Note

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# Compare under-sampling samplers#

The following example attends to make a qualitative comparison between the different under-sampling algorithms available in the imbalanced-learn package.

```
# Authors: Guillaume Lemaitre <g.lemaitre58@gmail.com>
# License: MIT
```

```
print(__doc__)
import seaborn as sns
sns.set_context("poster")
```

The following function will be used to create toy dataset. It uses the
`make_classification`

from scikit-learn but fixing
some parameters.

```
from sklearn.datasets import make_classification
def create_dataset(
n_samples=1000,
weights=(0.01, 0.01, 0.98),
n_classes=3,
class_sep=0.8,
n_clusters=1,
):
return make_classification(
n_samples=n_samples,
n_features=2,
n_informative=2,
n_redundant=0,
n_repeated=0,
n_classes=n_classes,
n_clusters_per_class=n_clusters,
weights=list(weights),
class_sep=class_sep,
random_state=0,
)
```

The following function will be used to plot the sample space after resampling to illustrate the specificities of an algorithm.

```
def plot_resampling(X, y, sampler, ax, title=None):
X_res, y_res = sampler.fit_resample(X, y)
ax.scatter(X_res[:, 0], X_res[:, 1], c=y_res, alpha=0.8, edgecolor="k")
if title is None:
title = f"Resampling with {sampler.__class__.__name__}"
ax.set_title(title)
sns.despine(ax=ax, offset=10)
```

The following function will be used to plot the decision function of a classifier given some data.

```
import numpy as np
def plot_decision_function(X, y, clf, ax, title=None):
plot_step = 0.02
x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
xx, yy = np.meshgrid(
np.arange(x_min, x_max, plot_step), np.arange(y_min, y_max, plot_step)
)
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)
ax.contourf(xx, yy, Z, alpha=0.4)
ax.scatter(X[:, 0], X[:, 1], alpha=0.8, c=y, edgecolor="k")
if title is not None:
ax.set_title(title)
```

```
from sklearn.linear_model import LogisticRegression
clf = LogisticRegression()
```

## Prototype generation: under-sampling by generating new samples#

`ClusterCentroids`

under-samples by replacing
the original samples by the centroids of the cluster found.

```
import matplotlib.pyplot as plt
from sklearn.cluster import MiniBatchKMeans
from imblearn import FunctionSampler
from imblearn.pipeline import make_pipeline
from imblearn.under_sampling import ClusterCentroids
X, y = create_dataset(n_samples=400, weights=(0.05, 0.15, 0.8), class_sep=0.8)
samplers = {
FunctionSampler(), # identity resampler
ClusterCentroids(
estimator=MiniBatchKMeans(n_init=1, random_state=0), random_state=0
),
}
fig, axs = plt.subplots(nrows=2, ncols=2, figsize=(15, 15))
for ax, sampler in zip(axs, samplers):
model = make_pipeline(sampler, clf).fit(X, y)
plot_decision_function(
X, y, model, ax[0], title=f"Decision function with {sampler.__class__.__name__}"
)
plot_resampling(X, y, sampler, ax[1])
fig.tight_layout()
```

## Prototype selection: under-sampling by selecting existing samples#

The algorithm performing prototype selection can be subdivided into two groups: (i) the controlled under-sampling methods and (ii) the cleaning under-sampling methods.

With the controlled under-sampling methods, the number of samples to be
selected can be specified.
`RandomUnderSampler`

is the most naive way of
performing such selection by randomly selecting a given number of samples by
the targeted class.

```
from imblearn.under_sampling import RandomUnderSampler
X, y = create_dataset(n_samples=400, weights=(0.05, 0.15, 0.8), class_sep=0.8)
samplers = {
FunctionSampler(), # identity resampler
RandomUnderSampler(random_state=0),
}
fig, axs = plt.subplots(nrows=2, ncols=2, figsize=(15, 15))
for ax, sampler in zip(axs, samplers):
model = make_pipeline(sampler, clf).fit(X, y)
plot_decision_function(
X, y, model, ax[0], title=f"Decision function with {sampler.__class__.__name__}"
)
plot_resampling(X, y, sampler, ax[1])
fig.tight_layout()
```

