Probabilistic Cardinal Direction Queries On Spatio -Temporal Data

1. Probabilistic Cardinal Direction Queries On Spatio-Temporal Data Ganesh Viswanathan Midterm Project Report CIS 6930 Data Science: Large-Scale Advanced Data Analytics University of Florida September 3rd, 2011

2. Outline • Introduction • Uncertainty in spatio-temporal data • Advanced queries on spatio-temporal data • Cardinal direction relations (CDR) • Probabilistic CDR • Project Goals • Methodology and analysis • what has been done • timeline for the future • Conclusions

3. Uncertainty in Spatio-Temporal Data • Systems for continuous monitoring or tracking of mobile objects receive updated locations of objects as they move in space • Limitations of the bandwidth and battery power of mobile devices, make it infeasible for tracking the movement of objects with 100% certainty • Example: If there is a time delay between capture of location and its insertion in the database, location values received by object may be different from actual locations In GIS, the root-mean-square-error (RMSE) is one approach to report this positional (in)accuracy

4. 1 Km A B Advanced Queries on Spatio-Temporal Data • Spatial relations can be Topological, Distance or Direction based • Nearest-neighbor (NN), distance-range and direction-relation queries are important query types in spatial databases disjoint contains inside equal meet covers coveredBy overlap B lies to the East of A • Probabilistic version of these advanced queries can speed up similarity joins among spatial relations

5. Applications • Applications in GIS, Cognitive Sciences, AI, Robotics, Qualitative spatial reasoning, density-based data mining techniques. • In weather event analysis, probabilistic approaches can be used to • improve the performance of join processing over large relations that contain moving object trajectories, • to model the positional uncertainty of the moving eye of the hurricane

6. Project Goals • Query the trajectory of a hurricane to determine the direction taken by it at any instant t during its lifetime • Incorporate uncertainty: Enable probabilistic direction-relation queries among the spatio-temporal objects • Provide a visualization for the results based on tropical weather event data Example:Given objects O1 and O2 evaluate dir( ) and return a set of tuples of the form (O1, O2, d, pd) such that pd is the probability of occurrence of the cardinal direction d between O1 and O2

7. Cardinal Direction Relations • Besides its application in wayfinding, direction relationships are used in spatial databases and GIS as selection and join criteria in queries. • Given two objects A and B, a function dirt(A,B) yields the direction relation of A w.r.t B at time t. • Cardinal directions is an important qualitative spatial concept • Direction relations • Absolute (North, South, East, West, etc.) • Relative (front, behind, left, right, etc.)

8. Cardinal Direction Relations • Objects interaction grid (OIG) for direction finding A B

9. Cardinal Direction Relations • Objects interaction grid (OIG) for direction finding OIG(A,B) = A B

10. Cardinal Direction Relations • Interpretation A 1. Determine the location of each component of object A & object B 2. Determine cardinal directions between the components B

11. Probabilistic Cardinal Direction Relations • Useful in performing similarity join queries • Useful for positionally uncertain moving objects • Probability of the direction between the tropical cyclone event at current location(s) and the location(s) at the next subsequent time instant • Allows to leverage predictive models for forecasting the trajectory of newer storms and hurricanes based on previous patterns

12. Methodology and Analysis • Steps involved • Study of Related Work • Data Collection • Extensions to OIM for Probabilistic Direction Querying (PDQ) • Predictive analysis of weather events using the probabilities, based on top-k or thresholding • Visualization for PDQ results • Experiments

13. Data Collection • Best-track tropical weather information is obtained from three sources: • National Hurricane Center (NHC) • the National Oceanic and Atmospheric Administration (NOAA) • the Joint Typhoon Warning Center (JTWC) • These datasets contain over 120k rows accounting for the spatio-temporal variation of tropical storm and hurricane events over the continental United States from 1990 to 2010. • Spatial data for map boundaries of Continents, Counties, States, Counties and City locations obtained from data.gov • All data has been downloaded, files parsed and converted into normalized database tables DONE!

14. Uncertainty Model and Probabilistic Queries Uncertainty of an object can be characterized as: • Definition 1. An uncertainty region of an object Oi at time t, denoted by Ui(t), is a closed region such that Oi can be found only inside this region. • Definition 2. The uncertainty probability density function of an object Oi, denoted by fi(x, y, t), is a probability density function of Oi’s location (x, y) at time t, that has a value of 0 outside Ui(t) Let p be a point in 2D space whose position is uncertain. If is the uncertainty parameter associated with p, then the probability that p is located within a circle of radius r centered at p is given by the Circular Normal distribution • Probabilistic Directions: For a set of n object instances O1,O2, . . .,Onwith uncertainty regions and probability density functions at time t0 to tn, a PDQ returns a set of tuples in the form of (Oi, Oj, d, pi), where pi is the nonzero probability that Oj at t2 is located at a cardinal direction d w.r.t Oiat time t0.

15. Evaluation Idea Enabling probabilistic direction relation queries on spatio-temporal data: t2 t1

16. Evaluation Idea Enabling probabilistic direction relation queries on spatio-temporal data: t2 t1

17. Evaluation Idea Enabling probabilistic direction relation queries on spatio-temporal data: UB Closed objects-interaction grid Generate probabilities for each <Ui, Ui+1> & update database UA Tiling & OIM generation for all t p dir { NE, p>0 } Interpretation

18. Timeline • Data collection – NHC, NOAA and JTWC hurricane data obtained and loaded into Oracle database (done) • Performing cardinal direction queries on spatio-temporal data (done) • Generation of direction pdfs for NHC, NOAA and JTWC datasets • Implementation of Probabilistic Direction Query (PDQ) algorithm • Testing and experiment analysis • Visualization using Google Maps API (partly done)

19. Conclusions • The work studies probabilistic queries on spatio-temporal data and defines a novel query type: probabilistic cardinal direction query on them • Illustrates a large-scale data science application for using probabilistic cardinal direction querying to improve weather event analysis • Future work can include: Extensions of probabilistic Nearest Neighbor queries using both distance and direction, testing of similarity joins with PDQ and exploration of probabilistic topological querying operations on uncertain data. Questions?