When lookout sees crackle: Anomaly detection via kernel density estimation

2026-03-23

AI Summary

This work proposes an adaptive kernel density estimation method based on topological features to address the challenges of accuracy and robustness in anomaly detection within high-dimensional, complex data. By leveraging the death diameters from the persistent homology of Rips complexes, the approach automatically determines kernel bandwidths and incorporates a multivariate scaling strategy to ensure stability and efficiency across diverse data distributions. The resulting kernel density estimator is theoretically consistent and substantially enhances the generalization capability of anomaly detection. Experimental results demonstrate that the proposed method outperforms existing Lookout algorithms on multiple benchmark datasets, achieving significant improvements in both detection performance and computational efficiency.

Technology Category

• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Machine Learning: Kernel Methods
• Search and Optimization: Distributed Search

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

We present an updated version of lookout -- an algorithm for detecting anomalies using kernel density estimates with bandwidth based on Rips death diameters -- with theoretical guarantees. The kernel density estimator for updated lookout is shown to be consistent, and the proposed multivariate scaling is robust and efficient. We show our updated algorithm performs better than the previous version on diverse examples.

Problem

• anomaly detection
• kernel density estimation
• multivariate data
• outlier identification

Innovation

• anomaly detection
• kernel density estimation
• Rips death diameters
• consistency
• multivariate scaling