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Where Next? Data Mining Techniques and Challenges for

Trajectory Prediction

Slides credit: Layla Pournajaf

o Navigational services.

o Traffic management.

o Location-based advertising.

Source: A. Monreale, F. Pinelli, R. Trasarti, F. Giannotti. WhereNext: a Location Predictor on Trajectory Pattern Mining. KDD 2009

o Destination prediction

o Path prediction with known destination

o Path prediction with unknown destinationoSimilar to predicting next N locations


Raw Trajectories


Raw Trajectories

Preprocessed Trajectories


Raw Trajectories


Prediction Model


Source: www.openstreetmap.org

http://www.openstreetmap.org/

Real-world data include raw trajectories of continuous GPS coordinates which are noisy and inaccurate!

Source: www.openstreetmap.org

http://www.openstreetmap.org/

Raw Trajectories



o Discretizing Timeo30 seconds, one hour

oTemporal Representationo Location-series

o Fixed-interval time-location series

o Variable-interval time-location

series


o Discretizing LocationoGrid-based (uniform vs

hierarchical)

oMining Frequent RegionsClustering

Semantic-based


Source: Xue, Andy Yuan, et al. "Destination prediction by sub-trajectory synthesis and privacy protection against such prediction." ICDE 2013.

Map of Beijing with 30 × 30 grid overlay: Each cell ≈ 1.78km2

o Clusteringo DBScan

o Hierarchical Clustering

o Semantic-basedo Using points of interests

Source: Lei, Po-Ruey, et al. "Exploring spatial-temporal trajectory model for location prediction." MDM 2011.

Raw Trajectories


Prediction Models


Personalized / Individual-based:o Utilize only the history of one object to predict its future locations

General:o Utilize the history of all objects to predict future locations

Model-based (formulate the movement of moving objects using mathematical models)o Markov Models

o Hidden Markov Models (Zhou et. al., ACM SIGKDD 2013)

o Recursive Motion Function (Y. Tao et. al., ACM SIGMOD 2004)

oDeep learning models Pattern-based (exploit pattern mining algorithms for prediction)

o Sequential Pattern Mining (G. Yavas et. al., DKE 2005)

o Trajectory Pattern Mining

Hybrido Recursive Motion Function + Sequential Pattern Mining (H. Jeung et. al.,

ICDE 2008)

2𝑝45 = 3

1𝑝56 = 3


Partial Trajectory:<𝑟1, 𝑡1> , <𝑟2, 𝑡2>, …., <𝑟𝑐, 𝑡𝑐>

Prediction:• Having a partial trajectory (discretized) including the current

region 𝑟𝑐, find the most probable region at time point 𝑡𝑐+1

arg max P(𝑅𝑐+1 = 𝑟𝑐+1| 𝑟1 , … 𝑟𝑐) 𝑟𝑐+1

<?, 𝑡𝑐+1>

Embedding Higher-Order Chains

• Each new state depends on fixed-length

window of preceding state values

• We can represent this as a first-order model

via state augmentation:

(N2 augmented states)

Semi-Lazy Hidden Markov Approach (SIGKDD ‘13)

• Find similar trajectories from historical trajectories (reference objects)

• Build a hidden Markov Model on the fly (vs. eager or lazy approach)

• Self-correcting continuous prediction (real time)• Refine prediction model• Adjust weights for reference objects

Model-based (formulate the movement of moving objects using mathematical models)o Markov Models

o Hidden Markov Models (Zhou et. al., ACM SIGKDD 2013)

o Recursive Motion Function (Y. Tao et. al., ACM SIGMOD 2004)

oDeep learning models Pattern-based (exploit pattern mining algorithms for prediction)

o Sequential Pattern Mining (G. Yavas et. al., DKE 2005)

o Trajectory Pattern Mining (Monreale et al ACM SIGKDD 2009)

Hybrido Recursive Motion Function + Sequential Pattern Mining (H. Jeung et. al.,

ICDE 2008)

1. Preprocess raw trajectories and

extract frequent sequential patterns

(T-Pattern)




(T-Pattern)

2. Build a Prefix Tree (T-Pattern Tree)




(T-Pattern)

2. Build a Prefix Tree (T-Pattern Tree)

3. Predict Next Location


<𝑥1, 𝑦1, 𝑡1> , <𝑥2, 𝑦2, 𝑡2>, …., <𝑥𝑛, 𝑦𝑛, 𝑡𝑛>


• Two points match if one falls within a spatial neighborhood N()of the other

• Two transition times match if their temporal difference is ≤ τ

<𝑥1, 𝑦1, 𝑡1> , <𝑥2, 𝑦2, 𝑡2>, …., <𝑥𝑛, 𝑦𝑛, 𝑡𝑛>


• Two points match if one falls within a spatial neighborhood N()of the other

• Two transition times match if their temporal difference is ≤ τ

<𝑥1, 𝑦1, 𝑡1> , <𝑥2, 𝑦2, 𝑡2>, …., <𝑥𝑛, 𝑦𝑛, 𝑡𝑛>


• Calculate support for each T-pattern

Generating all association rules from each T-pattern and using them to build aclassifier is too expensive.

R1 R2 R3 R4T-Pattern

Rules R1 R2 R3 R4

R1 R2 R3 R4

R1 R2 R3 R4

α1 α2α3


To avoid the rules generation, the T-Pattern set is organized as a prefix tree.

For Each node v

•Id identifies the node v

•Region is a spatial component of the T-Pattern

•Support is the support of the T-pattern

For Each edge j

[a,b] correspond to the time interval αn of the T-Pattern

Three steps:1. Search for best match

2. Candidate generation

3. Make predictions

Best Match

Prediction

Three steps:1. Search for best match

2. Candidate generation

3. Make predictions

The Best Match is the path having: the maximum path score using the time and location matching

and support at least one admissible prediction.

o Prediction errors (distance and time)

o Prediction accuracy (precision and recall)

o Prediction rate

H. Jeung, Q. Liu, H. T. Shen, and X. Zhou. A hybrid prediction model for moving objects. In Data Engineering, 2008. ICDE 2008. IEEE 24th International Conference on, pages 70-79. IEEE, 2008.

J. Krumm and E. Horvitz. Predestination: Inferring destinations from partial trajectories. In Ubiquitous Computing, pages 243-260. Springer, 2006. A. Monreale, F. Pinelli, R. Trasarti, and F. Giannotti. Wherenext: a location predictor on trajectory pattern mining. In Proceedings of the 15th ACM SIGKDD

international conference on Knowledge discovery and data mining, pages 637-646. ACM, 2009. G. Yavas, D. Katsaros, O. Ulusoy, and Y. Manolopoulos. A data mining approach for location prediction in mobile environments. Data & Knowledge

Engineering, 54(2):121-146, 2005. Y. Tao, C. Faloutsos, D. Papadias, and B. Liu. Prediction and indexing of moving objects with unknown motion patterns. In Proceedings of the 2004 ACM

SIGMOD international conference on Management of data, pages 611-622. ACM, 2004. A. Y. Xue, R. Zhang, Y. Zheng, X. Xie, J. Huang, and Z. Xu. Destination prediction by sub-trajectory synthesis and privacy protection against such prediction.

In Data Engineering (ICDE), 2013 IEEE 29th International Conference on, pages 254-265. IEEE, 2013.

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