Clustering Activity–Travel Behavior Time Series using Topological Data Analysis

Abstract

Over the last few years, traffic data has been exploding and the transportation discipline has entered the era of big data. It brings out new opportunities for doing data-driven analysis, but it also challenges traditional analytic methods. This paper proposes a new Divide and Combine based approach to do K-means clustering on activity-travel behavior time series using features that are derived using tools in Time Series Analysis and Topological Data Analysis. Our approach facilitates a case study, where each individuals daily activity-travel behavior is characterized as a categorical time series consisting of three different levels. Clustering data from five waves of the National Household Travel Survey ranging from 1990 to 2017 suggests that activity-travel patterns of individuals over the last three decades can be grouped into three clusters. Results also provide evidence in support of recent claims about differences in activity-travel patterns of different survey cohorts. The proposed method is generally applicable and is not limited only to activity-travel behavior analysis in transportation studies. Driving behavior, travel mode choice, household vehicle ownership, when being characterized as categorical time series, can all be analyzed using the proposed method.

Enhancing Statewide Annual Average Daily Traffic Estimation with Ubiquitous Probe Vehicle Data

“…With recent advances in location and communication technologies (e.g., GPS, smart phones), probe vehicle data are now widely available and accessible. Because these data are collected from the traffic stream, they contain rich information on how transportation systems are used as well as their traffic conditions ( 4 ). A recent NCHRP Synthesis study found that at least 20 state DOTs have acquired and used probe vehicle speed/travel time data from third-party vendors ( 5 ).…”

An introduction to persistent homology for time series

“…Persistent homology on functions can be used to construct features via persistence landscapes that enable us to carry out unsupervised or supervised learning of time series. In the literature, different representations of time series have been used, such as the weighted Fourier transform in Wang et al (2018) or the WFT in Chen et al (2019). We describe these situations in the following sections.…”

“…In Figure 11, the first column shows categorical time series on activity‐travel behavior of two randomly chosen adults from the National Household Travel Survey (Chen et al, 2019). The length of each time series is T = 1440, corresponding to the number of minutes in a day.…”

“…After the first‐order persistence landscapes are constructed, Chen et al (2019) used a divide and combine K‐means approach for clustering a large number of subjects and identified three distinct temporal patterns among them. The main contribution of this paper was to implement clustering of a large set of activity‐travel time series through persistent homology of non‐Morse functions.…”

Detecting Traffic Incidents Using Persistence Diagrams

“…Topological data analysis has been used previously in the context of traffic data: [19] uses TDA as a model for tracking vehicles and [20] uses TDA to understand individual travel behaviors. TDA has also been used previously for anomaly detection in [21,22].…”