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Trajectory Pattern Mining

Trajectory Pattern Mining. NTU IM Hsieh, Hsun-Ping. Trajectory Pattern Mining. Reporter ： Hsieh, Hsun-Ping 解巽評 (R96725019) Fosca Giannotti Mirco Nanni Dino Pedreschi Fabio Pinelli Pisa KDD Laboratory KDD’07

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Trajectory Pattern Mining

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  1. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Trajectory Pattern Mining Reporter：Hsieh, Hsun-Ping 解巽評(R96725019) Fosca Giannotti Mirco Nanni Dino Pedreschi Fabio Pinelli Pisa KDD Laboratory KDD’07 ISTI - CNR, Area della Ricerca di Pisa, Via Giuseppe Moruzzi, 1 - 56124 Pisa, Italy Computer Science Dep., University of Pisa, Largo Pontecorvo, 3 - 56127 Pisa, Italy

  2. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Outline Introduction T-Patterns with Static ROI Background and Related Work T-Patterns with Dynamic ROI Problem Definition Experiments & Conclusion Regions-Of-Interest

  3. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Spatio-temporalpattern • Spatio-Temporal pattern ： • Space & time element should be considered • In this paper, Spatio-Temporal pattern is used to apply on Trajectory Pattern Mining. TrajectoryPattern Introduction Background &Related Work Algorithm Summery ProblemDefinition Region-Of- Interest T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment &Conclusion

  4. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Spatio-temporalpattern • Trajectory pattern application： • Pervasiveness of location-acpuisition technologies (GPS, GSM network) • Spatio-temporal datasets to discovery usable knowledge about movement behaviour. • the movement of people or vehicles within a given area can be observed from the digital devices. • Useful in the domain of sustainable mobility and traffic management. TrajectoryPattern Introduction Background &Related Work Algorithm Summery ProblemDefinition Region-Of- Interest T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment &Conclusion

  5. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Spatio-temporalpattern • Trajectory pattern ： • a set of individual trajectories that share the property of visiting the same sequence of places with similar travel times. • Two notions are central:(i) the region of interest in the given space (ii) the typical travel time of moving object from region to region TrajectoryPattern Introduction Background &Related Work Approach Summery ProblemDefinition Region-Of- Interest T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment &Conclusion

  6. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Spatio-temporalpattern • Trajectory pattern example： TrajectoryPattern Introduction Background &Related Work Approach Summery ProblemDefinition We only require that such trajectories visit the same sequence of places with similar transitiontimes, even if they start at diffierent absolute times Region-Of- Interest T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment &Conclusion

  7. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Spatio-temporalpattern • Three Trajectory pattern mining Approach： • Pre-conceived regions of interest • Popular regions • the identification of the regions of interest is dynamically intertwined with the mining of sequences with temporal information. TrajectoryPattern Introduction Background &Related Work Approach Summery ProblemDefinition Region-Of- Interest T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment &Conclusion

  8. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Spatio-temporalpattern • Contributions in this paper： • (i) the definition of the novel trajectory pattern • (ii) a density-based algorithm for discovering regions of interest • (iii) a trajectory pattern mining algorithm with predefined regions of interest • (iv) a trajectory pattern mining algorithm which dynamically discovers regions of interest. TrajectoryPattern Introduction Background &Related Work Approach Summery ProblemDefinition Region-Of- Interest T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment &Conclusion

  9. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping • Spatio-temporal sequential patterns: • frequent sequential pattern(FSP) problem, is defined over a database of sequences D, where each element of each sequence is a time stamped set of items (itemset). • FSP problem consists in finding all the sequences that are frequent in D. • A sequence α = α1→ · · · →αkis a subsequence of β = β1→ ·· · → βm if there exist integers 1 ≤ i1< . . . < ik ≤ m such that ∀1≤n≤k αn ⊆ βin. • Define support suppD(S) of a sequence S as the percentage of transactions T ∈ D • S is frequent w.r.t. threshold smin if suppD(S) ≥ smin. Introduction Spatio-temporalsequential patterns Background &Related Work PreviousResearch ProblemDefinition TemporallyAnnotatedSequence Region-Of- Interest TASexample T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment &Conclusion

