Isolation Forests for Anomaly Detection

Isolation Forest is an unsupervised anomaly detection algorithm particularly effective for high-dimensional data. It operates under the principle that anomalies are rare and distinct, making them easier to isolate from the rest of the data. Unlike other methods that profile normal data, Isolation Forests focus on isolating anomalies. At its core, the Isolation Forest algorithm, it banks on the fundamental concept that anomalies, they deviate significantly, thereby making them easier to identify.

Isolation Forests excel at anomaly detection by leveraging a unique approach: isolating anomalies instead of profiling normal data points. The workings of isolation forests are defined below:

• Building Isolation Trees: The algorithm starts by creating a set of isolation trees, typically hundreds or even thousands of them. These trees are similar to traditional decision trees, but with a key difference: they are not built to classify data points into specific categories. Instead, isolation trees aim to isolate individual data points by repeatedly splitting the data based on randomly chosen features and split values.
• Splitting on Random Features: Isolation trees introduce randomness at each node of the tree, a random feature from the dataset is selected. Then, a random split value is chosen within the range of that particular feature’s values. This randomness helps ensure that anomalies, which tend to be distinct from the majority of data points, are not hidden within specific branches of the tree.
• Isolating Data Points: The data points are then directed down the branches of the isolation tree based on their feature values.
  • If a data point’s value for the chosen feature falls below the split value, it goes to the left branch. Otherwise, it goes to the right branch.
  • This process continues recursively until the data point reaches a leaf node, which simply represents the isolated data point.
• Anomaly Score: The key concept behind Isolation Forests lies in the path length of a data point through an isolation tree.
  • Anomalies, by virtue of being different from the majority, tend to be easier to isolate. They require fewer random splits to reach a leaf node because they are likely to fall outside the typical range of values for the chosen features.
  • Conversely, normal data points, which share more similarities with each other, might require more splits on their path down the tree before they are isolated.
• Anomaly Score Calculation: Each data point is evaluated through all the isolation trees in the forest.
  • For each tree, the path length (number of splits) required to isolate the data point is recorded.
  • An anomaly score is then calculated for each data point by averaging the path lengths across all the isolation trees in the forest.
• Identifying Anomalies: Data points with shorter average path lengths are considered more likely to be anomalies. This is because they were easier to isolate, suggesting they deviate significantly from the bulk of the data. A threshold is set to define the anomaly score that separates normal data points from anomalies. This threshold can be determined based on domain knowledge, experimentation, or established statistical principles.

Key Takeaways:

• Isolation Forests leverage randomness to isolate data points effectively.
• Anomalies require fewer splits on average due to their distinct nature.
• The average path length across all trees serves as an anomaly score.
• Lower scores indicate a higher likelihood of being an anomaly.

Anomaly detection is vital across industries, revealing outliers in data that signal problems or unique insights. Isolation Forests offer a powerful solution, isolating anomalies from normal data. In this tutorial, we will explore the Isolation Forest algorithm’s implementation for anomaly detection using the Iris flower dataset, showcasing its effectiveness in identifying outliers amidst multidimensional data.