Braced Fourier Continuation and Regression for Anomaly Detection

TL;DR

This paper introduces Braced Fourier Continuation and Regression (BFCR), a new efficient method for nonlinear trend detection in 1D data, with applications in anomaly detection and comprehensive discussion of its properties and challenges.

Contribution

The paper presents BFCR, a novel computational technique for nonlinear regression and anomaly detection in 1D data, including algorithm details, properties, and mitigation strategies.

Findings

BFCR effectively detects anomalies in 1D data.

BFCR is computationally efficient and suitable for edge detection.

Source code and data are available on GitHub.

Abstract

In this work, the concept of Braced Fourier Continuation and Regression (BFCR) is introduced. BFCR is a novel and computationally efficient means of finding nonlinear regressions or trend lines in arbitrary one-dimensional data sets. The Braced Fourier Continuation (BFC) and BFCR algorithms are first outlined, followed by a discussion of the properties of BFCR as well as demonstrations of how BFCR trend lines may be used effectively for anomaly detection both within and at the edges of arbitrary one-dimensional data sets. Finally, potential issues which may arise while using BFCR for anomaly detection as well as possible mitigation techniques are outlined and discussed. All source code and example data sets are either referenced or available via GitHub, and all associated code is written entirely in Python.