Analyse et fouille de donnes de trajectoires dobjets mobiles Thse - PowerPoint PPT Presentation

Analyse et fouille de données de trajectoires d’objets mobiles Thèse présentée et soutenue publiquement par Mohamed Khalil EL MAHRSI 30 septembre 2013 Devant le jury composé de : M. Talel ABDESSALEM (Président du jury) Mme Barbara HAMMER (Rapporteur) Mme Karine ZEITOUNI (Rapporteur) M. Pierre BORGNAT (Examinateur) M. Etienne CÔME (Examinateur) M. Ludovic DENOYER (Examinateur) M. Cédric DU MOUZA (Examinateur) M. Fabrice ROSSI (Directeur de thèse)

The Traffic Congestion Problem Traffic congestion and road jams Frustrating travel delays Economical losses Environmental damage Countermeasures are needed Infrastructure improvement Prohibiting/favoring specific routes Based on the analysis of drivers’ behavior Context and Motivations 1 / 41

How is Road Traffic Monitored? Traffic counters/recorders Expensive Partially deployed Count traffic on their local section Consequences: Incomplete vision of traffic A valuable information is missed: vehicles’ identities Context and Motivations 2 / 41

Main Motivation: Trajectory Analysis as a Complement? Why not collect the trajectories of vehicles moving on the road network... Many fleet management companies already do this Commuters can contribute their trajectories Context and Motivations 3 / 41

Main Motivation: Trajectory Analysis as a Complement? ... and analyze them to discover Groups of vehicles that followed the same routes Groups of roads that are often traveled together during a considerable number of commutes Etc. Context and Motivations 4 / 41

But... Modern devices can sample their positions at high rates At such rates, the data are inherently redundant Transmitting and storing the entirety of the trajectories are impractical Important space requirements Computational overheads We have to intelligently reduce the size of the data T 1 T 1 T 2 T 2 T 3 T 3 T 4 T 4 Context and Motivations 5 / 41

Research Problems Explored in this Thesis Main objective: Clustering Trajectory Data in Road Network Environments How to discover meaningful groupings of “similar” trajectories and road segments in the specific context of road networks? But first, a small detour: Sampling Trajectory Data Streams How to reduce the size of trajectory data streams while trying to preserve the most of their spatiotemporal features? Context and Motivations 6 / 41

Outline 1 Context and Motivations 2 Sampling Trajectory Data Streams 3 Graph-Based Clustering of Network-Constrained Trajectory Data 4 Co-Clustering Network-Constrained Trajectory Data 5 Conclusions, Future Work and Open Issues

Outline 1 Context and Motivations 2 Sampling Trajectory Data Streams 3 Graph-Based Clustering of Network-Constrained Trajectory Data 4 Co-Clustering Network-Constrained Trajectory Data 5 Conclusions, Future Work and Open Issues

Anatomy of a Trajectory Data Stream (Raw) Trajectory A trajectory T is a series of discrete, timestamped positions: T = � id , { P 1 ( t 1 , x 1 , y 1 ) , P 2 ( t 2 , x 2 , y 2 ) , ..., P i ( t i , x i , y i ) , ... }� id : identifier t i : timestamp (time of capture) ( x i , y i ) : coordinates (in the Euclidean space) P 2 ( t 2 , x 2 , y 2 ) P 7 ( t 7 , x 7 , y 7 ) P 3 ( t 3 , x 3 , y 3 ) P 1 ( t 1 , x 1 , y 1 ) P 5 ( t 5 , x 5 , y 5 ) P 4 ( t 4 , x 4 , y 4 ) P 6 ( t 6 , x 6 , y 6 ) Figure : Illustration of a raw trajectory Sampling Trajectory Data Streams 7 / 41

Anatomy of a Trajectory Data Stream (Raw) Trajectory A trajectory T is a series of discrete, timestamped positions: T = � id , { P 1 ( t 1 , x 1 , y 1 ) , P 2 ( t 2 , x 2 , y 2 ) , ..., P i ( t i , x i , y i ) , ... }� id : identifier t i : timestamp (time of capture) ( x i , y i ) : coordinates (in the Euclidean space) Interpolation is used to approximate missing positions P 2 ( t 2 , x 2 , y 2 ) P 7 ( t 7 , x 7 , y 7 ) P 3 ( t 3 , x 3 , y 3 ) P 1 ( t 1 , x 1 , y 1 ) P 5 ( t 5 , x 5 , y 5 ) P 4 ( t 4 , x 4 , y 4 ) P 6 ( t 6 , x 6 , y 6 ) Figure : Illustration of a linearly-interpolated trajectory Sampling Trajectory Data Streams 7 / 41

Problem Formulation, Objectives, and Constraints Compressed (Sampled) Trajectory Given a trajectory T , a compressed trajectory T C of T is a subset of the original points forming T , such as: T C covers T from start to finish ∀ P i ∈ T C , P i ∈ T Objectives Reduce data size (obviously) Small, preferably configurable approximation errors Constraints On-the-fly processing Low computational complexity Low in-memory complexity Sampling Trajectory Data Streams 8 / 41

