Shape-based Similarity Query for Trajectory of Mobile Object NTT Communication Science Laboratories, NTT Corporation, JAPAN. Yutaka Yanagisawa Jun-ichi Akahani Tetsuji Satoh “Rickshaw” (NARA/KYOTO)

/ 312 BackgroundBackground The Recent technologies allow us to track moving objects using highly accurate positioning devices. There are many applications using such location information have been developed. –Navigation Systems, Location-based Information Systems, etc. A Navigation System Digital City Kyoto: A Location-based Information System

/ 313 Motion Pattern Analysis Motion pattern analysis is one of the most interesting technologies of these applications. –By analyzing their motion patterns, it is possible to extract the behavioral characteristics of moving objects. –The applications can predict the future behavior of the moving objects using extracted characteristics. Single Motion Analysis –focuses on the statistical characteristics of a moving object. Relative Motion Analysis –focuses on the similarity between motion patterns. We discuss the approach based on the similarity of trajectory shapes because it is a simple and intuitive approach.

/ 314 Similarity of Trajectory Shapes Entrance Exit A B C D Show information about B, C, and D. The trajectories of visitors are stored in a database. It retrieves trajectories that are similar to A … It is possible to predict the future route of the new visitor. This approach is called shape-based approach. Exhibition hall An example of an information providing system.

/ 315 ProblemProblem However, there are few database systems which can search trajectories based on shapes. –Many database systems retrieve moving objects based on only “distance”. D1 LL1 L2 D2 X Y The minimum distance between L and L2 is less than the distance between L and L1. However, L2 is more similar in shape to L than L1 intuitively. Not appropriate for shape-based approach

/ 316 Our Approaches We propose a shape-based similarity query for searching trajectories from moving object databases. Moreover, we present an efficient indexing method for retrieving moving objects based on our proposed query.

Shape-based Similarity Query

/ 318 Data Model for Trajectory In real world, a trajectory of a moving object can be modeled as a continuous line in space. –However, positioning devices can not track a moving object continuously. In our work, a trajectory is stored as a sequence of points (discrete line) in databases. –This model is used as a popular data model. In Real WorldIn Databases

/ 319 A Similarity of Time Series Data The key idea have been proposed in the technique for time series database. The similarity between two time series data is defined as the Euclidean distance between the points in n dimensional space. W = W’ = t x t1t1 t8t8 t x D(W, W’) w1w1 w2w2 w9w9 w’ 1 w’ 9 (n=9)

/ 3110 A Similarity of Time Series Data W = W’ = Distance between W and W’ is = 3 The key idea have been proposed in the techniques for time series database. The similarity between two time series data is defined as the Euclidean distance between the points in n dimensional space.

/ 3111 A Similarity of Time Series Data W = W’ = In this case, the distance is zero. Smaller distance means higher similarity The key idea have been proposed in the techniques for time series database. The similarity between two time series data is defined as the Euclidean distance between the points in n dimensional space.

/ 3112 A Similarity of Time Series Data The distance fits to intuitive similarity of line shapes. There is an effective search algorithm to calculate this distance. We will extend the similarity for trajectory in 2 or more dimensional space.

/ 3113 Our Proposed Similarity of Trajectories The similarity of trajectories can be defined as an extension of the distance of time series data. –The distance can be given as the following expression. X Y ’ p7p7 p1p1 p’ 7 p’ 1

/ 3114 Shape-based Similarity Query for Trajectories We define a shape-based similarity query for trajectories as a subsequence matching query. –Because the length of trajectories are often difference. ＋ Stored trajectories A given trajectory Answer trajectories SSQ( ,,  )  : A set of stored trajectories in database. : A trajectory to be compared.  : The distance from. Answer  a : A set of sub-trajectories

/ 3115 Shape-based Similarity Query for Trajectories - The database calculates the distance between the given trajectory and each sub-trajectory. - If the distance is less than the given distance , the database adds the sub-trajectory to the answer set of trajectories  a. A Given Trajectory An Answer Sub-Trajectory

IndexingIndexing

/ 3117 ApproachApproach The existing spatial structures are appropriate for retrieving an object based on the distance. –However, these structures have no method for searching the data based on the similarity between trajectories. We extend the spatial data structure for our proposed query.

/ 3118 An Efficient Calculation Process for the Shape-based Similarity: 1 The essential idea was presented as a PAA: Piecewise Aggregate Approximation [Keogh01] ． –PAA is an efficient method of approximating the time series data for a similarity search. W W ‘ t x Using the `average sequences’ of a sub-sequences. t x (N=3)

/ 3119 An Efficient Calculation Process for the Shape-based Similarity: 2 The distance between the average sequences is the lower bound of the distance between the original two sequences. W W’ t x t D( W, W’) By comparing average sequences, we can know the lower bound of the distance between original sequences.

/ 3120 An Efficient Calculation Process for the Shape-based Similarity: 3 In the case of trajectories, the distance between the center points of trajectories is the lower bound of the distance between the original trajectories. X Y L’ L v1 v7 v’1 v’7 Calculating center points X Y The distance between these center points is the lower bound of the original distance.

