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On-the-fly Visualization of Scientific Geospatial Data Using Wavelets GeoDA Cyrus Shahabi, Farnoush Banaei-Kashani, Kai Song

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

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USC-JPL SURP Project Cyrus Shahabi and Farnoush Banaei-Kashani Information Laboratory (InfoLab) University of Southern California (USC) Los Angeles, CA Yi Chao and Peggy Li Climate, Oceans, and Solid Earth Science Section Jet Propulsion Laboratory (JPL) Pasadena, CA

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Earth Science Data Visualization Range Selection Without Re-scaling With Re-scaling

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

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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

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

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a 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 a =Wa â Multi-resolution view:Compression! Discrete Wavelet Transform

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Wavelets in Databases Others work 1 : 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-PODS02, Schmidt-EDBT02, Jahangiri-SIGMOD05

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WOLAP Example Original Wavelet* Result= Result= Result=178.19*2.83= Result= * *(-.35)+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) ~303 (99% accuracy!)

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WOLAP Query Complexity: O(log n) 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.

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Related Work Abbadi-ICDE'99 Agrawal-SIGMOD'97 Abbadi-Dawak'00 d=number of dimensions N=domain size for each dimension

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

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

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

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Presentation Tier Implementation Cross-language development – JavaScript, C#, ASP.NET AJAX Multi-thread programming Progressive Visualization GeoDA

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

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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.

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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.

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Q & A

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