`NearMiss`

algorithms implement some
heuristic rules in order to select samples. NearMiss-1 selects samples from
the majority class for which the average distance of the \(k`\) nearest
samples of the minority class is the smallest. NearMiss-2 selects the samples
from the majority class for which the average distance to the farthest
samples of the negative class is the smallest. NearMiss-3 is a 2-step
algorithm: first, for each minority sample, their \(m\)
nearest-neighbors will be kept; then, the majority samples selected are the
on for which the average distance to the \(k\) nearest neighbors is the
largest.

```
from imblearn.under_sampling import NearMiss
X, y = create_dataset(n_samples=1000, weights=(0.05, 0.15, 0.8), class_sep=1.5)
samplers = [NearMiss(version=1), NearMiss(version=2), NearMiss(version=3)]
fig, axs = plt.subplots(nrows=3, ncols=2, figsize=(15, 25))
for ax, sampler in zip(axs, samplers):
model = make_pipeline(sampler, clf).fit(X, y)
plot_decision_function(
X,
y,
model,
ax[0],
title=f"Decision function for {sampler.__class__.__name__}-{sampler.version}",
)
plot_resampling(
X,
y,
sampler,
ax[1],
title=f"Resampling using {sampler.__class__.__name__}-{sampler.version}",
)
fig.tight_layout()
```

```
/home/circleci/project/imblearn/under_sampling/_prototype_selection/_nearmiss.py:203: UserWarning: The number of the samples to be selected is larger than the number of samples available. The balancing ratio cannot be ensure and all samples will be returned.
warnings.warn(
/home/circleci/project/imblearn/under_sampling/_prototype_selection/_nearmiss.py:203: UserWarning: The number of the samples to be selected is larger than the number of samples available. The balancing ratio cannot be ensure and all samples will be returned.
warnings.warn(
/home/circleci/project/imblearn/under_sampling/_prototype_selection/_nearmiss.py:203: UserWarning: The number of the samples to be selected is larger than the number of samples available. The balancing ratio cannot be ensure and all samples will be returned.
warnings.warn(
/home/circleci/project/imblearn/under_sampling/_prototype_selection/_nearmiss.py:203: UserWarning: The number of the samples to be selected is larger than the number of samples available. The balancing ratio cannot be ensure and all samples will be returned.
warnings.warn(
```

`EditedNearestNeighbours`

removes samples of
the majority class for which their class differ from the one of their
nearest-neighbors. This sieve can be repeated which is the principle of the
`RepeatedEditedNearestNeighbours`

.
`AllKNN`

is slightly different from the
`RepeatedEditedNearestNeighbours`

by changing
the \(k\) parameter of the internal nearest neighors algorithm,
increasing it at each iteration.

```
from imblearn.under_sampling import (
AllKNN,
EditedNearestNeighbours,
RepeatedEditedNearestNeighbours,
)
X, y = create_dataset(n_samples=500, weights=(0.2, 0.3, 0.5), class_sep=0.8)
samplers = [
EditedNearestNeighbours(),
RepeatedEditedNearestNeighbours(),
AllKNN(allow_minority=True),
]
fig, axs = plt.subplots(3, 2, figsize=(15, 25))
for ax, sampler in zip(axs, samplers):
model = make_pipeline(sampler, clf).fit(X, y)
plot_decision_function(
X, y, clf, ax[0], title=f"Decision function for \n{sampler.__class__.__name__}"
)
plot_resampling(
X, y, sampler, ax[1], title=f"Resampling using \n{sampler.__class__.__name__}"
)
fig.tight_layout()
```

`CondensedNearestNeighbour`

makes use of a
1-NN to iteratively decide if a sample should be kept in a dataset or not.
The issue is that `CondensedNearestNeighbour`

is sensitive to noise by preserving the noisy samples.
`OneSidedSelection`

also used the 1-NN and
use `TomekLinks`

to remove the samples
considered noisy. The
`NeighbourhoodCleaningRule`

use a
`EditedNearestNeighbours`

to remove some
sample. Additionally, they use a 3 nearest-neighbors to remove samples which
do not agree with this rule.

```
from imblearn.under_sampling import (
CondensedNearestNeighbour,
NeighbourhoodCleaningRule,
OneSidedSelection,
)
X, y = create_dataset(n_samples=500, weights=(0.2, 0.3, 0.5), class_sep=0.8)
fig, axs = plt.subplots(nrows=3, ncols=2, figsize=(15, 25))
samplers = [
CondensedNearestNeighbour(random_state=0),
OneSidedSelection(random_state=0),
NeighbourhoodCleaningRule(n_neighbors=11),
]
for ax, sampler in zip(axs, samplers):
model = make_pipeline(sampler, clf).fit(X, y)
plot_decision_function(
X, y, clf, ax[0], title=f"Decision function for \n{sampler.__class__.__name__}"
)
plot_resampling(
X, y, sampler, ax[1], title=f"Resampling using \n{sampler.__class__.__name__}"
)
fig.tight_layout()
```

`InstanceHardnessThreshold`

uses the
prediction of classifier to exclude samples. All samples which are classified
with a low probability will be removed.

```
from imblearn.under_sampling import InstanceHardnessThreshold
samplers = {
FunctionSampler(), # identity resampler
InstanceHardnessThreshold(
estimator=LogisticRegression(),
random_state=0,
),
}
fig, axs = plt.subplots(nrows=2, ncols=2, figsize=(15, 15))
for ax, sampler in zip(axs, samplers):
model = make_pipeline(sampler, clf).fit(X, y)
plot_decision_function(
X,
y,
model,
ax[0],
title=f"Decision function with \n{sampler.__class__.__name__}",
)
plot_resampling(
X, y, sampler, ax[1], title=f"Resampling using \n{sampler.__class__.__name__}"
)
fig.tight_layout()
plt.show()
```

**Total running time of the script:** (0 minutes 9.581 seconds)

**Estimated memory usage:** 47 MB