Data adaptive functional outlier detection: Analysis of the Paris bike sharing system data

Abstract

Bike sharing systems (BSSs) have become an increasingly popular means of sustainable transportation, and have been implemented in many cities worldwide. Our approach contributes to the identification of abnormal patterns by applying real-time occupancy data from Paris. In particular, we propose a novel functional outlier detection algorithm based on a two-step approach: In the first stage, a clean dataset is obtained based on the combined effect of two extreme statistics calculated from random sampling; in the second stage, a multiple testing approach based on the clean dataset is proposed, in which the false discovery rate (FDR) control procedure is used to adaptively choose the thresholds for the hypothesis tests. Extensive numerical simulations were conducted to compare the outlier detection performance with those of other state-of-art methods. The proposed approach is then applied to the Paris Vélib’ bike sharing system dataset to identify abnormal patterns that are of particular interest to BSS operators for identifying system inefficiencies and update policies.