  10. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping • Previous Research about trajectory: • The work in [3] considers patterns that are in the form of trajectory segments and searches approximate instances in the data. • The work in [7] provides a clustering-based perspective, and considers patterns in the form of moving regions within time intervals • Finally, a similar goal, but focused on cyclic patterns, • is pursued in [8] • This focused on the extraction of patterns over sequences of events that describe also the temporal relations between events, Introduction Spatio-temporalsequential patterns Background &Related Work PreviousResearch ProblemDefinition TemporallyAnnotatedSequence Region-Of- Interest TASexample T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment &Conclusion

  11. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping • Temporally Annotated Sequence : • Temporally annotated sequences (TAS), introduced in [5],are an extension of sequential patterns that enrich sequences with information about the typical transition times between their elements. Introduction Spatio-temporalsequential patterns Background &Related Work PreviousResearch ProblemDefinition TemporallyAnnotatedSequence Region-Of- Interest TASexample • Example: T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment &Conclusion

  12. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping • Definition 1 : Introduction Spatio-temporalsequential patterns Background &Related Work PreviousResearch ProblemDefinition TemporallyAnnotatedSequence Region-Of- Interest TASexample T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment &Conclusion

  13. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping • Example : Introduction Spatio-temporalsequential patterns Background &Related Work PreviousResearch ProblemDefinition TemporallyAnnotatedSequence Region-Of- Interest TASexample T-Patterns with Static ROI if τ = 2 and smin = 1, not only T is frequent, but also any other variant of T having transition times t1, t2 where t1 ∈ [1, 5] and t2 ∈ [9, 13]. T-Patterns with Dynamic ROI Experiment &Conclusion

  14. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Introduction ST-sequence Background &Related Work • The key task in sequence mining consists in counting the occurrences of a pattern, i.e., those segments of the input data that match a candidate pattern. • In this paper it requires locationsapproximated match and error tolerance when matching spatial . • neighborhood function N :R2→P(R2), which assigns to each pair (x, y) a set N (x, y) of neighboring points. Spatial containment ProblemDefinition T-pattern Region-Of- Interest Spatio-temporalcontainment T-Patterns with Static ROI T-patternMining T-Patterns with Dynamic ROI Experiment &Conclusion

  15. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Introduction ST-sequence Background &Related Work Spatial containment ProblemDefinition T-pattern Region-Of- Interest Spatio-temporalcontainment T-Patterns with Static ROI T-patternMining T-Patterns with Dynamic ROI Experiment &Conclusion

  16. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Introduction ST-sequence Background &Related Work Spatial containment ProblemDefinition T-pattern Region-Of- Interest Spatio-temporalcontainment T-Patterns with Static ROI T-patternMining T-Patterns with Dynamic ROI Experiment &Conclusion

  17. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Introduction ST-sequence Background &Related Work Spatial containment ProblemDefinition T-pattern Region-Of- Interest Spatio-temporalcontainment T-Patterns with Static ROI T-patternMining T-Patterns with Dynamic ROI Experiment &Conclusion

  18. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Introduction ST-sequence Background &Related Work Spatial containment ProblemDefinition T-pattern Region-Of- Interest Spatio-temporalcontainment T-Patterns with Static ROI Figure 1 spatial and temporal constraints essentially form a spatio-temporal neighborhood around each point of the reference trajectory T-patternMining T-Patterns with Dynamic ROI Experiment &Conclusion

  19. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Introduction ST-sequence Background &Related Work Spatial containment ProblemDefinition T-pattern Region-Of- Interest Spatio-temporalcontainment T-Patterns with Static ROI T-patternMining T-Patterns with Dynamic ROI Experiment &Conclusion

