Representation Methods¶

Comparison of different cluster representation methods: medoid, maxoid, mean, minmax, and duration.

Author: Maximilian Hoffmann

In [1]:

%load_ext autoreload
%autoreload 2

import pandas as pd
import plotly.express as px
import plotly.io as pio

import tsam
from tsam import ClusterConfig

pio.renderers.default = "notebook_connected"
import warnings

# Added to every example notebook: silence the v3 column-order
# FutureWarning in the rendered docs (tsam v4 returns result columns in
# input order; see migration guide).
warnings.filterwarnings(
    "ignore", category=FutureWarning, message=".*sorted alphabetically.*"
)

%load_ext autoreload %autoreload 2 import pandas as pd import plotly.express as px import plotly.io as pio import tsam from tsam import ClusterConfig pio.renderers.default = "notebook_connected" import warnings # Added to every example notebook: silence the v3 column-order # FutureWarning in the rendered docs (tsam v4 returns result columns in # input order; see migration guide). warnings.filterwarnings( "ignore", category=FutureWarning, message=".*sorted alphabetically.*" )

Input data¶

In [2]:

raw = pd.read_csv("testdata.csv", index_col=0)
raw

raw = pd.read_csv("testdata.csv", index_col=0) raw

Out[2]:

	GHI	T	Wind	Load
2009-12-31 23:30:00	0	-2.1	7.1	375.478394
2010-01-01 00:30:00	0	-2.8	8.6	364.541326
2010-01-01 01:30:00	0	-3.3	9.7	357.416844
2010-01-01 02:30:00	0	-3.2	9.8	350.191306
2010-01-01 03:30:00	0	-3.2	9.4	345.161449
...	...	...	...	...
2010-12-31 18:30:00	0	0.9	4.1	413.094373
2010-12-31 19:30:00	0	0.6	3.8	396.424646
2010-12-31 20:30:00	0	0.3	3.4	386.052577
2010-12-31 21:30:00	0	-0.3	4.1	383.066817
2010-12-31 22:30:00	0	-1.1	5.3	365.189007

8760 rows × 4 columns

Medoid representation¶

Picks the actual observed period closest to each cluster centroid.

In [3]:

result_medoid = tsam.aggregate(
    raw,
    n_clusters=8,
    period_duration=24,
    cluster=ClusterConfig(method="hierarchical", representation="medoid"),
)
result_medoid.accuracy

result_medoid = tsam.aggregate( raw, n_clusters=8, period_duration=24, cluster=ClusterConfig(method="hierarchical", representation="medoid"), ) result_medoid.accuracy

Out[3]:

AccuracyMetrics(
  rmse=0.1097 (weighted),
  mae=0.0766 (weighted),
  rmse_duration=0.0374 (weighted)
)

In [4]:

result_medoid.plot.cluster_members()

result_medoid.plot.cluster_members()

Maxoid representation¶

Picks the period that maximizes the sum of all column values in each cluster.

In [5]:

result_maxoid = tsam.aggregate(
    raw,
    n_clusters=8,
    period_duration=24,
    cluster=ClusterConfig(method="hierarchical", representation="maxoid"),
    preserve_column_means=False,
)
result_maxoid.accuracy

result_maxoid = tsam.aggregate( raw, n_clusters=8, period_duration=24, cluster=ClusterConfig(method="hierarchical", representation="maxoid"), preserve_column_means=False, ) result_maxoid.accuracy

Out[5]:

AccuracyMetrics(
  rmse=0.1907 (weighted),
  mae=0.1329 (weighted),
  rmse_duration=0.1110 (weighted)
)

In [6]:

result_maxoid.plot.cluster_members()

result_maxoid.plot.cluster_members()

Mean representation¶

Averages all member periods of each cluster.

In [7]:

result_mean = tsam.aggregate(
    raw,
    n_clusters=20,
    period_duration=24,
    cluster=ClusterConfig(method="hierarchical", representation="mean"),
)
result_mean.accuracy

result_mean = tsam.aggregate( raw, n_clusters=20, period_duration=24, cluster=ClusterConfig(method="hierarchical", representation="mean"), ) result_mean.accuracy

Out[7]:

AccuracyMetrics(
  rmse=0.0803 (weighted),
  mae=0.0554 (weighted),
  rmse_duration=0.0294 (weighted)
)

In [8]:

result_mean.plot.cluster_members()

result_mean.plot.cluster_members()

MinMax Mean representation¶

Like mean, but preserves the minimum and maximum values per column.

In [9]:

result_minmax = tsam.aggregate(
    raw,
    n_clusters=20,
    period_duration=24,
    cluster=ClusterConfig(method="hierarchical", representation="minmax_mean"),
    preserve_column_means=False,
)
result_minmax.accuracy

result_minmax = tsam.aggregate( raw, n_clusters=20, period_duration=24, cluster=ClusterConfig(method="hierarchical", representation="minmax_mean"), preserve_column_means=False, ) result_minmax.accuracy

Out[9]:

AccuracyMetrics(
  rmse=0.0803 (weighted),
  mae=0.0554 (weighted),
  rmse_duration=0.0294 (weighted)
)

In [10]:

result_minmax.plot.cluster_members()

result_minmax.plot.cluster_members()

Distribution representation¶

Preserves the full value distribution (duration curve) within each cluster.

In [11]:

result_duration = tsam.aggregate(
    raw,
    n_clusters=20,
    period_duration=24,
    cluster=ClusterConfig(method="hierarchical", representation="distribution"),
    preserve_column_means=False,
)
result_duration.accuracy

result_duration = tsam.aggregate( raw, n_clusters=20, period_duration=24, cluster=ClusterConfig(method="hierarchical", representation="distribution"), preserve_column_means=False, ) result_duration.accuracy

Out[11]:

AccuracyMetrics(
  rmse=0.0957 (weighted),
  mae=0.0643 (weighted),
  rmse_duration=0.0055 (weighted)
)

In [12]:

result_duration.plot.cluster_members()

result_duration.plot.cluster_members()