1 17 Christian Böhm, Bernhard Braunmüller, Florian Krebs, and Hans-Peter Kriegel, University of Munich Epsilon Grid Order: An Algorithm for the Similarity Join on Massive High- Dimensional Data
Feb 25, 2016
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Christian Böhm, Bernhard Braunmüller, Florian Krebs, and Hans-Peter Kriegel,University of Munich
Epsilon Grid Order: An Algorithm for the Similarity Join on Massive High-Dimensional Data
217 Feature Based Similarity
317 Simple Similarity Queries
Specify query object and• Find similar objects – range query• Find the k most similar objects – nearest neighbor q.
417 Join Applications: Catalogue Matching
Catalogue matching• E.g. Astronomic catalogues
R
S
517 Join Applications: Clustering
Clustering (e.g. DBSCAN)
Similarity self-join
617 Grid partitioning
General idea: Grid approximation where grid line distance =
Similar idea in the -kdB-tree[Shim, Srikant, Agrawal: High-dimensional Similarity Joins, ICDE 1997]
Disadvantage of any grid approach:Number of neighboring grid cells: 3d 1
717 Scalability of the -kdB-tree
Assumption: 2 adjacent -stripes fit in main mem. Unrealistic for large data sets which are ...
• clustered, • skewed and • high-dimensional data
817 Epsilon Grid Order
917 -Grid-Order Is a Total Strict Order
Strict Order:• Irreflexivity• Transitivity• Asymmetry
-grid-order can be used in any sorting algorithm
1017 -Interval
Coarse approximation of join mates:Used for I/O processing
1117 I/O Processing for the Self Join
Decompose the sorted file into I/O units
1217 Epsilon Grid Order
1317 CPU Processing
I/O units are further decomposed before joining Simple divide-and-conquer: No further sorting Decomposition: maximize active dimensions
1417 CPU Processing
Point distance computations: Order of dimensions• Neighboring inactive dimensions• Unspecified dimensions• Active dimension • Aligned inactive dimensions
1517 Experimental Results
8-dimensional uniformly distributed vectors
1617 Experimental Results (2)
16-d feature vectors from CAD application
1717 Conclusions
Summary• High potential for performance gains of the similarity
join by page capacity optimization• Necessary to separately optimize I/O and CPU
Future research potential• Similarity join for metric index structures• Approximate similarity join• Parallel similarity join algorithms