  20. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping REGIONS-OF-INTEREST neighborhood function is used to model Regions-of-Interest (RoI), that represent a natural way to partition the space into meaningful areas and to associate spatial points with region labels. Introduction Background &Related Work • Integrating ROI & trajectories : • Input:set R of disjoint spatial regions • Neigborhood function: Region-Of-Interest ProblemDefinition TrajectoryPreproceing Region-Of- Interest DiscoveringROI T-Patterns with Static ROI • two points are considered similar iff they fall in the same region. • points disregarded by R will be virtually deleted from trajectories and spatio-temporal patterns. Popualr pointsdetection T-Patterns with Dynamic ROI ROIConstruction Experiment &Conclusion

  21. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Introduction Background &Related Work Region-Of-Interest ProblemDefinition • The regions associated with each point, i.e., • NR(x, y), are essentially used as labels representing events of the form “the trajectory is in region NR(x, y) at time t” • the methods developed for extracting frequent TAS’s can be directly applied to the translated input sequences, and each pattern (TAS) of the form A →B represents the set of T-patterns TrajectoryPreprocessing Region-Of- Interest DiscoveringROI T-Patterns with Static ROI Popular pointsdetection T-Patterns with Dynamic ROI ROIConstruction Experiment &Conclusion

  22. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Static preprocessed spatial regions When Regions-of-Interest are not provided by external means they have to be automatically computed through some heuristics. Introduction Background &Related Work The underlying idea is that locations frequently visited by moving objects probably represent interesting places Region-Of-Interest ProblemDefinition TrajectoryPreproceing Region-Of- Interest consideration the density of spatial regions. DiscoveringROI T-Patterns with Static ROI Popualr pointsdetection T-Patterns with Dynamic ROI ROIConstruction Experiment &Conclusion

  23. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Trajectory preprocessing • Assuming to know a suitable set of RoI, applying them to the T-pattern mining problem simply consists in preprocessing the input sequences to corresponding sequences of RoI. • provide a model for such point movement, e.g., linear regression.it is not obvious which time-stamp should be associated with the event “Region A” in the translated sequence. • Different way in this paper: 1. if the trajectory starts at time t from a point already inside a region A, yield the couple (A, t); 2.An object can enter several times in a region, and each entry will be associated with a different time-stamp. Introduction Background &Related Work Region-Of-Interest ProblemDefinition TrajectoryPreprocessing Region-Of- Interest DiscoveringROI T-Patterns with Static ROI Popular pointsdetection T-Patterns with Dynamic ROI ROIConstruction Experiment &Conclusion

  24. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Discovering Region-of-Interest When Regions-of-Interest are not known a priori, some heuristics that enable to automatically identify them are needed. Several different methods are possible: •selecting among a database of candidate places • automatically computing candidate places through the analysis of trajectories,EX: selecting all minimal square regions that were visited by at least 10% of the objects; • mixing the two approaches Introduction Background &Related Work Region-Of-Interest ProblemDefinition TrajectoryPreprocessing Region-Of- Interest DiscoveringROI T-Patterns with Static ROI • Second type: • dense (i.e., popular) points in space are detected • a set of significant regions are extracted to represent them succinctly. Popular pointsdetection T-Patterns with Dynamic ROI ROIConstruction Experiment &Conclusion

  25. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Popular points detection • modeling the popularity of a point as the number of distinct moving objects that pass close to it w.r.t. a neighborhood function. • discretize the working space through a regular grid with cells of small size. • set cell width at a given fraction of the chosen neighborhood. Then, the density of cells is computed by taking each single trajectory and incrementing the density of all the cells that contain any of its points Introduction Background &Related Work Region-Of-Interest ProblemDefinition TrajectoryPreprocessing Region-Of- Interest DiscoveringROI T-Patterns with Static ROI Popular pointsdetection T-Patterns with Dynamic ROI ROIConstruction Experiment &Conclusion

