Indexing Uncertain SpatioTemporal Data Jacob Arndt Coleman Shepard

Indexing Uncertain Spatio-Temporal Data Jacob Arndt Coleman Shepard CSCI 8715 Spatial Data Science Research Emrich, T. , Kriegel, H. P. , Mamoulis, N. , Renz, M. , & Zufle, A. (2012, October). Indexing uncertain spatio-temporal data. In Proceedings of the 21 st ACM international conference on Information and knowledge management (CIKM) (pp. 395 -404). ACM. 1

Motivation: Societal Importance • Application in multiple domains – – – – Military Emergency Management Disaster Management Environmental Monitoring Ecology Biology Geographic Information Science (GIS) Location Based Services (LBS) ars. els-cdn. com/content/image/1 -s 2. 0 -S 0306437910000426 -gr 1. jpg • Data volume • Uncertainty • • Data gaps between discrete time steps Measurement error mdpi. com/sensors-16 -01768/article_deploy/html/images/sensors-16 -01768 -g 004. png 2

Problem Statement • Input – Spatiotemporal Data (e. g. , GPS points) • Output – Indexed Uncertain Spatiotemporal Data • Goal – Computational efficiency • Constraints – Low sampling rate (e. g. once per second or 5 seconds) for a fast moving object Emrich et al. 2012 3

Question True or False • An uncertain spatiotemporal object is an object whose location is known at all times 4

Related Work and Challenges • Modeling uncertain movement – Markov Chain Models – Beads (or necklace) model – Brownian motion • Challenges – An objects trajectory is almost always uncertain. – The space of possible trajectories between two observations is very large – Need to approximate these trajectories somehow 5

Contributions • Novel approximation technique – Uncertain spatiotemporal (UST) data and its movement – probabilistically bound the uncertain movement • UST-tree – New index tree for indexing uncertain spatiotemporal data. • More efficient than traditional methods (Scan+, R*-tree) for spatiotemporal selection query. • Support for querying large spatiotemporal datasets 6

Key Concepts I • Uncertain spatiotemporal object (UST) • Modeling uncertain movement (beads model, Markov-Chain model) • Spatiotemporal selection query – Probabilistic Spatiotemporal <probability threshold> Exists Query • Spatiotemporal diamonds – Spatiotemporal approximation of possible paths between known points – Spatiotemporal filtering using spatiotemporal diamonds Emrich et al. 2012 7 Emrich et al. 2012

Key Concepts II • Spatiotemporal subdiamonds – Probabilistic UST object approximation – Probabilistic filtering using spatiotemporal subdiamonds • Optimal Probabilistic Diamond • Linear approximations function Emrich et al. 2012 8

Key Concepts III • UST-tree Emrich et al. 2012 • Query evaluation using UST-tree – – – 9 Filter using mbrs Filter the results using the diamond approximations Filter using the probabilities precomputed from the linear approximation functions Store all objects which pass all filter steps in a list Access the exact object data if probability does not fall below the threshold

Validation Methodology • Experimental goals – Determine which indexing method is the most efficient in terms of query time and page accesses. • Candidates – Scan+ – R*-tree – UST-tree • Benchmark datasets – Bejing taxi data – Synthetic dataset 10

Validation Methodology Emrich et al. 2012 • Scan+ has a slower query time than R*-Tree and UST-Tree • UST-Tree has a longer filter step but shorter refinement step compared to R*-Tree • UST-Tree is about 3 times better in terms of overall query performance. 11

Quiz • How is a UST-Tree similar to an R*-Tree? – – 12 A. They both use probability thresholds for filtering B. They both use spatiotemporal diamonds C. They both use MBRs D. They both only use MBRs for filtering during query evaluation

Assumptions • Considers time and space as discrete. • Three-dimensional model of space and time. • Assumes the movement of each object follows a Markov-Chain model. – Consider movement a stochastic process • Comparative experiments were carried out on Synthetic data created in the study. • Does not account for measurement error • Potential real world obstacles were not addressed. 13 ars. els-cdn. com/content/image/1 -s 2. 0 -S 0921889013002212 -gr 5. jpg

Revisions • Consider an object’s location before it’s first and after its last observation. • Use other datasets such as AIS or pedestrian data to compare restricted networks such as streets to more open networks. • Perform more experiments with other spatiotemporal queries and datasets • Consider obstacles in space that alter the object’s potential path. • Visualization of data. 14