1. G10 Anuj Karpatne Vijay Borra
Finding Sequential Patterns with Time Lags in Spatio-temporal Earth Science Datasets
G10
Anuj Karpatne
Vijay Borra

2. Outline Motivation Example of Dataset Problem Statement
First principle example
Challenges
Novelty
Proposed Approach
Validation outline and future work

3. Motivation
Deforestation in Indonesian peat lands for palm-oil plantation 2) 1)
Increase in average winter temperature in higher latitudes due to global warming
Degradation of soil due to poor soil moisture
Increase in Pine Beetle Infestation
Increased susceptibility of Forest Fires
Forest Fires
Sources: NASA Earth Observatory, Environment Protection Agency, National Oceanic and Atmospheric Administration, National Resources Canada

4. An example Dataset Neighborhood Relationship Time Lag Time Lag
Active Fire
Time Lag
Neighborhood Relationship
Time Lag
Active Fire

5. Problem Definition Problem Statement: Input: Output: Objective:
Finding sequential patterns in spatio-temporal real-valued events using multiple variables
with time lags
Input:
Spatio-temporal gridded data with multiple variables
Event Detection schemes for each variable with parameters and threshold
Prevalence Threshold measures for a sequential pattern
Spatial Neighborhood relationship
Statistical Parameters of Time Lag Distribution
Output:
Patterns of the form where T denotes the time lag distribution of the event relationship
(a vector of time lag values for which the relationship is prevalent)
Examples:
Constraints:
Events are point processes occurring with time lags and not interval-based
Chains of events being detected with ‘total orderedness’ assumption
Homogenous data variables spanning the same range of time
Event detection algorithms are robust in handling noise and seasonality of time series
Algorithm is correct and complete
Objective:
Minimize computational time

6. First-Principle ExampleeA
Time of Occurrence A1 3 A2 4 A3 6 A4 A5 A6 A7 5 A8 A9
A10
A11
A12
A13
A14 2
A15 eB
Time of Occurrence B1 6 B2 2 B3 5 B4 B5 B6 4 B7 B8 B9
B10 eC
Time of Occurrence C1 5 C2 6 C3 3 C4 2 C5 C6 4 C7 C8

7. Challenges Novelty Exponential size of search space
A vector of prevalence thresholds to be considered for pruning at multiple time lag values . . . . . . . . . . . .
Novelty
Spatio-temporal sequential pattern mining
Sequential pattern mining for Boolean events without time Lag
Huang et al.
Mohan et al. (Cascade)
Moving Object Trajectory Mining
Cao et al.
STAR
Sequential pattern mining for Real-valued events with time lag
Our approach

8. Approach: Computing Prevalence Index: PI(t)
For a pattern of size two, : For each possible Time Lag value t, Prevalence Ratio of A at time lag t: Prevalence Ratio of B at time lag t: Prevalence Index of at time lag t: minimum of Prevalence ratios of A and B at time lag t For patterns of size greater than two, : Find as the set of events in which participate in minimum of and

9. Running Example
eAB
Time Lag
A1B1 3
A1B3 2
A1B7
A2B1
A2B3 1
A2B7
A3B1
A4B1
A4B3
A4B4
A4B6
A4B10
A6B3
A6B10
A7B10
A8B1
A9B1
A9B3
A9B6
A10B1
A11B3
A12B6
A13B6
A14B6
A14B4
A15B4
A15B10
eAB(0)
eAB(1)
eAB(2)
eAB(3)
A3B1
A2B3
A1B3
A1B1
A10B1
A2B7
A1B7
A4B1
A15B4
A4B6
A2B1
A4B10
A7B10
A4B3
A6B10
A9B6
A4B4
A9B1
A11B3
A6B3
A14B4
A12B6
A8B1
A13B6
A9B3
A14B6
PI(0) = 0.2
PI(1) = 0.5
PI(2) = 0.47
PI(3) = 0.3
Let eAB be the set of pairs of events in(A,B) satisfying
Spatial neighborhood condition:
events in eAB fall in spatial neighborhood
Positive time lag condition:
event in B occurs after event in A in eAB eA
Time of Occurrence A1 3 A2 4 A3 6 A4 A5 A6 A7 5 A8 A9
A10
A11
A12
A13
A14 2
A15 eB
Time of Occurrence B1 6 B2 2 B3 5 B4 B5 B6 4 B7 B8 B9
B10 eC
Time of Occurrence C1 5 C2 6 C3 3 C4 2 C5 C6 4 C7 C8
Output additional statistical properties of event pair occurrences at the prevalent Time Lags

10. Pruning Strategy Lattice Growing Region
If Prevalent Time Lag is empty, remove the candidate pattern from the list of frequent patterns
Else, prune the prevalent time lags using statistical properties of the event occurrence distributions over the prevalent time lags
Accept middle quantile of
prevalent time Lag distribution as pruned time lags

11. Proposed Approach
For size of patterns from 1 to n (number of variables)
Generate candidate patterns of size (k+1) from frequent patterns of size (k)
Compute Prevalence Index: PI(t) for each candidate pattern at each time lag
Generate pattern instance distributions for time lags which have PI(t) > threshold
If set of prevalent time lags is empty
Discard the candidate pattern
Else
Prune the prevalent time lags using middle quantile of distribution and add the candidate pattern with the pruned time lags into set of frequent patterns of size (k+1)
end

12. Properties of PI and the proposed approach
Prevalence Index is anti-monotonic
Prevalence Ratio is anti-monotonic:
An event instance participates in a sequence only if it participates in all the subsequences of the pattern
The approach is complete
Prevalence Index is anti-monotonic for each time lag
Apriori-based Candidate Generation Technique is complete
Enumeration of event pairs for each spatial join is complete
The approach is correct
is correct only if:
Events in A and B occur in a spatial neighborhood
Events in B follow events in A with a time lag distribution T
Pruning approach is correct

13. Insight into Real-world datasets Future Work
Region of Interest – Peatland forests in Indonesia (tile h29v08 and tile h29v09)
Types of datasets to be used and their respective event detection algorithms:
Vegetation Index (EVI)
Deforestation: V2delta, Gradual Decrease, Segmentation
Forest Fire: KD6 + ID6
Land Surface Temperature
Increase in annual land surface temperature because of fire
Thermal Anomaly Index
Precipitation
Soil Moisture
Aerosol Information
EVI for Forest Fire
EVI for Deforestation
Land Surface Temperature (Day)
Thermal Anomaly Index