# Anamoly Detection using Machine Learning

## Anamolies in Data

Outlier detection is similar to novelty detection in the sense that the goal is to separate a core of regular observations from some polluting ones, called *outliers*. Yet, in the case of outlier detection, we don’t have a clean data set representing the population of regular observations that can be used to train any tool.

## Isolation Forest

One efficient way of performing outlier detection in high-dimensional datasets is to use random forests. The *ensemble.IsolationForest* ‘isolates’ observations by randomly selecting a feature and then randomly selecting a split value between the maximum and minimum values of the selected feature.

Since recursive partitioning can be represented by a tree structure, the number of splittings required to isolate a sample is equivalent to the path length from the root node to the terminating node.

This path length, averaged over a forest of such random trees, is a measure of normality and our decision function.

Random partioning produces noticeable shorter paths for anomalies. Hence, when a forest of random trees collectively produce shorter path lengths for particular samples, they are highly likely to be anomalies.

## Example

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import numpy as np
import matplotlib.pyplot as plt
rng = np.random.RandomState(1082)
# Generate train data
X = 0.3 * rng.randn(100, 2)
X_train = np.r_[X+2, X-2]
# Generate some regular novel observations
X = 0.3 * rng.randn(20, 2)
X_test = np.r_[X+2, X-2]
# Generate some abnormal novel observations
X_outliers = rng.uniform(low=-4, high=4, size=(20,2))
# fit the model
from sklearn.ensemble import IsolationForest
clf = IsolationForest(behavior='new', max_samples=100, random_state=rng, contamination='auto')
clf.fit(X_train)
y_pred_train = clf.predict(X_train)
y_pred_test = clf.predict(X_test)
y_pred_outlier = clf.predict(X_outliers)
# plot the line, the samples, and the nearest vectors to the plane
xx, yy = np.meshgrid(np.linspace(-5, 5, 50), np.linspace(-5, 5, 50))
Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)
plt.title("IsolationForest")
plt.contourf(xx, yy, Z, cmap=plt.cm.Blues_r)
b1 = plt.scatter(X_train[:, 0], X_train[:, 1], c='white',
s=20, edgecolor='k')
b2 = plt.scatter(X_test[:, 0], X_test[:, 1], c='green',
s=20, edgecolor='k')
c = plt.scatter(X_outliers[:, 0], X_outliers[:, 1], c='red',
s=20, edgecolor='k')
plt.axis('tight')
plt.xlim((-5, 5))
plt.ylim((-5, 5))
plt.legend([b1, b2, c],
["training observations",
"new regular observations", "new abnormal observations"],
loc="upper left")
plt.show()