Aug. 15, 2013 Slide 1

Discovering Persistent Change Windows (PCW) in Spatiotemporal Climate Datasets

3rd Annual Workshop of NSF Expeditions in Computing:

Understanding Climate Change: A Data Driven Approach.

Evanston, IL, August 15th-16th, 2013

Sponsor: NSF CISE/EIA

Shashi Shekhar

Peter K. Snyder

Joseph F. Knight

Stefan Liess Students:

Xun Zhou

Zhe Jiang

Aug. 15, 2013 Slide 2

Change Windows

• Time-Window of Change, e.g., interesting interval in a time series

• Space-window of Change (e.g., Region or Sub-path ):

• Spatio-Temporal Window of Change:

Desertification Deforestation Urban sprawl

2001 2006 2012

Irrigation in Saudi Arabia (Google Time Lapse[5])

Aug. 15, 2013 Slide 4

Spatiotemporal (ST) footprint of changes

• “Where” and “when” a change occurs?

• A taxonomy of ST change footprint:

Temporal

footprint

Interval in time series

Point in time series

Between Few snapshots

Single Snapshots

Spatial

footprint

Local

Focal

Zonal

Point

Lines

Polygon

Raster Vector

4

Aug. 15, 2013 Slide 5

Spatiotemporal change footprint (raster)

Temporal

Snapshot Few

Snapshots

Time series

(point)

Time series

(interval)

Time series

collections

Spat

ial

Loca

l

Remote

sensing

change

detection

Change Point

Detection (e.g.,

CUSUM)

Time series

change interval

(published)

Foca

l

Edge Detection

(Wombling)

Zonal

Sub-path of

change

(published)

Persistent Change Window (in progress)

5

Aug. 15, 2013 Slide 6

Spatial Sub-path of Change

• Spatial footprint of Change

• Ex. Sahel – sharp change in vegetation cover

• Transition between ecological zones (ecotones)

• Vulnerable to climate change

11.3 16.8 22.2 27.6 33.0NA

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Latitude

ND

VI

Va

lue

The change is

persistent and rapid

W1=[12N, 17N]

A snapshot of vegetation cover in Africa [6]

Aug. 15, 2013 Slide 7

Temporal Sub-path of Change

• Time footprint of Change

৹ Abrupt shift in precipitation, temperature, etc.

৹ Climate change detection.

Raw Sahel precipitation anomaly (JJASO)[7] Smoothed Sahel precipitation anomaly (JJASO)

Aug. 15, 2013 Slide 8

Computer Sc. Problem: Interesting Sub-path Query (ISQ)

• Input

• A statistical interest measure & thresholds.

• A path and its attribute

• Output

• All dominant interesting sub-path

• Constraints

• Correctness & completeness

• Automation & scalability to large datasets

• Algebraic Interest Measure,e.g., average slope

Average change (slope) ≥ 3.5

[1,2], [5,11]

Aug. 15, 2013 Slide 9

Related Work, Its Limitations, Novelty of Our Approach

Interesting sub-region query

Change-points sub-paths e.g., ISQ (Our Work) e.g., CUSUM[8]

sub-regions (PCW) (Our new Work)

[1,2], [5,11] [6]

Aug. 15, 2013 Slide 10

Naive Approach does not scale!

Naive approach

Phase 1: Evaluate interest measure for all O(N2) sub-intervals

Phase 2: Identify dominant sub-paths (compare sub-path pairs)

Complexity: O(n4) for a path,

where n = number of locations on the path

Example: Find intervals of high gradient along all longitudes

using 0.07 degree resolution dataset

=> 103 locations per path, 102 longitudes,

=>1014 computations

Window footprint

1-D (path)

2-D (spatial) 3-D (spatiotemporal)

# locations 103 106 109

# windows 108 1012 1018

computation 1014 1024 1036

Search spaces O(n2) O(n4) O(n6)

Aug. 15, 2013 Slide 11

Computational Structure of ISQ

• Not Dynamic Programming!

• GRID-DAG (Directed Acyclic Graph)

• Node = sub-paths

• Edge = Dominance relationship

• Interest Measure (node) = f ( leftmost & rightmost leafs )

• Q? Which traversal order avoids unnecessary work?