  26. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping ROI construction In general, the set of popular regions can be extremely large – even infinite, if we work on a continuous space.Therefore, some additional constraints should be enforced to select a significant, yet limited, subset of them. Introduction Background &Related Work Region-Of-Interest ProblemDefinition TrajectoryPreprocessing Region-Of- Interest (i) Each r ∈ R forms a rectangular region(ii) sets in R are pairwise disjoint;(iii) all dense cells in Gare contained in some set r ∈ R; (iv) all r ∈ R have avg (i, j) ∈r G( i, j) ≥ δ (v) Assuming that r ∈ R has size h × k, all its rectangular supersets r ⊇ r of size (h + 1) × k or h × (k + 1) violate (iv) or r and r contain exactly the same number of dense cells. DiscoveringROI T-Patterns with Static ROI Popular pointsdetection T-Patterns with Dynamic ROI ROIConstruction Experiment &Conclusion

  27. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping ROI construction Introduction Background &Related Work Region-Of-Interest ProblemDefinition TrajectoryPreprocessing Region-Of- Interest DiscoveringROI T-Patterns with Static ROI Popular pointsdetection T-Patterns with Dynamic ROI ROIConstruction Experiment &Conclusion

  28. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping ROI construction example Introduction Background &Related Work ProblemDefinition Region-Of- Interest T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment &Conclusion

  29. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping T-Patterns with Static ROI Introduction Background &Related Work ProblemDefinition Region-Of- Interest T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment &Conclusion

  30. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Introduction T-Patterns with Dynamic ROI Background &Related Work T-patterns exacerbate the difficulty of the density estimation task in two ways: (i) the dimensionality of working spaces of TAS’s grows less quickly (ii) the sequence component in each TAS strongly limits the number of instances that can be found within each input sequence, making the density estimation task easier. ProblemDefinition Region-Of- Interest DynamicneighborhoodApproach T-Patterns with Static ROI T-Patterns with Dynamic ROI A step-wiseheuristic Experiment &Conclusion Implement

  31. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping A step-wise heuristic Introduction any frequent T-pattern of length n + 1 is the extension of some frequent T-pattern of length n, as stated by the following property: Background &Related Work ProblemDefinition Region-Of- Interest DynamicneighborhoodApproach T-Patterns with Static ROI T-Patterns with Dynamic ROI This property implies that the support of a T-pattern is less than or equal to the support of any its prefixes, allows us to adopt a level-wise approach by mining step-by-step A step-wiseheuristic Experiment &Conclusion Implement

  32. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Implementation of the method Introduction Background &Related Work ProblemDefinition only a segment of such trajectories really needs to be searched, since we only need to find continuations of the pattern pn, and no point occurring before the end time of pn can be appended to pn to obtain pn+1. Therefore, any point occurring before such end time can be removed from the trajectory. Region-Of- Interest DynamicneighborhoodApproach T-Patterns with Static ROI T-Patterns with Dynamic ROI A step-wiseheuristic Experiment &Conclusion Implement

  33. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Introduction Background &Related Work ProblemDefinition Region-Of- Interest DynamicneighborhoodApproach T-Patterns with Static ROI T-Patterns with Dynamic ROI A step-wiseheuristic Experiment &Conclusion Implement

  34. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Experiment-Real data Introduction The real data used in these experiments describe the GPS traces of a fleet of 273 trucks in Athens, Greece, for a total of 112203 points6. Running both the Static RoI T-pattern and Dynamic RoI T-pattern algorithms with various parameter settings Background &Related Work ProblemDefinition Region-Of- Interest T-Patterns with Static ROI T-Patterns with Dynamic ROI (Δt1,Δt2) ∈ [330, 445] × [116, 190] (Δt1,Δt2) ∈ [400, 513]×[41, 61] Dynamic approach: Experiment &Conclusion Static approach:

  35. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Introduction Performance-synthetic data Background &Related Work ProblemDefinition Region-Of- Interest T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment &Conclusion

  36. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Introduction Performance-synthetic data Background &Related Work ProblemDefinition Region-Of- Interest T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment &Conclusion

  37. Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Introduction Conclusion Background &Related Work T-patterns are a basic building block for spatio-temporal data mining, around which more sophisticated analysis tools can be constructed, including: • integration with background geographic knowledge • adequate visualization metaphors for T-patterns • adequate mechanisms for spatio-temporal querying ProblemDefinition Region-Of- Interest T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment &Conclusion

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