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# IsolationForest example¶

An example using `IsolationForest`

for anomaly
detection.

The Isolation Forest is an ensemble of “Isolation Trees” that “isolate” observations by recursive random partitioning, which can be represented by a tree structure. The number of splittings required to isolate a sample is lower for outliers and higher for inliers.

In the present example we demo two ways to visualize the decision boundary of an Isolation Forest trained on a toy dataset.

## Data generation¶

We generate two clusters (each one containing `n_samples`

) by randomly
sampling the standard normal distribution as returned by
`numpy.random.randn`

. One of them is spherical and the other one is
slightly deformed.

For consistency with the `IsolationForest`

notation,
the inliers (i.e. the gaussian clusters) are assigned a ground truth label `1`

whereas the outliers (created with `numpy.random.uniform`

) are assigned
the label `-1`

.

```
import numpy as np
from sklearn.model_selection import train_test_split
n_samples, n_outliers = 120, 40
rng = np.random.RandomState(0)
covariance = np.array([[0.5, -0.1], [0.7, 0.4]])
cluster_1 = 0.4 * rng.randn(n_samples, 2) @ covariance + np.array([2, 2]) # general
cluster_2 = 0.3 * rng.randn(n_samples, 2) + np.array([-2, -2]) # spherical
outliers = rng.uniform(low=-4, high=4, size=(n_outliers, 2))
X = np.concatenate([cluster_1, cluster_2, outliers])
y = np.concatenate(
[np.ones((2 * n_samples), dtype=int), -np.ones((n_outliers), dtype=int)]
)
X_train, X_test, y_train, y_test = train_test_split(X, y, stratify=y, random_state=42)
```

We can visualize the resulting clusters:

```
import matplotlib.pyplot as plt
scatter = plt.scatter(X[:, 0], X[:, 1], c=y, s=20, edgecolor="k")
handles, labels = scatter.legend_elements()
plt.axis("square")
plt.legend(handles=handles, labels=["outliers", "inliers"], title="true class")
plt.title("Gaussian inliers with \nuniformly distributed outliers")
plt.show()
```

## Training of the model¶

```
from sklearn.ensemble import IsolationForest
clf = IsolationForest(max_samples=100, random_state=0)
clf.fit(X_train)
```

## Plot discrete decision boundary¶

We use the class `DecisionBoundaryDisplay`

to
visualize a discrete decision boundary. The background color represents
whether a sample in that given area is predicted to be an outlier
or not. The scatter plot displays the true labels.

```
import matplotlib.pyplot as plt
from sklearn.inspection import DecisionBoundaryDisplay
disp = DecisionBoundaryDisplay.from_estimator(
clf,
X,
response_method="predict",
alpha=0.5,
)
disp.ax_.scatter(X[:, 0], X[:, 1], c=y, s=20, edgecolor="k")
disp.ax_.set_title("Binary decision boundary \nof IsolationForest")
plt.axis("square")
plt.legend(handles=handles, labels=["outliers", "inliers"], title="true class")
plt.show()
```

## Plot path length decision boundary¶

By setting the `response_method="decision_function"`

, the background of the
`DecisionBoundaryDisplay`

represents the measure of
normality of an observation. Such score is given by the path length averaged
over a forest of random trees, which itself is given by the depth of the leaf
(or equivalently the number of splits) required to isolate a given sample.

When a forest of random trees collectively produce short path lengths for
isolating some particular samples, they are highly likely to be anomalies and
the measure of normality is close to `0`

. Similarly, large paths correspond to
values close to `1`

and are more likely to be inliers.

```
disp = DecisionBoundaryDisplay.from_estimator(
clf,
X,
response_method="decision_function",
alpha=0.5,
)
disp.ax_.scatter(X[:, 0], X[:, 1], c=y, s=20, edgecolor="k")
disp.ax_.set_title("Path length decision boundary \nof IsolationForest")
plt.axis("square")
plt.legend(handles=handles, labels=["outliers", "inliers"], title="true class")
plt.colorbar(disp.ax_.collections[1])
plt.show()
```

**Total running time of the script:** (0 minutes 0.428 seconds)