Shashi Shekhar

Affiliation: Faculty of Computer Sc. and Eng., Univ. of Minnesotawww.cs.umn.edu/~shekhar

Collaboration Profile:• Role : Build novel data analysis tools • To facilitate science engineering or medicineTo facilitate science, engineering or medicine• Near future opportunities

• NSF Cyber-driven Discovery and Innovation, NSF/CISE/IIS, …• Research Focus: Spatial Database, Spatial Data MiningResearch Focus: Spatial Database, Spatial Data Mining

Spatial Databases: Example Projects

Evacutation Route Planning

Parallelize Range Queries

only in old planOnly in new plan In both plans

Storing graphs in disk blocksShortest Paths

Secret Sauce: Representation of (Spatio-)temporal Networks

N21

N211

N2 11

N2 11 N2 1

21

N..Node: Travel timeEdge:(1) Snapshot Model [Guting 04]

t=1

N1

N3

N4 N5

2

2

2

t=2

N1

N3

N4 N5

22

t=3

N1

N3

N4

N5

22

t=4

N1

N3

N4 N5

22

t=5

N1

N3

N4

N5

2

22

(2) Time Expanded Graph (TEG) [Ford 65]

N1 N1 N1N1 N1 N1 N1Attributes aggregated over edges and nodes.

(3) Time Aggregated Graph (TAG) [Our Approach]

N1

N2

N3

N1

N2

N3

N1

N2

N3

N1

N2

N3

N1

N2

N3

N1

N2

N3

N1

N2

N3 N1

[∞,1,1,1,1] [1,1,1,1,1]

[2,∞, ∞, ∞,2]

N2

N4 N5

t=1

N4

N5t=2

N4

N5t=3

N4

N5t=4

N4

N5

N4

N5t=5

N4

N5t=6

N4

N5t=7

[2,2,2,2,2] [2,2,2,2,2]N3

3Holdover EdgeTransfer Edges

[m1,…..,(mT] mi- travel time at t=iEdge

Power of Representation: Ex. Routing Algorithms

Predictable

Stationary Dijkstra’s, A*….

SP-TAG, SP-TAG*,CapeCodPredictable Future

Non-stationary

Special case (FIFO)[Kanoulas07]

Unpredictable Future

General Case TEG: LP, Label-correcting

TAG: Transform to Stationary TAG

[Orda91, Kohler02, Pallotino98]

y

N2[1 1 1 1 1] [1 1 1 1 1]

N2[2 3 4 5 6] [2 3 4 5 6]

N2[2 3 4 5 6] [2 3 4 5 6]

travel times → arrival times at end node → Min. arrival time series

N1

N3

N4 N5

[1,1,1,1,1] [1,1,1,1,1]

[2,2,2,2,2] [2,2,2,2,2]

[1,2,5,2,2] N1

N3

N4 N5

[2,3,4,5,6]

[3,4,5,6,7]

[2,3,4,5,6]

[2,4,6,6,7]

[3,4,5,6,7]

N1

N3

N4 N5

[2,3,4,5,6]

[3,4,5,6,7]

[2,3,4,5,6]

[2,4,8,6,7]

[3,4,5,6,7]

4

N3 N3N3

Non-stationary TAG → Stationary TAG

Spatial and Spatio-temporal Data Mining

• What is it?– Identifying interesting, useful, non-trivial patterns

• Hot-spots, discontinuities, co-locations, trends, …– in large spatial or spatio-temporal datasets

• Satellite imagery, geo-referenced data, e.g. census• gps-tracks, geo-sensor network, …

• Why is it important ?– Potential of discoveries and insights to improve human lives

E i H i E h h i ? C f h ?• Environment: How is Earth system changing? Consequences for humans?• Public safety: Where are hotspots of crime? Why?• Public health: Where are cancer clusters? Environmental reasons?• Transportation, National Security, …

– However, (d/dt) (Spatial Data Volume) >> (d/dt) (Number of Human Analysts)

• Need automated methods to mine patterns from spatial data• Need tools to amplify human capabilities to analyze spatial data• Need tools to amplify human capabilities to analyze spatial data

Spatial Data Mining: Example Projects

Nest locations Distance to open waterLocation prediction: nesting sites Spatial outliers: sensor (#9) on I-35

Vegetation durability Water depth

Co location Patterns Tele connectionsCo-location Patterns Tele connections

(Ack: In collaboration w/V. Kumar, M. Steinbach, P. Zhang)

HotSpots

What is it?Unusally high spatial concentration of a phenomena

Cancer clusters, crime hotspots, p

Traditional Approach:Spatial statistics based ellipsoidsp p

Our Recent Focus:Computational Structure p

Spatial Join-index reduces computational costsTransportation network based hotspots

Next: Spatio-temporalEx. Emerging hot-spots

Colocation, Co-occurrence, Interaction

What is it?Subset of event types, whose instances occur togetherEx. Symbiosis, (bar, misdemeanors), …. Sy b os s, (ba , sde ea o s), …

Traditional Approach:Neighbor-unaware Transaction based approachesg pp

Our Approach:Aggregate Functions on Neighbor relationshipsgg g g pBalance statistical rigor and computational cost

Next: Spatio-temporal interactionsp pItem-types that sell well before or after a hurricaneObject-types that move together Tele-connections

Spatial/Spatio-temporal Outliers, Anamolies

What is it?Location different from their neighbors

Discontinuities, flow anomaliesDiscontinuities, flow anomaliesRelated Work

Transient spatial outliersAnomalous trajectoriesjComputational Structure: Spatial Join

Very scalable using spatial DBMSNext

(Dominant) Persistent anomaliesMultiple object types, Scale

Space/Time Prediction

What is it?Models to predict location, time, path, …

Nest sites, minerals, earthquakes, tornadoes, …Related Work

Interpolation, e.g. KriggingHeterogeneity, e.g. geo. weighted regressionAuto correlation e g spatial auto regression βW ++Auto-correlation, e.g. spatial auto-regression

Challenge: Independence assumption Models, e.g. Decision trees, linear regression, …Measures, e.g. total square error, precision, recall

εxβWyy ++= ρ

, g q , p ,Next

Spatio-temporal vector fields (e.g. flows, motion), physicsScalable algorithms for parameter estimation

SSEnnL −−−−=)ln()2ln(ln)ln(

2σπρWIDistance based errors SSEL =

22ln)ln( ρWI