En

d l

oca

tion

1

2

3

4

5

6

7

8

9

10

11

12

1 2 3 4 5 6 7 8 9 10 11 12 Start location

Dominated by

Valid interval

Dominant

Dominated

5-11

1-2

1-12

Aug. 15, 2013 Slide 13

Backup slides start here A Comparison of Techniques for Traversing G-DAG

DFS or BFS

Bottom-Up with in-Row Pruning (BURP)

BFS with Sub-Graph Pruning (BSGP)

Row-Traversal with Column Pruning (RTCP)

A: Avoid Redundant leaf visits No Yes Yes Yes

B: Avoid Unnecessary visits to dominated non-leafs

No No Yes Yes

C: Memory need for B (n = number of locations in path)

O(n2) O(n) O(n2) O(1)

5-11

1-2

1-12

Insights: • Interest measure is a algebraic function => leaf scan • Dominance = partial order among sub-paths => pruning • The partial order is a Grid-DAG => O(1) memory traversal & pruning via row-wise scan (of non-leaf)

Aug. 15, 2013 Slide 18

• Theoretical Evaluation:

• RTCP is Correct and Complete

• Correct: All the reported sub-paths are qualifying dominant sub-paths

• Complete: All the dominant interesting sub-paths are reported

• Experimental Evaluation

• RTCP is faster than competitions

• RTCP needs less memory than competition

Theoretical and Experimental Evaluations

Aug. 15, 2013 Slide 19

Effect of Dataset Size on Memory Needs

• Setup: Pattern length ratio (PLR) is fixed at 0.1

Dataset – synthetic (left), real (right)

• Trends: RTCP has smaller memory cost than competitions

• Memory cost are not sensitive to pattern length ratio

Aug. 15, 2013 Slide 20

Effect of Data Size on Computational Cost

• Setup:

• Data: GFDL-CM2.0 coupled model realization (1861-2000, entire world)

• Global weighted average of max daily temperature

• Data length: 51100 :: Pattern Length Ration (PLR) = either 0.1 or 1

• Note difference in scale across 2 plots

• Trends: RTCP is faster than competitions

RTC

P

PLR = 0.1 PLR = 1

Aug. 15, 2013 Slide 21

• Pattern Length Ratio =

• Ratio of length of longest interesting sub-path and the length of the entire path,

• between 0 and 1.

• Synthetic data: generated with Gaussian distributed unit values.

• Trend: RTCP is faster than competitions with any pattern length

Effect of Pattern Length

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1

2

3

4

Pattern Length Ratio (PLR)

Ru

n t

ime

(seco

nd

s)

BSGP

BURP

RTCP

Data length: fixed at 20k units

RTCP

Aug. 15, 2013 Slide 22

Case Study

AVG{∆}

AVG≥α{∆}

• Data: NDVI by GIMMS [4], Africa, 1981 August.

• Resolution: 8km. Smoothed within 1x1 degree.

• Path: along each longitude (south north)

• Interest measure: (Slope) Sameness degree

• ∆ : unit slope

• Thresholds: α= 20% percentile, SD ≥0.5 CUSUM

ISQ

Aug. 15, 2013 Slide 23

Case Study: Global Data and Ecotones

• NDVI of the entire world

• Aug 1-15 1981, 0.07 degree (8km) resolution

• a = 10%, SD ≥ 0.5

Sahel

region

Boundary

of

Amazon

Rocky

Mountain Himalaya

Mountain

Gobi Deserts

23

Aug. 15, 2013 Slide 26

Contributions : Summary

• Formalize Interesting Sub-path Query (ISQ) problem

• Computational structure of efficient 1D interval enumeration

• Grid-DAG traversal strategy

• Bottom-up with in-row pruning (BURP) 1, BFS with sub-graph pruning (BSGP)2

• Row-wise with column-pruning (RTCP)3

• Evaluation : Experiments, Case Studies

• Next Steps

• GPU platform

• Efficient 3D region enumeration

• submitted to ACMGIS 2013.

• Visit poster session for details

1 From our early work: J. Kang, et al, Discovering Flow Anomalies: A SWEET Approach. In IEEE conference on Data Mining

(ICDM 2008). 2 Published in ACM SIGSPATIAL GIS 2011. 3 Manuscript to be submitted to IEEE Transaction on Knowledge and Data Engineering (TKDE).

1-D (path)

2-D (spatial) 3-D (spatio-temporal)

# locations 103 106 109

# windows 108 1012 1018

computation 1014 1024 1036

Search spaces O(n2) O(n4) O(n6)

Aug. 15, 2013 Slide 27

Accelerating ISQ with GPUs – Preliminary Results

• Motivation: Google Time-lapse like visualization of spatio-temporal change windows

• Example: GIMMS NDVI

• 611 snapshots (26 years every 16 days)

• Africa, 8km resolution: 1152 pixels x 1152 pixels

• Initial results with BURP (Bottom-up with in-row pruning)

• Setup: Platform: CUDA, 1 thread per longitude

• Trend: 10x speedup with 1 GPU

• CPU time (matlab): 240 seconds / video

• GPU/CUDA: 19 seconds / video

• Next steps: • More algorithms (e.g., RTCP), Platforms (e.g., multi-GPU), Datasets

* Collaborated with Dr. S. Prasad et al. in Georgia State Univ. Results submitted to CyberGIS AHM’13

Aug. 15, 2013 Slide 28

Case Study

CUSUM (pre-selected area) vs. Proposed approach (a=20% quantile, SD = 0.5)

