normal(size=nper)
df = pd.concat([df, pd.DataFrame({'dtime' : dtime_range, 'dev': 'B1', 'sw1': ts, 'city':'C1'})], sort=False)
ts = baseline_linspace + np.random.normal(size=nper)
df = pd.concat([df, pd.DataFrame({'dtime' : dtime_range, 'dev': 'C1', 'sw1': ts, 'city':'C1'})], sort=False)

# steady baseline
baseline_start = 5
baseline_stop = 5
baseline_linspace = np.linspace(baseline_start, baseline_stop, nper)
ts = baseline_linspace + np.random.normal(size=nper)
df = pd.concat([df, pd.DataFrame({'dtime' : dtime_range, 'dev': 'D2', 'sw1': ts, 'city':'C1'})], sort=False)
ts = baseline_linspace + np.random.normal(size=nper)
df = pd.concat([df, pd.DataFrame({'dtime' : dtime_range, 'dev': 'E2', 'sw1': ts, 'city':'C1'})], sort=False)
ts = baseline_linspace + np.random.normal(size=nper)
df = pd.concat([df, pd.DataFrame({'dtime' : dtime_range, 'dev': 'F2', 'sw1': ts, 'city':'C1'})], sort=False)


# falling baseline
baseline_start = 5
baseline_stop = 0
baseline_linspace = np.linspace(baseline_start, baseline_stop, nper)
ts = baseline_linspace + np.random.normal(size=nper)
df = pd.concat([df, pd.DataFrame({'dtime' : dtime_range, 'dev': 'G3', 'sw1': ts, 'city':'C1'})], sort=False)
ts = baseline_linspace + np.random.normal(size=nper)
df = pd.concat([df, pd.DataFrame({'dtime' : dtime_range, 'dev': 'H3', 'sw1': ts, 'city':'C1'})], sort=False)
ts = baseline_linspace + np.random.normal(size=nper)
df = pd.concat([df, pd.DataFrame({'dtime' : dtime_range, 'dev': 'I3', 'sw1': ts, 'city':'C1'})], sort=False)

df.insert(3, 'sw2', df.sw1 + np.random.normal(size=len(df)))

df

如果我只有一个开关（sw1），我将按照以下方式进行集群：

df_sw1 = df.pivot(index='dev', values='sw1', columns='dtime')
dist = pdist(df_sw1, metric='euclidean')
Z = scipy.cluster.hierarchy.linkage(dist)

fig, ax = plt.subplots(figsize=(20,15))
scipy.cluster.hierarchy.dendrogram(Z, labels=df_sw1.index, orientation='top');

from sklearn.cluster import AgglomerativeClustering

hclust = AgglomerativeClustering(n_clusters=3)
hclust.fit(df_sw1)

hclust.labels_

array([0, 0, 0, 2, 2, 2, 1, 1, 1], dtype=int64)

在考虑两个开关的情况下，如果两个设备相同，SW1将（几乎）与其他设备的SW1具有相同的值，同时SW2将（几乎）与其他设备的SW2相同。 我不知道该怎么做

为了计算pdist，数据帧应该具有什么格式？ 如果必须考虑两个交换机，如何进行聚类？< /P>