Traveling Salesman in Reverse: Conditional Markov Entropy for Trajectory Segmentation

Abstract

Abstract-We are interested in inferring the set of waypoints (or intermediate destinations) of a mobility trajectory in the absence of timing information. We find that, by mining a dataset of real mobility traces, computing the entropy of conditional Markov trajectory enables us to uncover waypoints, even though no timing information nor absolute geographic location is provided. We build on this observation and design an efficient algorithm for trajectory segmentation. Our empirical evaluation demonstrates that the entropy-based heuristic used by our segmentation algorithm outperforms alternative approaches as it is 43% more accurate than a geometric approach and 20% more accurate than path-stretch based approach. We further explore the link between trajectory entropy, mobility predictability and the nature of intermediate locations using a route choice model on real city maps.

Different Closed-Form Expressions for Generalized Entropy Rates of Markov Chains

“…A corner stone for the results to follow is (17), known as the quasi-power property (QPP); see [31], [5] and [12]. For denumerable Markov chains, a Perron-Frobenius eigenvalue λ(s) for P (s) again generally exists.…”

“…If E is finite, then both Conditions C2 and C3 are satisfied with σ 0 = −∞, thus leading to (17). In the denumerable case, necessarily σ 0 > 0.…”

“…Proof Thanks to Assumptions 1, for any sequence i n 0 , the probability m(i n 0 ) converges to 0 as n tends to infinity. Since, by (9), ϕ is QPL at 0, and thanks to the QPP (17),…”

“…See for instance [7] and the references therein for computation of the entropy rate of paths connecting two states. See also [17] for plug-in estimation of the entropy rate of Markov trajectories between two states, conditional to given intermediate states, a quantity used as a discriminant measure in classification procedures.…”

A Graph-Based Visual Query Method for Massive Human Trajectory Data

“…In the field of data mining, previous works based on the spatio-temporal preferences of user activities through points of interest (POI) data and the recommendation of target location based on time perception emerge in an endless stream. There are plenty of trajectory mining approaches, such as Markov model [5], [6], frequent based model on empirical measurement, and LDA(Latent Dirichlet Allocation) topic model, LSTM(Long Short-Term Memory) Networks and so on. However, barely did they provide a systematic approach to fuse high-dimensional heterogeneous data, but most methods are limited to plain analysis and mining and ignore the inherent coupling, such as the interaction and connection between people and regions.…”