Aug. 15, 2013 Slide 32

Persistent Change Window (PCW) Discovery: Problem

• Given：

• A spatial time series dataset

• An average change rate threshold

• A spatial aggregate function (e.g., sum, average)

• Find:

• All the dominant persistent change windows {Si, Ti}

• Constraints

• Correctness & completeness • Automation & scalability to large datasets

Highlighted (3x3) over Time [1,4]: Sum(T1) = 90, Sum(T4) = 53

Average decrease rate = [(90-53)/90]/3= 17.3%

T = 1 T = 2 T = 3 T = 4

Aug. 15, 2013 Slide 33

Persistent Change Window (PCW) Discovery: Challenges

• A six-dimensional enumeration space

• An interval along each dimension

(0, 0, 0)

(0, 1, 0)

(2, 2, 2)

(0, 2, 0) [0,2],[0, 2],[0, 2]

[0,1],

[0,2],

[0,2]

[0,2]

[0,1]

[0,2]

[0,2]

[0,2]

[0,1]

[1,2],

[0,2],

[0,2]

[0,2]

[1,2]

[0,2]

[0,2]

[0,2]

[1,2] (1, 0, 0) (2, 0, 0)

[0,1],

[0,1],

[0,2]

[0,1]

[0,2]

[0,1]

[0,0]

[0,2]

[0,2]

[0,1],

[1,2],

[0,2]

[0,1]

[0,2]

[1,2]

[0,2]

[0,1]

[0,1]

[1,2]

[0,1]

[0,2]

[0,2]

[0,1]

[1,2]

[0,2]

[1,2]

[0,1]

[0,2]

[1,2]

[0,1]

[0,2]

[0,0]

[0,2]

[0,2]

[0,1]

[0,1]

[0,2]

[0,2]

[0,0]

[1,2]

[0,2]

[0,1]

[1,2]

[1,2]

[0,2]

[1,2]

[0,2]

[1,2]

[1,1]

[0,2]

[0,2] …

Aug. 15, 2013 Slide 35

2000 2002 2004 2006 2008 2010 2012

0.2

0.25

0.3

0.35

0.4

Year

ND

VI

An annual increase of

11.5%, 2001-2012

Persistent Change Window Discovery: Case Study

• Initial Results • Initial algorithms

• Case Study: MODIS 250m NDVI data (16 days)

• Time:2000-2012. Annual: July 27/28 of each year.

50 100 150 200 250 300 350 400

20

40

60

80

100

120

140

160

180

200 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

50 100 150 200 250 300 350 400

20

40

60

80

100

120

140

160

180

200 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

50 100 150 200 250 300 350 400

20

40

60

80

100

120

140

160

180

200 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Study area

2001 2006 2012

Average NDVI in outlined window

Irrigation in Saudi Arabia, shown by

Google Time lapse [5]

Results of the

proposed algorithm

with average change

rate >= 10%

(outlined window)

Aug. 15, 2013 Slide 38

List of Publications and References

Contributors’ Publications:

[1] Xun Zhou, Shashi Shekhar, Pradeep Mohan, Stefan Liess, Peter K. Snyder: Discovering interesting sub-paths in spatiotemporal datasets: a summary of results. GIS 2011: 44-53

(A full journal version to be submitted to IEEE Transection on Knowledge and Data Engineering)

[2] Xun Zhou, Shashi Shekhar, Pradeep Mohan. Spatiotemporal (ST) Change Pattern Mining: A Multi disciplinary Perspective. In Book: Mei-Po Kwan, Douglas Richardson, Donggen Wang and Chenghu Zhou (eds) (2013) Space-Time Integration in Geography and GIScience: Research Frontiers in the US and China. Dordrecht: Springer (in Press)

[3] Xun Zhou, Shashi Shekhar, Reem Y. Ali. Spatiotemporal (ST) Change Pattern Mining: A Multi-disciplinary Perspective. Submitted to the Wiley’s Interdisciplinary Review on Data Mining and Knowledge Discovery (DMKD).

[4] Xun Zhou, Shashi Shekhar, Dev Oliver. Discovering Spatiotemporal (ST) Persistent Change Windows: A Summary of Results. Submitted to ACM SIG SPATIAL GIS 2013.

References:

[5] Google Earth Engine (Accessed: June 22, 2013).

[6] Tucker, C. J., J. E. Pinzon, M. E. Brown. Global inventory modeling and mapping studies. Global Land Cover Facility, University of Maryland, College Park, Maryland, 1981--2006.

[7]. Joint Institute for the Study of the atmosphere and Ocean(JISAO). Sahel rainfall index. http://jisao.washington.edu/data/sahel/.

[8] E. Page. Continuous inspection schemes. Biometrika, 41(1/2):100--115, 1954.

Aug. 15, 2013 Slide 39

Google Time lapse

• Google Time lapse main page

• Irrigation in Saudi Arabia

• Amazon Deforestation