Proceedings of the 11th International Conference on GeoComputation

Transcription

1 Proceedngs of the 11th Internatonal Conference on GeoComputaton Unversty College London, UK 20th 22nd July 2011 Spato-Temporal Analyss of Network Data and Route Dynamcs

2 Proceedngs of the 11th Internatonal Conference of Geocomputaton 2011 Unversty College London 20 th 22 nd July 2011 Edtors: Tao Cheng Paul Longley Clare Ellul Andy Chow

3 Trajectory Data Mnng: Classfcaton and Spato- Temporal Vsualzaton of Moble Objects A. Nara & Paul, M. Torrens Arzona State Unversty, 975 S. Myrtle Ave., Coor Hall, Tempe, AZ, Telephone: Emal: {anara; 1. Introducton Trajectory-based data mnng s a very actve research topc n the feld of Knowledge Dscovery n Databases (KDD) n response to the nflux of moble object data. Usng a set of spato-temporal sequences of moble object data collected from varous types of Locaton Aware Technologes (LATs) or generated by smulaton models, trajectory data mnng dscovers spato-temporal knowledge through exercses ncludng pattern detecton, clusterng, classfcaton, generalzaton, outler detecton, and vsualzaton. Potental applcatons across varous felds nclude, for example, vehcle and pedestran traffc control (e.g., transportaton management and facltes desgn); Locaton-Based Servces (LBS) (e.g., navgaton assstance and moble advertsng); weather forecastng (e.g., hurrcane trajectory predcton and rsk analyss); law enforcement (e.g., vdeo survellance for crmnal actvtes); anmal conservaton (e.g., trackng at-rsk anmal populatons); and logstcs for goods and human. In recent years, many approaches have been proposed and appled to varous felds to nvestgate patterns and trends from massve datasets of moble objects (e.g., Gaffney et al. 2007; Lee, et al. 2007; Andrenko et al. 2009; Guo et al. 2010). Research challenges dentfed n prevous works nclude characterzaton, generalzaton, and vsualsaton of massve and complex trajectores to dscover nterestng patterns, trends, and useful knowledge across scales. In ths paper, we propose a trajectory data mnng framework that employs trajectory parttonng and clusterng algorthms to extract behavoural patterns of moble objects, as well as vsual analyss to dsplay extracted patterns and trends n space and tme. As a case study, we developed an Agent-Based Model of pedestran evacuaton based on the socal force model and generated crowd evacuaton dynamcs on a street corrdor. The proposed framework successfully dfferentated and vsualzed spatotemporal clusters of local movement behavours ncludng smooth evacuaton and bottleneck. 2. Methodology To nvestgate movement behavours n trajectory datasets, our proposed trajectory data mnng framework ncludes three methodologcal steps, trajectory parttonng, trajectory clusterng, and spato-temporal vsualzaton of trajectory clusters. Step1: Trajectory parttonng o Dstance-Threshold approach 338