Previous Work Classic sampling techniques are inadequate They overlook the spatiotemporal properties of the trajectories Two types of trajectory oriented sampling techniques Configurable approximation errors but high complexity Low complexity but no guarantees for approximation errors To the best of our knowledge: no approaches combining low complexity and configurable approximation errors Sampling Trajectory Data Streams 9 / 41

The Spatiotemporal Stream Sampling (STSS) Algorithm [El Mahrsi et al., 2010] Intuition: use linear prediction to guess forthcoming positions The accuracy of the prediction (w.r.t. a threshold d Thres ) guides the sampling process P k ( t k , x k , y k ) Distance( P k , P k ) P i ( t i , x i , y i ) P j ( t j , x j , y j ) P k ( t k , x k , y k ) Figure : Linear prediction of incoming positions Sampling Trajectory Data Streams 10 / 41

STSS: How it Works P 1 Legend: real trajectory sampled trajectory prediction Figure : Illustration of the functioning of the STSS algorithm Sampling Trajectory Data Streams 11 / 41

STSS: How it Works P 1 Legend: real trajectory sampled trajectory prediction Figure : Illustration of the functioning of the STSS algorithm Sampling Trajectory Data Streams 11 / 41

STSS: How it Works P 1 P 2 Legend: real trajectory sampled trajectory prediction Figure : Illustration of the functioning of the STSS algorithm Sampling Trajectory Data Streams 11 / 41

STSS: How it Works P 1 P 2 Legend: real trajectory sampled trajectory prediction Figure : Illustration of the functioning of the STSS algorithm Sampling Trajectory Data Streams 11 / 41

STSS: How it Works P 3 P 1 P 2 Distance( P 3 , P 3 ) d Thres P 3 Legend: real trajectory sampled trajectory prediction Figure : Illustration of the functioning of the STSS algorithm Sampling Trajectory Data Streams 11 / 41

STSS: How it Works P 3 P 1 Legend: real trajectory sampled trajectory prediction Figure : Illustration of the functioning of the STSS algorithm Sampling Trajectory Data Streams 11 / 41

STSS: How it Works P 3 P 4 P 1 P 4 Legend: real trajectory sampled trajectory prediction Figure : Illustration of the functioning of the STSS algorithm Sampling Trajectory Data Streams 11 / 41

STSS: How it Works P 4 P 1 Legend: real trajectory sampled trajectory prediction Figure : Illustration of the functioning of the STSS algorithm Sampling Trajectory Data Streams 11 / 41

STSS: How it Works P 4 P 5 P 1 Distance( P 5 , P 5 ) > d Thres P 5 Legend: real trajectory sampled trajectory prediction Figure : Illustration of the functioning of the STSS algorithm Sampling Trajectory Data Streams 11 / 41

STSS: How it Works P 4 P 1 P 5 Legend: real trajectory sampled trajectory prediction Figure : Illustration of the functioning of the STSS algorithm Sampling Trajectory Data Streams 11 / 41

STSS: How it Works P 4 P 1 P 8 P 9 P 9 Legend: real trajectory sampled trajectory prediction Figure : Illustration of the functioning of the STSS algorithm Sampling Trajectory Data Streams 11 / 41

STSS: How it Works P 4 P 1 P 8 P 9 Legend: real trajectory sampled trajectory prediction Figure : Illustration of the functioning of the STSS algorithm Sampling Trajectory Data Streams 11 / 41

STSS in Action 5289000 5289000 5289000 5287000 5287000 5287000 y(m) y(m) y(m) 5285000 5285000 5285000 440000 441000 442000 443000 440000 441000 442000 443000 440000 441000 442000 443000 x(m) x(m) x(m) (a) Original trajectory (b) Tolerated error: 10m (c) Tolerated error: 50m (228 points) (117 points|comp. ratio: 1.9:1) (72 points|comp. ratio: 3.2:1) 5289000 5289000 5289000 5287000 5287000 5287000 y(m) y(m) y(m) 5285000 5285000 5285000 440000 441000 442000 443000 440000 441000 442000 443000 440000 441000 442000 443000 x(m) x(m) x(m) (d) Tolerated error: 100m (e) Tolerated error: 150m (f) Tolerated error: 200m (49 points|comp. ratio: 4.6:1) (40 points|comp. ratio: 5.7:1) (32 points|comp. ratio: 7.1:1) Figure : Example of a trajectory sampled with different error tolerances Sampling Trajectory Data Streams 12 / 41

STSS: Properties Single-pass, on-the-fly algorithm Linear computational complexity Constant in-memory complexity Easy to configure (only one parameter) Guaranteed upper bound for compression errors Sampling Trajectory Data Streams 13 / 41