# Functional Anomaly Detection: a Benchmark Study

arXiv: https://arxiv.org/abs/2201.05115 · HTML: https://mlsanity.com/paper/2201.05115/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 57 references that are in the map.
- First posted on arXiv 13 Jan 2022.

## Builds on (most cited first, 14 of 14)

- [A Deep Neural Network for Unsupervised Anomaly Detection and Diagnosis in Multivariate Time Series Data](https://mlsanity.com/paper/1811.08055/) (2018)
- [Deep Learning for Anomaly Detection: A Review](https://mlsanity.com/paper/2007.02500/) (2020)
- [Extended Isolation Forest](https://mlsanity.com/paper/1811.02141/) (2018)
- [Learning Representations of Ultrahigh-dimensional Data for Random Distance-based Outlier Detection](https://mlsanity.com/paper/1806.04808/) (2018)
- [Deep Graph-level Anomaly Detection by Glocal Knowledge Distillation](https://mlsanity.com/paper/2112.10063/) (2021)
- [Unsupervised Representation Learning by Predicting Random Distances](https://mlsanity.com/paper/1912.12186/) (2019)
- [Fence GAN: Towards Better Anomaly Detection](https://mlsanity.com/paper/1904.01209/) (2019)
- [Anomaly Detection by Robust Statistics](https://mlsanity.com/paper/1707.09752/) (2017)
- [Functional Isolation Forest](https://mlsanity.com/paper/1904.04573/) (2019)
- [A Pseudo-Metric between Probability Distributions based on Depth-Trimmed Regions](https://mlsanity.com/paper/2103.12711/) (2021)
- [The Area of the Convex Hull of Sampled Curves: a Robust Functional Statistical Depth Measure](https://mlsanity.com/paper/1910.04085/) (2019)
- [Affine-Invariant Integrated Rank-Weighted Depth: Definition, Properties and Finite Sample Analysis](https://mlsanity.com/paper/2106.11068/) (2021)
- [Multivariate Functional Data Visualization and Outlier Detection](https://mlsanity.com/paper/1703.06419/) (2017)
- [A Measure of Directional Outlyingness with Applications to Image Data and Video](https://mlsanity.com/paper/1608.05012/) (2016)

## Built on by (most cited first, 10 of 10)

- [Learning Disentangled Textual Representations via Statistical Measures of Similarity](https://mlsanity.com/paper/2205.03589/) (2022)
- [Hypothesis Transfer Learning with Surrogate Classification Losses: Generalization Bounds through Algorithmic Stability](https://mlsanity.com/paper/2305.19694/) (2023)
- [Beyond Mahalanobis-Based Scores for Textual OOD Detection](https://mlsanity.com/paper/2211.13527/) (2022)
- [Toward Stronger Textual Attack Detectors](https://mlsanity.com/paper/2310.14001/) (2023)
- [A Functional Data Perspective and Baseline On Multi-Layer Out-of-Distribution Detection](https://mlsanity.com/paper/2306.03522/) (2023)
- [A Novel Information-Theoretic Objective to Disentangle Representations for Fair Classification](https://mlsanity.com/paper/2310.13990/) (2023)
- [Fast kernel half-space depth for data with non-convex supports](https://mlsanity.com/paper/2312.14136/) (2023)
- [Signature Isolation Forest](https://mlsanity.com/paper/2403.04405/) (2024)
- [Preventing Model Collapse in Deep Canonical Correlation Analysis by Noise Regularization](https://mlsanity.com/paper/2411.00383/) (2024)
- [Bayesian Nonparametric Detection of Anomalies in Multivariate Functional Data](https://mlsanity.com/paper/2606.18412/) (2026)

## Abstract (arXiv)

The increasing automation in many areas of the Industry expressly demands to design efficient machine-learning solutions for the detection of abnormal events. With the ubiquitous deployment of sensors monitoring nearly continuously the health of complex infrastructures, anomaly detection can now rely on measurements sampled at a very high frequency, providing a very rich representation of the phenomenon under surveillance. In order to exploit fully the information thus collected, the observations cannot be treated as multivariate data anymore and a functional analysis approach is required. It is the purpose of this paper to investigate the performance of recent techniques for anomaly detection in the functional setup on real datasets. After an overview of the state-of-the-art and a visual-descriptive study, a variety of anomaly detection methods are compared. While taxonomies of abnormalities (e.g. shape, location) in the functional setup are documented in the literature, assigning a specific type to the identified anomalies appears to be a challenging task. Thus, strengths and weaknesses of the existing approaches are benchmarked in view of these highlighted types in a simulation study. Anomaly detection methods are next evaluated on two datasets, related to the monitoring of helicopters in flight and to the spectrometry of construction materials namely. The benchmark analysis is concluded by recommendation guidance for practitioners.