4 Step 2: Trajectory clusterng o Quantfcaton of sub-trajectory o Prncpal Component Analyss (PCA) o K-means cluster analyss Step3: 3D vsualzaton of trajectory clusters o Spato-Temporal Kernel Densty Estmate (STKDE) and volume renderng technque A set of trajectory dataset s descrbed as {Trajectory Set: TR set = TR 1,TR 2, TR 3,, TR, where denotes the number of moble objects}. Each trajectory s composed of a sequence of three-dmensonal ponts {{TR = p 1, p 2, p 3,, p j, where j denotes the number of ponts n the trajectory }, {p j = x, y, t }}. The trajectory parttonng process parttoned an entre trajectory nto trajectory parttons (sub-trajectores), the process of whch s a key to extract local movement behavours. In ths study, a Dstance-Threshold approach was employed. It uses a dstance threshold value to partton a trajectory nto sub-trajectores. Ths s based on the assumpton that n many stuatons human movements nvolve stoppng/stayng when a person changes ts behavour. Such behavours can be seen at multple scales; for example, when a pedestran decelerates and ultmately stops to make a sharp turn or to avod collsons wth other pedestrans; a commuter stays at home, walks to a bus stop, wats for a bus, and stays at ts offce to work; and a person may relocate and fnd a new home to stay wth ts lfe events. Methodologcally, parttonng a trajectory based on stayng behavour can be smply acheved by ntroducng a Dstance-Threshold (Th d ). If a dstance of each segment n a trajectory s less than Th d, then the segment s assgned as STAY and a trajectory s parttoned by the segment. If consecutve segments are assgned to STAY, those segments are consdered as one sub-trajectory n order to dfferentate short and long stayng behavours. For each trajectory partton (TR par() ), mult-dmensonal vectors are calculated to characterze the sub-trajectory. The vector values nclude total duraton (d t ), total horzontal dstance (d x ), total vertcal dstance (d y ), total two-dmensonal dstance (d 2D ), velocty vector on x-axs (v x ), velocty vector on y-axs (v y ), and velocty (v), horzontal beelne dstance (d sx ), vertcal beelne dstance (d sy ), two-dmensonal beelne dstance (d s2d ), area of mnmum boundng box (mbb), and sum of cosne of turnng angle between two consecutve segments (sct). All of these vector values are then normalzed wth mean equals to 0 and varance equals to 1. To reduce the dmensonalty of multple vectors of sub-trajectores, PCA s employed. PCA s a multvarate statstcal technque to the dmensonalty of a dataset consstng of nterrelated varables by fndng a new set of varables,.e., Prncpal Components (PCs), whch s smaller than the orgnal set of varables but stll contanng most of the nformaton n the orgnal dataset. Egenvalues of PCs measure the amount of varaton, and ths study uses PCs f ther egenvalues are greater than 1. PC scores of each sub-trajectory for each PC (Egenvalue 1) are computed, and then they are used as a new nput dataset for sub-trajectory clusterng. To classfy sub-trajectores for extractng local movement behavours, the K-means clusterng algorthm develped by Hartgan & Wong (1979) s appled. To estmate the optmal value of k n K-means clusterng, clusterng algorthms are run wth dfferent 339

5 values of k (mn:2, max:20), and the optmal value of k s selected by the Gap Statstc (Tbshran, Walther, & Haste, 2001). The Space-Tme Kernel Densty Estmatton (STKDE) (Brunsdon et al. 2007) and volume renderng technque (Levoy 1988; Nakaya & Yano 2010) are used for vsualsng cluster densty dstrbuton n space and tme. The nteractve approach of volume renderng s acheved usng an open source vsualzaton software, ParaVew (Henderson 2007). 3. Results As a case study to examne the proposed trajectory data mnng framework, data regardng pedestran evacuaton dynamcs was analyzed. The trajectory data was generated by an ABM based on the socal force model (Helbng and Molnár, 1995). In ts smplest form, there are three forces formulated as follows. 0 0 dv v ( t) e ( t) v ( t) m = m + f j + f w dt τ j( ) w The frst force s a drvng force toward a desred destnaton descrbed by a pedestran 0 0 of mass m, of desred velocty v, of desred drecton e, and of actual velocty v wth a certan characterstc tme τ. The second force s a repulsve force, f j, descrbng the j( ) nteracton effects wth other agents j (j ), and the thrd force s a repulsve force, w f w, to avod walls and obstacles. Pedestrans n ths basc form of the socal force model walk undrectonally,.e., each pedestran travels between an orgn and a destnaton. Ths s too smplstc, so to overcome the defcency, the dea of multple wayponts s mplemented. In the algorthm, each pedestran owns a sequenced lst of wayponts and walks toward the frst waypont n the lst. When t reaches at the waypont wthn a certan buffer zone descrbed by a two-dmensonal vector bz(bx, by), the waypont s removed from the lst and the pedestran walks toward the frst waypont n the new lst untl reachng the fnal destnaton. In ths study, pedestran evacuaton dynamcs on a dagonal corrdor was smulated. In the smulaton, pedestrans evacuate from North, West, and South corrdors to an East ext. Table 1 represents ntal settngs for model envronment and parameters used for the socal force model. To analyze trajectory data of smulated pedestran evacuaton dynamcs, locatons (x,y) of pedestrans and correspondng tme stamps were output at every one second (=30 frames). As a result of the Gap Statstc, we obtaned fve sub-trajectory clusters as the optmal k value. Fgure 1 llustrates the clusterng result of sub-trajectores usng the Dstance- Threshold parttonng approach (k=5). Fgure 2 presents the culster profles descrbng movement characterstcs wthn clusters. The vertcal axs represents ndependent varables for correspondng cluster IDs (k=5) and the horzontal axs shows the average of normalzed value of ndependent varables wthn a cluster. Fgure 3 vsualses subtrajectory cluster densty dstrbutons n space and tme estmated by STKDE. Ths explans when and where a partcular pattern of movement behavour occurred. 340

