Dimensionless Anomaly Detection on Multivariate Streams with Variance Norm and Path Signature

2020-06-05 · Zhen Shao, Ryan Sze-Yin Chan, Thomas Cochrane, Peter Foster, Terry Lyons

In this paper, we propose a dimensionless anomaly detection method for multivariate streams. Our method is independent of the unit of measurement for the different stream channels, therefore dimensionless. We first propose the variance norm, a generalisation of Mahalanobis distance to handle infinite-dimensional feature space and singular empirical covariance matrix rigorously. We then combine the variance norm with the path signature, an infinite collection of iterated integrals that provide global features of streams, to propose SigMahaKNN, a method for anomaly detection on (multivariate) streams. We show that SigMahaKNN is invariant to stream reparametrisation, stream concatenation and has a graded discrimination power depending on the truncation level of the path signature. We implement SigMahaKNN as an open-source software, and perform extensive numerical experiments, showing significantly improved anomaly detection on streams compared to isolation forest and local outlier factors in applications ranging from language analysis, hand-writing analysis, ship movement paths analysis and univariate time-series analysis.

📄 PDF Abstract BibTeX arXiv:2006.03487

Code (2)

sz85512678/signature_mahalanobis_knn 공식 구현

pafoster/conformance_distance_experiments_cochrane_et_al_2020

Tasks

Anomaly DetectionTime SeriesTime Series Analysis

Real-time Anomaly Detection for Multivariate Data Streams

2022-09-26 · Kenneth Odoh

We present a real-time multivariate anomaly detection algorithm for data streams based on the Probabilistic Exponentially Weighted Moving Average (PEWMA). Our formulation is resilient to (abrupt transient, abrupt distrib…

Anomaly Detection

Federated Low-Rank Koopman Learning for Multivariate Time-Series Anomaly Detection in IoT Systems

2026-07-09 · Tung-Anh Nguyen, Van-Phuc Bui, Anh Tuyen Le, Kim Hue Ta 외 arxiv

Distributed IoT systems generate multivariate time-series streams for monitoring physical assets, servers, and embedded sensing platforms. Detecting abnormal temporal behavior is critical for fault diagnosis, predictive …

Anomaly Detection Fault Diagnosis

MAD: Self-Supervised Masked Anomaly Detection Task for Multivariate Time Series

2022-05-04 · Yiwei Fu, Feng Xue

In this paper, we introduce Masked Anomaly Detection (MAD), a general self-supervised learning task for multivariate time series anomaly detection. With the increasing availability of sensor data from industrial systems,…

Anomaly Detection Self-Supervised Learning Time Series Time Series Analysis+1

Subset Multivariate Collective And Point Anomaly Detection

2019-09-04 · Alexander T. M. Fisch, Idris A. Eckley, Paul Fearnhead

In recent years, there has been a growing interest in identifying anomalous structure within multivariate data streams. We consider the problem of detecting collective anomalies, corresponding to intervals where one or m…

Anomaly Detection

Anomaly Detection for Multivariate Time Series of Exotic Supernovae

2020-10-21 · V. Ashley Villar, Miles Cranmer, Gabriella Contardo, Shirley Ho 외

Supernovae mark the explosive deaths of stars and enrich the cosmos with heavy elements. Future telescopes will discover thousands of new supernovae nightly, creating a need to flag astrophysically interesting events rap…

Anomaly Detection Time Series Time Series Analysis