Isolation Forest in Novelty Detection Scenario

TL;DR

The paper addresses novelty detection in streaming-like data by adapting the Half-Space Tree (HST) to function as a semi-supervised novelty detector, improving interpretability and the isolation of unseen patterns compared to the classic Isolation Forest. It provides a theoretical framework, including definitions, tree construction rules, and an analytical comparison of expected depths ($EXD$) between the original Isolation Forest and the proposed HST modification. Through detailed examples and probabilistic reasoning, the authors demonstrate that novelty points tend to reside deeper in the enhanced HST trees, supporting its suitability for novelty detection. The work concludes with implications, limitations (notably semi-supervised nature and hyperparameter choices), and future directions for robust range settings and benchmarking to validate practical efficacy across diverse datasets.

Abstract

Data mining offers a diverse toolbox for extracting meaningful structures from complex datasets, with anomaly detection emerging as a critical subfield particularly in the context of streaming or real-time data. Within anomaly detection, novelty detection focuses on identifying previously unseen patterns after training solely on regular data. While classic algorithms such as One-Class SVM or Local Outlier Factor (LOF) have been widely applied, they often lack interpretability and scalability. In this work, we explore the Half-Space Tree (HST) algorithm, originally proposed for streaming anomaly detection, and propose a novel theoretical modification to adapt it specifically for novelty detection tasks. Our approach is grounded in the idea that anomalies i.e., novelties tend to appear in the higher leaves of the tree, which are less frequently visited by regular instances. We analytically demonstrate the effectiveness of this approach using probabilistic analysis, expected depth (EXD) calculations, and combinatorial reasoning. A comparative analysis of expected depths between our modified HST and the original Isolation Forest highlights that novelty points are significantly more isolated in our approach. This supports the hypothesis that HSTs, with appropriate structural adaptation, can serve as interpretable and efficient novelty detectors. The paper contributes a theoretical foundation and supporting analysis for this adaptation, setting the stage for further application and experimentation.

Figures (6)

• Figure 1: Original solution. Rectangles created by recursive splitting.
• Figure 2: tree constructed using the original approach
• Figure 3: Enhanced approach. Rectangles created by recursive splitting.
• Figure 4: Tree constructed using the enhanced novelty approach.
• Figure 5: Probabilities for individual data points, original approach.

Theorems & Definitions (8)

• Definition 3.1
• Definition 3.2
• Definition 4.1
• Definition 4.2
• Example 4.1
• Example 4.2
• Example 5.1
• Example 5.2