Probabilistic Cardinal Direction Queries On Spatio-Temporal Data

Ganesh ViswanathanMidterm Project ReportCIS 6930 Data Science: Large-Scale Advanced Data AnalyticsUniversity of Florida September 3rd, 2011

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

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

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

• Probabilistic version of these advanced queries can speed up similarity joins among spatial relations

disjoint contains inside equal meet covers coveredBy overlap

1 KmA B B lies to the East of A

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

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 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

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.)

Cardinal Direction Relations• Objects interaction grid (OIG)

for direction finding A

B

Cardinal Direction Relations• Objects interaction grid (OIG)

for direction finding

OIG(A,B) =

A

B

Cardinal Direction Relations

• Interpretation

1 1 01 0 20 2 2

A

B

( , ( , )) {(1,1), (1,2), (2,1)}( , ( , )) {(2,3), (3,2), (3,3)}

loc A OIM A Bloc B OIM A B

1. Determine the location of each component of object A & object B

2. Determine cardinal directions between the components

((1,1), (2,3))((1,2), (3,2))

NWN

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

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

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!

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, . . .,On with 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 Oi at time t0.

Uncertainty Model and Probabilistic Queries

Enabling probabilistic direction relation queries on spatio-temporal data:

Evaluation Idea

t1t2

Enabling probabilistic direction relation queries on spatio-temporal data:

Evaluation Idea

t1t2

Enabling probabilistic direction relation queries on spatio-temporal data:

Evaluation Idea

p

Closed objects-interaction grid

UA

dir { NE, p>0 }

Tiling & OIM generation

Interpretation

UB

for all t

Generate probabilities for each <Ui, Ui+1> & update database

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 analysis6. Visualization using Google Maps API (partly done)

Timeline

Data Collection(Tropical weather event information)

Generation of direction pdfs for NHC, NOAA and JTWC datasets

Implementation of pOIM

Visualization and Experiments

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?