How K-SIF and SIF Revolutionize Anomaly Detection in Complex Datasets

Table of Links

Abstract and 1. Introduction

2. Background & Preliminaries

2.1. Functional Isolation Forest

2.2. The Signature Method

3. Signature Isolation Forest Method

4. Numerical Experiments

4.1. Parameters Sensitivity Analysis

4.2. Advantages of (K-)SIF over FIF

4.3. Real-data Anomaly Detection Benchmark

5. Discussion & Conclusion, Impact Statements, and References

Appendix

A. Additional Information About the Signature

B. K-SIF and SIF Algorithms

C. Additional Numerical Experiments

5. Discussion & Conclusion

This work presents two novel anomaly detection algorithms, K-SIF and SIF, rooted in the isolation forest structure and the signature approach from rough path theory. Our contributions extend Functional Isolation Forest in two vital dimensions: incorporating non-linear properties in data for improved adaptability to challenging datasets and introducing an entirely data-driven technique free from predefined dictionaries. Such flexibility accommodates diverse data

patterns and reduces the risk of overlooking certain types of anomalies. In this way, more complex real data pattern scenarios can be analysed, where non-linearity is highly present and, further, the unsupervised settings lacking labels highly affect the AD task. We demonstrate the advantages of utilizing K-SIF over FIF through a comprehensive parameter analysis, with consistent outperformance on real-world datasets. Notably, SIF achieves state-of-the-art performance while maintaining simplicity and computational efficiency, underscoring its effectiveness in functional anomaly detection. This work offers valuable advancements in anomaly detection methodologies, providing robust solutions for complex and diverse datasets.

Impact Statements

This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none which we feel must be specifically highlighted here.

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