# Adjustment for chance in Clustering Performance Evaluation in Scikit-learn

The following plots demonstrate the impact of the number of clusters and number of samples on various clustering performance evaluation metrics.

Non-adjusted measures such as the V-Measure show a dependency between the number of clusters and the number of samples: the mean V-Measure of random labeling increases significantly as the number of clusters is closer to the total number of samples used to compute the measure.

Adjusted for chance measure such as ARI display some random variations centered around a mean score of 0.0 for any number of samples and clusters.

Only adjusted measures can hence safely be used as a consensus index to evaluate the average stability of clustering algorithms for a given value of k on various overlapping sub-samples of the dataset.

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### Version¶

```
import sklearn
sklearn.__version__
```

### Imports¶

```
import plotly.plotly as py
import plotly.graph_objs as go
import numpy as np
import matplotlib.pyplot as plt
from time import time
from sklearn import metrics
```

### Calculations¶

```
def uniform_labelings_scores(score_func, n_samples, n_clusters_range,
fixed_n_classes=None, n_runs=5, seed=42):
"""Compute score for 2 random uniform cluster labelings.
Both random labelings have the same number of clusters for each value
possible value in ``n_clusters_range``.
When fixed_n_classes is not None the first labeling is considered a ground
truth class assignment with fixed number of classes.
"""
random_labels = np.random.RandomState(seed).randint
scores = np.zeros((len(n_clusters_range), n_runs))
if fixed_n_classes is not None:
labels_a = random_labels(low=0, high=fixed_n_classes, size=n_samples)
for i, k in enumerate(n_clusters_range):
for j in range(n_runs):
if fixed_n_classes is None:
labels_a = random_labels(low=0, high=k, size=n_samples)
labels_b = random_labels(low=0, high=k, size=n_samples)
scores[i, j] = score_func(labels_a, labels_b)
return scores
score_funcs = [
metrics.adjusted_rand_score,
metrics.v_measure_score,
metrics.adjusted_mutual_info_score,
metrics.mutual_info_score,
]
```

### Independent random clusterings with equal cluster number¶

```
n_samples = 100
n_clusters_range = np.linspace(2, n_samples, 10).astype(np.int)
plots = []
names = []
for score_func in score_funcs:
print("Computing %s for %d values of n_clusters and n_samples=%d"
% (score_func.__name__, len(n_clusters_range), n_samples))
t0 = time()
scores = uniform_labelings_scores(score_func, n_samples, n_clusters_range)
print("done in %0.3fs" % (time() - t0))
plots.append(
go.Scatter(
x=n_clusters_range, y=np.median(scores, axis=1),
name=score_func.__name__, mode='lines',
error_y=dict(visible=True, arrayminus=scores.std(axis=1)[0]),
line=dict(width=2))
)
```

```
layout = go.Layout(title="Clustering measures for 2 random uniform labelings<br>"
"with equal number of clusters",
hovermode='closest',
xaxis=dict(title='Number of clusters (Number of samples is fixed to %d)'
% n_samples),
yaxis=dict(title='Score value', range=[0, 5]))
fig = go.Figure(data=plots, layout=layout)
py.iplot(fig)
```

### Random labeling with varying n_clusters against ground class labels¶

```
n_samples = 1000
n_clusters_range = np.linspace(2, 100, 10).astype(np.int)
n_classes = 10
plots = []
names = []
for score_func in score_funcs:
print("Computing %s for %d values of n_clusters and n_samples=%d"
% (score_func.__name__, len(n_clusters_range), n_samples))
t0 = time()
scores = uniform_labelings_scores(score_func, n_samples, n_clusters_range,
fixed_n_classes=n_classes)
print("done in %0.3fs" % (time() - t0))
plots.append(
go.Scatter(
x=n_clusters_range, y=np.median(scores, axis=1),
name=score_func.__name__, mode='lines',
error_y=dict(visible=True, arrayminus=scores.std(axis=1)[0]),
line=dict(width=2))
)
```

```
layout = go.Layout(title="Clustering measures for random uniform labeling<br>"
"against reference assignment with %d classes" % n_classes,
hovermode='closest',
xaxis=dict(title='Number of clusters (Number of samples is fixed to %d)'
% n_samples),
yaxis=dict(title='Score value'))
fig = go.Figure(data=plots, layout=layout)
py.iplot(fig)
```

### License¶

Author:

```
Olivier Grisel <olivier.grisel@ensta.org>
```

License:

` BSD 3 clause`