1. On-the-fly Visualization of Scientific Geospatial Data Using Wavelets
GeoDA
On-the-fly Visualization of Scientific Geospatial Data Using Wavelets
Cyrus Shahabi, Farnoush Banaei-Kashani, Kai Song
Introduce: self (postdoc, USC), paper (title and GeoDA), coauthors
On behalf of Kai, Bear with me

2. Outline Motivation and Problem Definition Our Solution: GeoDA Summary
Underlying Technology
Background: Discrete Wavelet Transform
WOLAP
Prototype System Development
Summary
Future Work

3. USC-JPL SURP Project Cyrus Shahabi and Farnoush Banaei-Kashani
USC-JPL collaboration under a SURP project
Earth Science Data Visualization
Cyrus Shahabi and Farnoush Banaei-Kashani
Information Laboratory (InfoLab)
University of Southern California (USC)
Los Angeles, CA 90089
Yi Chao and Peggy Li
Climate, Oceans, and Solid Earth Science Section
Jet Propulsion Laboratory (JPL)
Pasadena, CA 91109

4. Earth Science Data Visualization
Without Re-scaling
Example: SST as data (dimensions and measure attribute), and average as the query
Generalize
Color-coded map: based on resolution each pixel is a aggregate query covering data of the corresponding area
Interactive: Range selection
Range Selection
With Re-scaling

5. Earth Science Data Visualization
Range Selection
Range Re-scaling
Aggregated query over latitude, longitude and/or time

6. Off-line vs. On-the-fly Visualization
Off-line Visualization
Pre-selected range (and resolution)
Visualization by query pre-computation
On-the-fly Visualization
On-the-fly range (and resolution) selection
Visualization by on-the-fly query computation to support dynamic data

7. Outline Motivation and Problem Definition Our Solution: GeoDA Summary
Underlying Technology
Background: Discrete Wavelet Transform
WOLAP
Prototype System Development
Summary
Future Work
Give overview of solution that enables on-the-fly visualization here

8. Discrete Wavelet Transform80 70 60 90 37 67 50 50 a
{1/2, 1/2}
{1/2, -1/2} 75 63 12
-15 75 52 50 5
-15
-15 75 51 1
=DWT(a) â
=Wa â 63 12
A transform where the generated data has interesting properites
Describe wavelet by example
Assume one dimensional dataset
How to generate?
What are properties?
Coefficients are representatives and they are ordered based on their energy
Compression as well
Multi-resolution view:
Compression! 75 60 90 36 66 50 a′ 80 70 37 67 50 60 90 75 51 63 75 52 50 63 12 5
-15 1 â
* For simplification, assume {1/2, 1/2} and {1/2, -1/2} as filters instead of the Haar filters {1/2, 1/2} and {1/2, -1/2}.

9. Wavelets in Databases Our work (WOLAP)2: Others’ work1:
Query Compression
Reason: fast response time
Define range-sum query as dot product of query vector and data vector
At the query time, we have the knowledge of what is important to the pending query
More opportunities:
Progressive results
Data-independent approximation
Others’ work1:
Data Compression
Reason: save space?
Implicit reason: queries deal with smaller datasets and hence faster
Problems:
Only approximate results!
Very data-dependant
Different error rates for different queries
1 See Vitter-CIKM'98, Vitter-SIGMOD'99,
Agrawal-CIKM'00, Garofalakis-VLDB'00
2 See Schmidt-PODS‘02, Schmidt-EDBT‘02,
Jahangiri-SIGMOD’05

10. WOLAP Example Original Wavelet* Result=504 Result=178.19*2.83=50480 70 60 90 37 67 50 80 70 60 90 37 67 50 80 70 60 90 37 67 50 â
178.19
33.94
7.07
-21.21 2
178.19
33.94
7.07
-21.21 2
178.19
33.94
7.07
-21.21 2 1
2.83
Result=504
Result=178.19*2.83=504
(Parseval Theorem) 1
1.73
-.35 -1 .5
.71
Result=304
Result=178.19* *(-.35)+2*.5
=304
(Parseval Theorem)
~303 (99% accuracy!)
O(N)
<<
O(log N)
* Here we assume the actual Haar filter: {1/2, 1/2} and {1/2, -1/2}

11. WOLAP Query Complexity: O(log n)1
1.4
1.4
1.4
1.4
1.4
1.4
0.7
0.7
1.0
2.0
2.0
1.5 -1
0.5
2.1
2.5
-.7
0.4
3.3
-.3
3.3
-.3
-.7
0.4 -1
0.5
0.7
So summarize WOLAP
Assuming that the query is of size N:
Theorem 1: Using “lazy wavelet transform” (computing only on the boundaries of the selected range), one can transform any polynomial range-aggregate query in O(log N) to wavelet domain.
Theorem 2: The query has O(log N) non-zero values in wavelet domain.

12. Related Work Agrawal-SIGMOD'97 Abbadi-ICDE'99 Abbadi-Dawak'00
Literature
Support not only for queries but for update
And more: progressiveness, e.g.
N=domain size for each dimension
d=number of dimensions

13. Outline Motivation and Problem Definition Our Solution: GeoDA Summary
Underlying Technology
Background: Discrete Wavelet Transform
WOLAP
Prototype System Development
Summary
Future Work

14. WOLAP Query Engine (ProDA)
GeoDA Architecture
Google Map Mashup
Presentation Tier
WOLAP Query Engine (ProDA)
Plotting Tools
Query Tier
Wavelet Datacubes
Data Tier
Text Files
NC Files

15. Helena Data Helene Dataset Helene Datacube 10+ dimensions (selected
longitude and latitude)
100+ Variables (selected
SST)
1km by 1km resolution,
daily samples, world-wide
36000  data points
per sample (~1/3 of which
are null)
Helene Datacube
Dimensions: Latitude, Longitude
Variable: SST

16. Presentation Tier Implementation Progressive Visualization
Cross-language development – JavaScript, C#, ASP.NET
AJAX
Multi-thread programming
Progressive Visualization
Demo:
Interface
Flexible ranges
Rescaling
GeoDA

17. Outline Motivation and Problem Definition Our Solution: GeoDA Summary
Underlying Technology
Background: Discrete Wavelet Transform
WOLAP
Prototype System Development
Summary
Future Work

18. Summary
We devised a framework for on-the-fly visualization of large-scale scientific datasets.
We designed and exploited a fast range-aggregate query processing technique, WOLAP, that enables on-the-fly visualization. WOLAP supports the family of polynomial range-aggregate queries.
We developed a prototype system, GeoDA, as a proof-of-concept based on the designed visualization framework and query processing technique.

19. Future Work
Supporting dynamic datasets by extending WOLAP to handle append of the data stream in wavelet domain.
Enhancing WOLAP via caching, to enable group/batch aggregate queries.

20. Q & A