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. 2/37 Trajectory Pattern Mining Introduction Background and Related Work Problem Definition Regions-Of-Interest T-Patterns with Static ROI T-Patterns with Dynamic ROI Outline Experiments & Conclusion NTU IM Hsieh, Hsun-Ping

3. 3/37 Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Summery Algorithm Trajectory Pattern Spatio- temporal pattern Spatio-Temporal pattern ： Space & time element should be considered In this paper, Spatio-Temporal pattern is used to apply on Trajectory Pattern Mining. Experiment & Conclusion Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping

4. 4/37 Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Summery Algorithm Spatio- temporal pattern 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. Experiment & Conclusion Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Trajectory Pattern

5. 5/37 Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Summery Approach Spatio- temporal pattern 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 Experiment & Conclusion Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Trajectory Pattern

6. 6/37 Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Summery Approach Spatio- temporal pattern Trajectory pattern example ： Experiment & Conclusion Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Trajectory Pattern We only require that such trajectories visit the same sequence of places with similar transition times, even if they start at diffierent absolute times

7. 7/37 Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Summery Spatio- temporal pattern 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. Experiment & Conclusion Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Trajectory Pattern Approach

8. 8/37 Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Approach Spatio- temporal pattern 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. Experiment & Conclusion Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Trajectory Pattern Summery

9. 9/37 Temporally Annotated Sequence Previous Research Spatio- temporal sequential patterns Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion 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 = α 1 → · · · →α k is a subsequence of β = β 1 → ·· · → β m if there exist integers 1 ≤ i 1 <... < i k ≤ m such that ∀ 1≤n≤k α n ⊆ β in. Define support supp D (S) of a sequence S as the percentage of transactions T ∈ D S is frequent w.r.t. threshold smin if supp D (S) ≥ smin. TAS example

10. 10/37 Temporally Annotated Sequence Spatio- temporal sequential patterns Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping TAS example 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, Previous Research

11. 11/37 Previous Research Spatio- temporal sequential patterns Example: Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion 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. TAS example Temporally Annotated Sequence

12. 12/37 TAS example Previous Research Spatio- temporal sequential patterns Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Definition 1 : Temporally Annotated Sequence

13. 13/37 Previous Research Spatio- temporal sequential patterns Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Example : Temporally Annotated Sequence if τ = 2 and s min = 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]. TAS example

14. 14/37 Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping 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 : R 2 →P(R 2 ), which assigns to each pair (x, y) a set N (x, y) of neighboring points. T-pattern Mining Spatio- temporal containment T-pattern Spatial containment ST-sequenc e

15. 15/37 T-pattern Mining Spatio- temporal containment T-pattern ST-sequence Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Spatial containment

16. 16/37 T-pattern Mining Spatio- temporal containment Spatial containment ST-sequence Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping T-pattern

17. 17/37 T-pattern Mining T-pattern Spatial containment ST-sequence Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Spatio- temporal containment

18. 18/37 T-pattern Mining T-pattern Spatial containment ST-sequence Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Figure 1 spatial and temporal constraints essentially form a spatio-temporal neighborhood around each point of the reference trajectory Spatio- temporal containment

19. 19/37 Spatio- temporal containment T-pattern Spatial containment ST-sequence Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping T-pattern Mining

20. 20/37 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. Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion ROI Construction Popualr points detection Discovering ROI Trajectory Preproceing Region-Of- Interest Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Integrating ROI & trajectories : Input:set R of disjoint spatial regions Neigborhood function: 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. REGIONS-OF-INTEREST

21. 21/37 Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion ROI Construction Popular points detection Discovering ROI Trajectory Preprocessing Region-Of- Interest Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping The regions associated with each point, i.e., N R (x, y), are essentially used as labels representing events of the form “the trajectory is in region N R (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

22. 22/37 When Regions-of-Interest are not provided by external means they have to be automatically computed through some heuristics. Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion ROI Construction Popualr points detection Discovering ROI Trajectory Preproceing Region-Of- Interest Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Static preprocessed spatial regions The underlying idea is that locations frequently visited by moving objects probably represent interesting places consideration the density of spatial regions.

23. 23/37 Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion ROI Construction Popular points detection Discovering ROI Region-Of- Interest Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping 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. Trajectory Preprocessing Trajectory preprocessing

24. 24/37 Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion ROI Construction Popular points detection Region-Of- Interest Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping 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 Trajectory Preprocessing Discovering Region-of-Interest Discovering ROI Second type: dense (i.e., popular) points in space are detected a set of significant regions are extracted to represent them succinctly.

25. 25/37 Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion ROI Construction Region-Of- Interest Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping 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 Trajectory Preprocessing Popular points detection Discovering ROI Popular points detection

26. 26/37 Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion Popular points detection Region-Of- Interest Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Discovering ROI Trajectory Preprocessing ROI construction 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. (i) Each r ∈ R forms a rectangular region (ii) sets in R are pairwise disjoint; (iii) all dense cells in G are 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.

27. 27/37 Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion Popular points detection Region-Of- Interest Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Discovering ROI Trajectory Preprocessing ROI construction ROI Construction

28. 28/37 Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping ROI construction example

29. 29/37 Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping T-Patterns with Static ROI

30. 30/37 Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion Implement A step-wise heuristic Dynamic neighborhood Approach Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping T-Patterns with Dynamic ROI 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.

31. 31/37 Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion Implement Dynamic neighborhood Approach Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping A step-wise heuristic 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: A step-wise heuristic 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

32. 32/37 Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion Dynamic neighborhood Approach Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping Implementation of the method A step-wise heuristic 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 p n can be appended to pn to obtain p n+1. Therefore, any point occurring before such end time can be removed from the trajectory. Implement

33. 33/37 Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion Implement Dynamic neighborhood Approach Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping A step-wise heuristic

34. 34/37 Experiment-Real data Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping 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 Dynamic approach: Static approach: (Δt1,Δt2) ∈ [330, 445] × [116, 190] (Δt1,Δt2) ∈ [400, 513]×[41, 61]

35. 35/37 Performance-synthetic data Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping

36. 36/37 Performance-synthetic data Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping

37. 37/37 Conclusion Background & Related Work Problem Definition Region-Of- Interest Region-Of- Interest Introduction T-Patterns with Static ROI T-Patterns with Static ROI T-Patterns with Dynamic ROI Experiment & Conclusion Trajectory Pattern Mining NTU IM Hsieh, Hsun-Ping 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