Christian B

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Christian BöhmUniversity for Health Informatics
and Technology, InnsbruckSimilarity Search and
Data Mining Database Techniques Supporting Next
Decade's ApplicationsKeynote at iiWAS 2002
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Similarity Search
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Feature Based Similarity
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Simple Similarity Queries

• Specify query object and
• Find similar objects range query
• Find the k most similar objects nearest
  neighbor q.

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Multidimensional Index Structure (R-tree)
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Range Query with Depth-First Traversal
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Nearest Neighbor Priority Algorithm
Hjaltason, Samet Ranking in Spatial Databases,
SSD 1995
4 page accesses
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Problems of High-Dim. Index Structures

• Curse of dimensionality
• Search performance of index deteriorates in high
  dim.
• Outperformed by sequential scan
• Solution
• Optimize various parameters of index structures
• Needed Cost model for queriesHow many pages are
  expected to be accessed for
• Range queries (with given e)
• Nearest neighbor queries (with given k)

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Cost Estimation (Uniformity/Independence)

• Minkowski sumEstimation of the access
  probability of a pageBöhm A Cost Model for
  Query Processing in High-Dimensional Data Spaces,
  TODS 25(2), 2000

Nearest neighbor Estimate distance by point
density
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Cost Estimation

• Boundary and saturation effects in high dim.
  space(considered by our model extension)
• Correlation between attributes(considered by the
  concept of fractal dimension)
• Cluster structure has also impact on performance
• Currently neglected by our model
• Histograms and similar data descriptions
  difficult in high-dimensional space (number of
  histo-bins exponential in dimensionality)
• Other descriptions of cluster structure
  (dendrograms)
• Subject to future work

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Optimization of Index Structures

• To avoid the possibility to outperform index
  based query processing by the sequential scan
• Optimize various parameters such as
• Logical block size of the index pages
• Indexed dimension
• I/O schedule optimization (fast index scan)
• Data quantization
• Observe the balance! (Master Confucius)

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Page Size Optimization
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Page Size Optimization
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Optimized Dimension Assignment
Hi-dim. Index
Inverted List
Matching
R-tree
B-tree
Problem in hi-dim Too few splits ineach
dimension
Problem in hi-dim Too many resultsin each
dimension
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Optimized Dimension Assignment
Hi-dim. Index
Inverted List
Matching
R-tree
B-tree
Compromise A moderate number of R-treeseach
indexing a few dimensions
OPTIMIZE!
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Schedule Optimization (Fast Index Scan)
Range Query Required Pages are known from the
directory
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Schedule Optimization (NN Queries)

• Current expenses are traded for possible later
  savings
• Start at 100 page and extend forward and
  backward
• Optimize the cumulated cost balance (CCB)

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Quantization

• Approximate the points by quantization grid
  based on quantiles
• Benefitfewer bits for representation
• Cost Grid cell partially intersectedÞ access
  the original point data
• How to choose grid resolution ???

Weber, Schek, Blott A Quantitative Analysis and
Performance Study..., VLDB 1998
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Independent Quantization (IQ tree)
Combines index, scan, and quantization Berchtold,
Böhm, Jagadish, Kriegel, Sander Independent
Quantization..., ICDE 2000
Grid resolution optimized by cost model
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Open Research Problems in Optimization

• Multi-Parameter Optimization
• How can parameters be optimized simultaneously?
• Are there conflicts between optimization goals?
• Example

Uniform dataÞ Quantization
Correlated dataÞ Tree Striping
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Open Research Problems in Optimization

• Consider Insert/Delete/Update
• If the data set faces heavy update, the
  constructed index should look differently
  compared with more static data sets
• Update-bound Construct index rather simple
• Query-bound Spend more effort to organize data
• Can be considered as an optimization problem

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Data Mining
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KDD Algorithms Based on Similarity Queries
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Join Applikationen

• Katalogkonversion (Catalogue Matching)
• z.B. Astronomie-Kataloge

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Clustering

• Clustering (e.g. DBSCAN)Ester, Kriegel, Sander,
  Xu A Density Based Algorithm for Discovering
  Clusters, KDD 1996

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Cache Behavior
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Clustering and Similarity Join

• DBSCAN uses similarity join as basic
  operationsBöhm, Braunmüller, Breunig, Kriegel
  High Perf. Clustering based on the Sim. Join,
  CIKM 2000

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k-Nearest Neighbor Classification

• Example

Objects with known class
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Distance Range Join (e-Join)

• Most widespread and best evaluated join
• Often also called the similarity join

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k-Closest Pair Query
SELECT FROM R, SORDER BY R.obj -
S.objSTOP AFTER k

• In SQL notation

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k-Nearest Neighbor Join
SELECT FROM R, SGROUP BY R.objORDER BY
R.obj - S.objSTOP AFTER K ( ¹ k )

• In SQL notation
• (limited to k 1)

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R-tree Spatial Join (RSJ)
procedure r_tree_sim_join (R, S, e) if IsDirpg
(R) Ù IsDirpg (S) then foreach r Î R.children
do foreach s Î S.children do if
mindist (r,s) e then CacheLoad(r)
CacheLoad(s) r_tree_sim_join (r,s,e)
else ( assume R,S both DataPg ) foreach
p Î R.points do foreach q Î S.points do
if p - q e then report (p,q)
R
S
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Modeling and Optimization

• Böhm, Kriegel A Cost Model and Index
  Architecture for the Similarity Join, Wednesday,
  1630
• Mating probability of index pages
• Probability that distance between two pages e
• Two-fold application of Minkowski sum

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Modeling and Optimization

• I/O cost
• High const. cost per page
• Large capacity optimum
• CPU cost
• Low const. cost per page
• Low capacity optimum
• CPU-performance like CPU optimized index
• I/O- performance like I/O optimized index

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Open Problems for Research (Sim. Join)

• Modeling and Optimization
• Dimension
• Quantization
• Page scheduling
• Caching strategies
• Nearest Neighbor Join
• Applications
• Algorithms
• General
• Integration into object-relational DBMS

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New Challenges
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New Challenges

• Incertain Features
• Application
• Biometric Identification
• Particularities
• Features individually associated with incertainty
  (e.g. as Gaussian distributions)
• Queries
• Probability of match
• Find objects with highes probability of match
• Find objects with probability of match gt e

Relative probability
Feature a1
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New Challenges

• Support of e-commerce in all phases
• Marketing ? customer segmentation
• Sales and booking ? advanced similarity search
• Add-on products ? Sales transaction analysis
• Advanced Similarity
• Adaptable
• Multimodal models
• Relevance-feedback
• Convex hull

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New Challenges

• Stock quota Technical chart analysis
• Known Database techniques for similarity search
  in time sequences (DFT, etc.)

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New Challenges

• Professional analyst tools use
• Trading signals generated by indicators (etc.
  MACD)
• Formations indicating trends in charts
• Relationships to the market and to derivatives

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Conclusion

• Database primitives abstraction from
  application Similarity Search Þ
  Clustering Classification Þ Similarity Join
  Outlier Detection
• Advantages
• General solution, reuse
• Separately optimizable

Range QueriesNearest Neighbor Queries