6 These results showed that sub-trajectores of Cluster 1 and 2 are dentfed as smooth evacuaton behavours because both have hgher average velocty values and contnuous trajectores wthout stayng or stoppng. In addton, these clusters are found beneath Cluster 4 near the ntersecton area and on the East corrdor n the STKDE map ndcatng that pedestrans who reached at the corner of the ntersecton earler have successful evacuaton. On the other hand, Cluster 4 and 5 are parttoned by Cluster 3 that represents stayng or stoppng behavours near the corners of the ntersecton. Ths explans the evacuaton bottleneck due to the overcrowdng. Model envronment Parameters for socal force model Number of pedestrans 120 Area wdth 800 Area heght 700 Smulaton Tck 1 frame Pedestran s mass m 1 Pedestran s desred velocty v 1.3 Characterstc tme τ 2 Table 1. Settngs of pedestran evacuaton model. 0 C1 C2 C3 C4 C5 All Fgure 1. 2D mages of sub-trajectores by each cluster (k=5) 341

7 ds2d dsy dsx mbb sct vy vx v d2d dy dx dt Fgure 2. Sub-trajectory cluster profles (k=5) 342

8 C1 C2 C3 C4 C5 All Fgure 3. Sub-trajectory cluster dstrbutons n space and tme (k=5) 4. References Andrenko, N., & Andrenko, G. (2011). Spatal Generalzaton and Aggregaton of Massve Movement Data. IEEE Transactons on Vsualzaton and Computer Graphcs, 17(2), Brunsdon, C., Corcoran, J., & Hggs, G. (2007). Vsualsng space and tme n crme patterns: A comparson of methods. Computers, Envronment and Urban Systems, 31, Gaffney, S., Robertson, A., Smyth, P., Camargo, S., & Ghl, M. (2006). Probablstc Clusterng of Extratropcal Cyclones Usng Regresson Mxture Models. Techncal Report, UCI-ICS 06-02, Unversty of Calforna, Irvne. 343

9 Guo, D., Lu, S., & Jn, H. (2010). A Graph-based Approach to Vehcle Trajectory Analyss. Journal of Locaton Based Servce, 4(3), Helbng, D., & Molnár, P. (1995). Socal force model for pedestran dynamcs. Physcal Revew E, 51, Henderson, A. (2007). ParaVew Gude, A Parallel Vsualzaton Applcaton. Ktware Inc. Lee, J. G., Han, J., & Whang, K. Y. (2007). Trajectory clusterng: A partton-and-group framework. Proceedngs of the ACM SIGMOD Internatonal Conference on Management of Data, (pp ). Bejng, Chna. Levoy, M. (1988). Volume renderng: Dsplay of surfaces from volume data. IEEE Computer Graphcs & Applcatons, 8(3), Nakaya, T., & Yano, K. (2010). Vsualsng crme clusters n a space-tme cube: an exploratory data-analyss approach usng space-tme kernel densty estmaton and scan statstcs. Transactons n GIS, 14(3), Tbshran, R., Walther, G., & Haste, T. (2001). Estmatng the number of clusters n a dataset va the Gap Statstcs. Journal of the Royal Statstc Socety: B, 2,