Probabilistic Cardinal Direction Queries On Spatio-Temporal Data

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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 3 rd, 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 Advanced Queries on Spatio-Temporal Data Spatial relations can be Topological, Distance or Direction based disjoint contains inside equal meet covers coveredby overlap 1 Km A B B lies to the East of A Nearest-neighbor (NN), distance-range and direction-relation queries are important query types in spatial databases 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 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 1. Query the trajectory of a hurricane to determine the direction taken by it at any instant t during its lifetime 2. Incorporate uncertainty: Enable probabilistic direction-relation queries among the spatio-temporal objects 3. Provide a visualization for the results based on tropical weather event data d NW, N, NE, W, O, E, SW, S, SE Example: Given objects O 1 and O 2 evaluate dir( ) and return a set of tuples of the form (O 1, O 2, d, p d ) such that p d is the probability of occurrence of the cardinal direction d between O 1 and O 2

7 Cardinal Direction Relations Cardinal directions is an important qualitative spatial concept Direction relations Absolute (North, South, East, West, etc. Relative (front, behind, left, right, etc.) 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 dir t (A,B) yields the direction relation of A w.r.t B at time t.

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

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

10 Cardinal Direction Relations Interpretation A B Determine the location of each component of object A & object B 2. Determine cardinal directions between the components loc( A, OIM ( A, B)) = {(1,1),(1, 2),(2,1)} loc( B, OIM ( A, B)) = {(2,3),(3, 2),(3,3)} ψ ((1,1),(2,3)) = NW ψ ((1, 2),(3, 2)) = N

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 topk 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 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 σ 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 Pr p r = 1 e r2 /2σ 2 Probabilistic Directions: For a set of n object instances O 1,O 2,...,O n with uncertainty regions and probability density functions at time t 0 to t n, a PDQ returns a set of tuples in the form of (O i, O j, d, p i ), where p i is the nonzero probability that O j at t 2 is located at a cardinal direction d w.r.t O i at time t 0.

15 Evaluation Idea Enabling probabilistic direction relation queries on spatio-temporal data: t 1 t 2

16 Evaluation Idea Enabling probabilistic direction relation queries on spatio-temporal data: t 1 t 2

17 Evaluation Idea Enabling probabilistic direction relation queries on spatio-temporal data: Closed objects-interaction grid U B U A Tiling & OIM generation Generate probabilities for each <U i, U i+1 > & update database for all t pooo(u A, U B) Interpretation dir B, A = { NE, p>0 }

18 Timeline 1. Data collection NHC, NOAA and JTWC hurricane data obtained and loaded into Oracle database (done) 2. Performing cardinal direction queries on spatio-temporal data (done) 3. Generation of direction pdfs for NHC, NOAA and JTWC datasets 4. Implementation of Probabilistic Direction Query (PDQ) algorithm 5. Testing and experiment analysis 6. Visualization using Google Maps API (partly done) Data Collection (Tropical weather event information) Generation of direction pdfs for NHC, NOAA and JTWC datasets Implementation of poim Visualization and Experiments

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?