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On-the-fly Visualization of Scientific On-the-fly Visualization of Scientific Geospatial Data Using WaveletsGeospatial Data Using Wavelets
GeoDGeoDAA
Cyrus Shahabi, Farnoush Banaei-Kashani, Kai Song
Outline
• Motivation and Problem Definition
• Our Solution: GeoDA – Underlying Technology
• Background: Discrete Wavelet Transform• WOLAP
– Prototype System Development
• Summary
• Future Work
USC-JPL SURP Project
Cyrus Shahabi and Farnoush Banaei-KashaniInformation Laboratory (InfoLab)
University of Southern California (USC)Los Angeles, CA 90089
[shahabi,banaeika]@usc.eduhttp://infolab.usc.edu
Yi Chao and Peggy LiClimate, Oceans, and Solid Earth Science Section
Jet Propulsion Laboratory (JPL)Pasadena, CA 91109
[yi.chao,peggy.li]@jpl.nasa.govhttp://science.jpl.nasa.gov/COSE/
Earth Science Data Visualization
Range Selection
Without Re-scaling
With Re-scaling
Aggregated query over latitude, longitude and/or time
Range SelectionRange Selection
Range Re-scaling Range Re-scaling
Earth Science Data Visualization
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
Outline
• Motivation and Problem Definition
• Our Solution: GeoDA – Underlying Technology
• Background: Discrete Wavelet Transform• WOLAP
– Prototype System Development
• Summary
• Future Work
80 70 60 90 37 67 50 50 a
75 75 52 50 5 -15 -15 0
75 51 0 1
63 12
63 12 5 -15 -15 0 0 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}.
{1/2, -1/2}{1/2, 1/2}
=DWT(a)â
75 75 60 90 36 66 50 50 a′
=Waâ
63 63 63 63 63 63 63 63 75 75 51 51 51 51 75 75 75 75 52 52 50 50 75 75 80 70 37 67 50 50 60 90
Multi-resolution view:Compression!
63 12 -15 -15
Discrete Wavelet Transform
Wavelets in Databases
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
Our work (WOLAP)2:
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
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
80 70 60 90 37 67 50 50 178.1933.94 7.07 -21.21-21.21 0 0 2
WOLAP Example
80 70 60 90 37 67 50 50 178.1933.94 7.07 -21.21-21.21 0 0 2
Original Wavelet*
1 1 1 1 1 1 1 1 2.83 0 0 0 0 0 0 0
Result=504
0 0 1 1 1 1 1 0
Result=304
80 70 60 90 37 67 50 50
Result=178.19*2.83=504
1.73 -.35 -1 .5 0 0 0 .71
Result=178.19*1.73+33.94*(-.35)+2*.5
178.1933.94 7.07 -21.21-21.21 0 0 2
=304
* Here we assume the actual Haar filter: {1/2, 1/2} and {1/2, -1/2}
a â
O(N) O(log N)<<
(Parseval Theorem)
(Parseval Theorem)~303 (99% accuracy!)
0 1.4 1.4 1.4 1.4 1.4 1.4 0.7
1.0 2.0 2.0 1.5
2.1 2.5
3.3 -.3
0 0 0 0 0 0 0 0.7
-1 0 0 0.5
-.7 0.4
WOLAP Query Complexity: O(log n)
0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0
3.3 -.3 -.7 0.4 -1 0 0 0.5 0 0 0 0 0 0 0 0.7
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.
Related Work
Abbadi-ICDE'99
Agrawal-SIGMOD'97
Abbadi-Dawak'00
d=number of dimensionsN=domain size for each dimension
Outline
• Motivation and Problem Definition
• Our Solution: GeoDA – Underlying Technology
• Background: Discrete Wavelet Transform• WOLAP
– Prototype System Development
• Summary
• Future Work
GeoDA Architecture
NC Files
Google Map Mashup
Wavelet Datacubes
Text Files
WOLAP Query Engine (ProDA) Plotting Tools
Presentation Tier
Query Tier
Data Tier
Helena Data
Helene Dataset 10+ dimensions (selected longitude and latitude) 100+ Variables (selected SST) 1km by 1km resolution, daily samples, world-wide 36000 18000 data points per sample (~1/3 of which are null)
Helene Datacube Dimensions: Latitude, Longitude Variable: SST
Presentation Tier
Implementation Cross-language development – JavaScript, C#, ASP.NET AJAX Multi-thread programming
Progressive Visualization
GeoDA
Outline
• Motivation and Problem Definition
• Our Solution: GeoDA – Underlying Technology
• Background: Discrete Wavelet Transform• WOLAP
– Prototype System Development
• Summary
• Future Work
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.
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.
Q & A