/ 3121 For making indexes, the database calculates the center points of sub-trajectories. –The length of each sub-trajectory must be fixed to the system parameter N. –In this example, N is four. X Y Y p1p1 p8p8 The center point of from p 5 to p 8 The center point of from p 1 to p 4 Combination of PAA and Spatial Data Structure: 1 p2p2 p3p3 p4p4 p5p5 p6p6 p7p7 X

/ 3122 Combination of PAA and Spatial Data Structure: 2 Next, the database makes indexes to the points using a traditional spatial data structure. –Our implemented system makes an index to every center point using R + -Tree. X Y X X Y Y Normal R + -Tree Our Proposed Index Structure The database can search objects based on the similarity of trajectories using the spatial data structure.

/ 3123 Query Processing: 1 When a SSQ(, Q,) is given, the database calculates the center point of Q at first. –Suppose that the length of stored center points is fixed to 4 (N=4) in the following example. Q X Y X Y p Q is the center point of a given trajectory. pQpQ If a query SSQ( , Q,  ) is given..

/ 3124 Query Processing: 2 X Y A B C BC A An index tree (R + -Tree) pQpQ Candidate points The region within the distance  from p Q Next, the database searches stored points within the distance  from the calculated point p Q using the spatial data structure.

/ 3125 Query Processing: 3 X Y pQpQ Finally, the database checks the distance between a given trajectory Q and each candidate trajectory. If the distance is less than a given threshold , the candidate trajectory is added to the answer set  a. Q Y p1p1 p2p2 1 1 is the original trajectory of p 1. If, 1 is added to  a

Performance Study

/ 3127 Performance Study We conducted an experiment for evaluating our proposed query and indexing method. –Measuring the processing time for retrieving trajectories required by a shape-based similarity query. For this evaluation, two types of trajectories are stored in a database. –tracked by GPS and generated by a simulator. We compared the processing time using both methods: - Our indexing method, - A spatial data structure (R + -Tree).

/ 3128 Trajectory Data: 1 RickshawA GPS Receiver (eTrex/GARMIN) This is an example of trajectory data captured by GPS receivers on rickshaws (in Nara city). –Rickshaw is tour guide, they work in Nara / Kyoto. A trajectory of a rickshaw in all day

/ 3129 Trajectory Data: 2 This figure displays trajectories generated by our implemented simulator. The simulator can generate trajectories such that people walk on a plane freely. Velocity and direction of each object are given as random values. But the changes of these values are slow and continuous.

/ 3130 The Result of the Experiment Using our index structureUsing R + -Tree For retrieving longer trajectories from stored data, our proposed method has high advantages to existing methods. The processing time to calculate 10 random queries is displayed: Amount of Stored Points Length of Q (=N)

/ 3131 ConclusionsConclusions We have proposed a shape-based similarity query to find moving objects. –Database users can find moving objects for analyzing their motion patterns. Moreover, we have presented an effective indexing method to search for the trajectories required by our proposed queries. –We demonstrated the advantage of our proposed method to existing spatial data structures.

/ 3132 Future Work [Human Tracking by using Laser Scanners] - University of Tokyo (Dr. Zhao and Prof. Shibasaki) - Captured at Geoinformation Forum Japan 2002 ( people visited) [Motion Capture Data] - Tokyo University of Technology (Creative Labo) - 76 moving points on bodies (120fps) - Playing football and judo We will evaluate our proposed method using these data.

/ 3133 Our Proposed Similarity of Trajectories The similarity of trajectories can be defined as an extension of the distance of time series data. X Y ’ p7p7 p1p1 p’ 7 p’ 1 For comparing these trajectories, Plotting on … X-T plane Y-T plane. X Y T (time) x x ’ y y ’ p i = (x i, y i )

/ 3134 Our Proposed Similarity of Trajectories The similarity of trajectories can be defined as an extension of the distance of time series data. –We extend it to 2 or more dimensional space. X Y T (time) x x ’ y y ’ Calculating distances on each plane; X-T plane, and Y-T plane.

/ 3135 Our Proposed Similarity of Trajectories The similarity of trajectories can be defined as an extension of the distance of time series data. –We extend it to 2 or more dimensional space. Finally, integrating these distances. We define the distance between and’ :..is given as the squire root of the sum of them.

/ 3136 Other Applications Security system for exhibition halls Arrangement of items in a shop Traffic forecaster Guidance system for tourists

/ 3137 An Efficient Calculation Process for the Shape-based Similarity: 4 A Simple Example W = W’ = W = W’ = = 3.0 = = 1.8 Using average sequences, we can know the lower bound. (N=2) The distance between the average sequences is the lower bound of the distance between the original two sequences.

/ 3138 Query Processing: 4 If the length of Q is larger than N, the database calculates several center points of Q. The database repeats searching process several times for Q if necessary. Q Y Where N = 4 and the length of Q is 7, X Y p Q1 p Q2 These two center points are available for searching. X

/ 3139 An Efficient Calculation Process for the Shape-based Similarity: 3 A Simple Example W = W’ = = 3.0 The distance between the average sequences is the lower bound of the distance between the original two sequences.

/ 3140 ExampleExample Query Stored Trajectory