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.