Compression of GPS Trajectories

1. Compression of GPS Trajectories Minjie Chen, MantaoXu and PasiFränti Speech and Image Processing Unit (SIPU)School of Computing University of Eastern Finland, FINLAND Presented on Apr 10th for Data Compression Conference, Snowbird, Utah, USA.

2. Motivation User upload GPS file to OpenstreetMap.org Example of GPS Trajectories Many GPS Trajectories are collected by Geo-position devices to depict the movement of human, car, animals... It includes latitude, longitude and time information Dataset in MOPSI Project Microsoft Geolife dataset BerlinMOD Cycling dataset Animal Movement

3. Motivation (cont.) • Plenty of date space are needed in client side to store these data • In GPX format, Storage cost is around : 43KB/hour(binary) , 300+KB/hour(GPX) if the data is collected at 1 second interval. For 10,000 users, it is 30GB/day, 10TB/year. Geolife and MOPSI BerlinMOD

4. Existed Software • From http://onestepahead.de

5. Data Reduction • Trajectory simplification (TS) • Top-down time-ratio (TD-TR) • Open Window (OW) • Threshold-guided algorithm • STTrace • Spatial join • SQUISH • Generic Remote Trajectory Simplification (GRTS) • Multi-resolution Polygonal Approximation (MRPA) With different error measures • synchronous Euclidean distance (SED) • position, speed and orientation • spatial join • Fréchet distance • local integral square synchronous Euclidean distance

6. Error Measures • Maximum Synchronous Euclidean distance (max SED) is used as the error metrics. • The errors were measured through distances between pairs of temporally synchronized positions.

7. Reduction and Compression Reduction • The reduced data points are saved directly with a fixed bit length • Support both the visualization process and the effective trajectory queues in database. Compression (This is discussed in this paper) • Optimizes both for the reduction and the quantization in the encoding process • A better compression ratio, appropriate for data storage.

8. Data Reduction Example in MOPSI 44 points 13 points 6 points The original route has 575 points in this example

9. Existing Compression Algorithms Only lossy compression of Vector data are considered (No timestamp information) • Uniform quantization • Product scalar quantization • Clustering-based method • Reference line approach • Combine scalar quantization and reduction via Dynamic Programming differential coordinates UK map

10. Differential Coordinates vs. Speed and Direction Change For GPS Trajectory, speed and direction change will be robust variant in the encoding process distance speed After Simpli-fication

11. Approximation Speed and direction changes are incorporated in the encoding process instead of using the differential coordinates. • Line simplification and quantization are combined in order to seek an approximation result for compression. • A greedy solution is used for the trajectory approximation in this paper.

12. Approximation(cont.)

13. Encoding Process (Time Difference) Lossless Compression by adaptive arithmetic coding • Probability estimation • Updating tspmin: minimum sampling time internal δt= 0.01, bias factor rt: rtspmax x 1 vector μt = 0.995, forgetting factor, higher weight for recent encoded values

14. Encoding Process (Speed) Predict mean and variance, quantized level determined by time difference

15. Encoding Process(Direction Change) Quantized level determined by time difference and speed P(Δθk) P(Δθ0) Update P(Δθ0) P(Δθ0 |Δθk)

16. Time Complexity Time cost is 2s for 10,000 points using Matlab implementation

17. Performance Only 35% comparing with those “compression” algorithm + 7-Zip (Lempel-Ziv Markov chain Algorithm) on Geolife dataset KB/h on the compression algorithm

18. Performance KB/h on the compression algorithm

19. Performance Estimated Storage Cost for a long time period

20. Visual Example 3m maxSED, 0.36 KB/h 10m maxSED, 0.19KB/h 50m maxSED, 0.06KB/h A demo is published on http://cs.joensuu.fi/~mchen/GPSTrajComp.htm

21. Use a filtering Process before compression? KB/h on the compression algorithm The bit-rate can be reduced around 30%, 20%, 15% for 1m, 3m, 10m max SED. Bit-rate will not be changed for 30m, 100m max SED.

22. Conclusions • State-of-the-art lossy compression algorithm for GPS Trajectories with 0.39KB/h bit-rate for geolife dataset • Approximate the encoding curve by both data reduction and quantization, on speed and direction change variant. • Extension can be done on: • Online compression • Improvement of approximation and encoding process by dynamic programming (improve 15%-20%) • In urban area, road network can be considered • Consider similarity of multiple Trajectories (only time is needed to encode in similar part)

23. Related Paper • N. Meratnia and R. A. de By. "Spatiotemporal Compression Techniques for Moving Point Objects", Advances in Database Technology, vol. 2992, 551–562, 2004. • M. Potamias, K. Patroumpas, T. Sellis, "Sampling Trajectory Streams with Spatiotemporal Criteria", Scientific andStatistical Database Management (SSDBM), 275-284, 2006. • H. Cao, O. Wolfson, G. Trajcevski, "Spatio-temporal data reduction with deterministic error bounds", VLDB Journal, 15(3), 211-228, 2006. • A. Akimov, A. Kolesnikov and P. Fränti, "Coordinate quantization in vector map compression", IASTED Conference onVisualization, Imaging and Image Processing (VIIP’04), 748-753, 2004. • S. Shekhar, S. Huang, Y. Djugash, J. Zhou, "Vector map compression: a clustering approach", ACM Int. Symp.Advances in Geographic Inform, 74-80, 2002. • A. Kolesnikov, "Optimal encoding of vector data with polygonal approximation and vertex quantization", SCIA’05, LNCS, vol. 3540, 1186–1195. 2005. • M. Chen, M. Xu and P. Fränti, "Fast dynamic quantization algorithm for vector map compression", IEEE Int. Conf. on Image Processing, 4289-4292, September 2010.” • Y. Chen, K. Jiang, Y. Zheng, C. Li, N. Yu, "Trajectory Simplification Method for Location-Based Social Networking Services", ACM GIS workshop on Location-based social networking services, 33-40, 2009. • J. Muckell, J. H. Hwang, C. T. Lawson, S. S. Ravi, "Algorithms for compressing GPS trajectory data: an empirical evaluation", SIGSPATIAL International Conference on Advances in Geographic Information Systems, 402-405, 2010. • J. Muckell, J. H. Hwang, V. Patil, C. T. Lawson, F. Ping , S. S. Ravi, "SQUISH: an online approach for GPS trajectory compression", International Conference on Computing for Geospatial Research & Applications, 1-8, 2011. • M. Chen, M. Xu and P. Fränti, "A Fast O(N) Multi-resolution Polygonal Approximation Algorithm for GPS Trajectory Simplification", IEEE Transactions on Image Processing (in press). • G. Kellaris, N.  Pelekis and Y.  Theodoridis, "Trajectory Compression under Network Constraints", Lecture Notes in Computer Science, Vol. 5644, pp.392-398, 2009. • F. Schmid, K. F.  Richter and P. Laube, "Semantic Trajectory Compression", Lecture Notes in Computer Science, Vol. 5644, pp.411-416, 2009. • M. Koegel, M. Mauve,”On the Spatio-Temporal Information Content and Arithmetic Coding of Discrete Trajectories”, International Conference on Mobile and Ubiquitous Systems: Computing, Networking and Services, Copenhagen, Denmark, December 2011.

24. Additional Pages Speed at x direction Speed at ydirection Speed Direction Change