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

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User upload GPS file to OpenstreetMap.org Dataset in MOPSI ProjectMicrosoft Geolife datasetBerlinMOD Cycling datasetAnimal Movement Many GPS Trajectories are collected by Geo-position devices to depict the movement of human, car, animals... It includes latitude, longitude and time information Example of GPS Trajectories

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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 MOPSIBerlinMOD

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From

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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

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

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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.

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44 points13 points6 points The original route has 575 points in this example

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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 UK map differential coordinates

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For GPS Trajectory, speed and direction change will be robust variant in the encoding process distancespeed

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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.

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Probability estimation Updating tsp min : minimum sampling time internal δ t = 0.01, bias factor r t : rtsp max x 1 vector μ t = 0.995, forgetting factor, higher weight for recent encoded values Lossless Compression by adaptive arithmetic coding

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Predict mean and variance, quantized level determined by time difference

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Quantized level determined by time difference and speed P( Δθ 0 ) P( Δθ k ) P( Δθ 0 |Δθ k ) Update P( Δθ 0 )

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

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

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Estimated Storage Cost for a long time period

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3m maxSED, 0.36 KB/h10m maxSED, 0.19KB/h50m maxSED, 0.06KB/h A demo is published on

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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. KB/h on the compression algorithm

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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)

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N. Meratnia and R. A. de By. "Spatiotemporal Compression Techniques for Moving Point Objects", Advances in Database Technology, vol. 2992, 551–562, M. Potamias, K. Patroumpas, T. Sellis, "Sampling Trajectory Streams with Spatiotemporal Criteria", Scientific and Statistical Database Management (SSDBM), , H. Cao, O. Wolfson, G. Trajcevski, "Spatio-temporal data reduction with deterministic error bounds", VLDB Journal, 15(3), , A. Akimov, A. Kolesnikov and P. Fränti, "Coordinate quantization in vector map compression", IASTED Conference on Visualization, Imaging and Image Processing (VIIP’04), , S. Shekhar, S. Huang, Y. Djugash, J. Zhou, "Vector map compression: a clustering approach", ACM Int. Symp. Advances in Geographic Inform, 74-80, A. Kolesnikov, "Optimal encoding of vector data with polygonal approximation and vertex quantization", SCIA’05, LNCS, vol. 3540, 1186– M. Chen, M. Xu and P. Fränti, "Fast dynamic quantization algorithm for vector map compression", IEEE Int. Conf. on Image Processing, , 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, 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, , 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, 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 , F. Schmid, K. F. Richter and P. Laube, "Semantic Trajectory Compression", Lecture Notes in Computer Science, Vol. 5644, pp , 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.

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Speed at x direction Speed at y direction Speed Direction Change

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