Functional Outlier Detection by Means of h-Mode Depth and Dynamic Time Warping

Abstract

Finding outliers in functional infinite-dimensional vector spaces is widely present in the industry for data that may originate from physical measurements or numerical simulations. An automatic and unsupervised process of outlier identification can help ensure the quality of a dataset (trimming), validate the results of industrial simulation codes, or detect specific phenomena or anomalies. This paper focuses on data originating from expensive simulation codes to take into account the realistic case where only a limited quantity of information about the studied process is available. A detection methodology based on different features, such as h-mode depth or the dynamic time warping, is proposed to evaluate the outlyingness both in the magnitude and shape senses. Theoretical examples are used to identify pertinent feature combinations and showcase the quality of the detection method with respect to state-of-the-art methodologies of detection. Finally, we show the practical interest of the method in an industrial context thanks to a nuclear thermal-hydraulic use case and how it can serve as a tool to perform sensitivity analysis on functional data.

Special Issue on Unsupervised Anomaly Detection

“…Furthermore, a new interesting research direction is addressed by Rollón de Pinedo et al [8]: Functional outlier detection, where anomalies in terms of magnitude and shape are detected based on using h-mode depth and dynamic time warping. The authors also investigate a not very commonly used but interesting application scenario: The detection of anomalies within data originating from costly simulations.…”

“…Among others, intrusion detection [2][3][4][5], payment fraud detection, public safety, complex system monitoring [6][7][8][9][10], and medical data analytics are possible application domains.…”

Exploring rainfall variabilities using statistical functional data analysis

“…Functional data analysis techniques have been successfully carried out by several researchers in various fields [1][2][3][4][5][6]. Suhaila and Yusop [7] used a functional analysis of variance to explain the geographical and temporal variability in rainfall.…”