Database%20Implementation%20of%20a%20Model-Free%20Classifier

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Database Implementation of a Model-Free
Classifier
ADBIS 2007

• Konstantinos Morfonios

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Introduction
Motivation
LOCUS
Parallel Execution
Experimental Evaluation
Conclusions Future Work
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Introduction
Motivation
LOCUS
Parallel Execution
Experimental Evaluation
Conclusions Future Work
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Introduction
Classification
x ltx1, x2, , xDgt
? f(x)
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Introduction
ltx1,1, x1,2, , x1,D, ?1gt ltx2,1, x2,2, , x2,D,
?2gt ltx3,1, x3,2, , x3,D, ?1gt ltx4,1, x4,2, ,
x4,D, ?1gt . . .
x1 ltx1, x2, , xDgt
x2 ltx1, x2, , xDgt
Lazy
Eager
(Nearest Neighbors)
(Decision Trees)
() Faster decisions
( - ) Large/complex datasets
( - ) Dynamic datasets
( - ) Dynamic models
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Introduction
Motivation
LOCUS
Parallel Execution
Experimental Evaluation
Conclusions Future Work
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Introduction
Motivation
LOCUS
Parallel Execution
Experimental Evaluation
Conclusions Future Work
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Motivation

• Large/complex datasets

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Motivation
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Motivation

• Large/complex datasets
• Dynamic datasets

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Motivation
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Motivation

• Large/complex datasets
• Dynamic datasets
• Dynamic models

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Motivation
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Motivation

• Large/complex datasets
• Dynamic datasets
• Dynamic models

Lazy (model-free)
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Motivation

• Large/complex datasets
• Dynamic datasets
• Dynamic models

Lazy (model-free)
Nearest Neighbors
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Motivation
LOCUS
(Lazy Optimal Classifier of Unlimited Scalability)
Suffers from curse of dimensionality

• Not reliable Beyer et al., ICDT 1999

• Not indexable Shaft et al., ICDT 2005

Nearest Neighbors
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Motivation
LOCUS
(Lazy Optimal Classifier of Unlimited Scalability)

• Category?

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Motivation
LOCUS
(Lazy Optimal Classifier of Unlimited Scalability)

• Lazy

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Motivation
LOCUS
(Lazy Optimal Classifier of Unlimited Scalability)

• Lazy

• Scaling?

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Motivation
LOCUS
(Lazy Optimal Classifier of Unlimited Scalability)

• Lazy

• Based on simple SQL queries

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Motivation
LOCUS
(Lazy Optimal Classifier of Unlimited Scalability)

• Lazy

• Based on simple SQL queries

• Accuracy?

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Motivation
LOCUS
(Lazy Optimal Classifier of Unlimited Scalability)

• Lazy

• Based on simple SQL queries

• Converges to optimal Bayes Classifier

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Motivation
LOCUS
(Lazy Optimal Classifier of Unlimited Scalability)

• Lazy

• Based on simple SQL queries

• Converges to optimal Bayes Classifier

• Other features?

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Motivation
LOCUS
(Lazy Optimal Classifier of Unlimited Scalability)

• Lazy

• Based on simple SQL queries

• Converges to optimal Bayes Classifier

• Parallelizable

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Introduction
Motivation
LOCUS
Parallel Execution
Experimental Evaluation
Conclusions Future Work
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Introduction
Motivation
LOCUS
Parallel Execution
Experimental Evaluation
Conclusions Future Work
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LOCUS
Example
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LOCUS
Ideally Dense space
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LOCUS
f2
?(lt7, 4gt) ?
Ideally Dense space
f1
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LOCUS
f2
?(lt7, 4gt)
f1
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LOCUS
f2

• Many features
• Large domains

?? Sparse space
Reality
f1
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LOCUS
f2
?(lt7, 4gt) ?
?
f1
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LOCUS
?1 2
f2
?
?(lt7, 4gt) ?
?2 1
f1
3-NN
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LOCUS
?1 2
f2
?
?(lt7, 4gt)
?2 1
f1
3-NN
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LOCUS
f2
?(lt7, 4gt) ?
f1
LOCUS
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LOCUS
?1 7
f2
?
?(lt7, 4gt) ?
?2 3
f1
LOCUS
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LOCUS
?1 7
f2
?
?(lt7, 4gt)
?2 3
f1
LOCUS
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LOCUS
f2
Disk-based implementation
f1
LOCUS
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LOCUS
SELECT ?, count() FROM R WHERE f1x1-d1 AND
f1x1d1 AND f2x2-d2 AND f2x2d2 GROUP BY ?
R(f1, f2, ?)
?1 7
?
?(lt7, 4gt)
?2 3
ltx1, x2gt
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LOCUS
SELECT ?, count() FROM R WHERE f1x1-d1 AND
f1x1d1 AND f2x2-d2 AND f2x2d2 GROUP BY ?
R(f1, f2, ?)
What if R is large?
Classical optimization techniques for a
well-known type of aggregate queries

• Indexing

• Materialized views

• Presorting

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LOCUS
SELECT ?, count() FROM R WHERE f1x1-d1 AND
f1x1d1 AND f2x2-d2 AND f2x2d2 GROUP BY ?
R(f1, f2, ?)
Method reliability?
LOCUS converges to the optimal Bayes classifier
as the size of the dataset increases (proof in
the paper)
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LOCUS
SELECT ?, count() FROM R WHERE f1x1-d1 AND
f1x1d1 AND f2x2-d2 AND f2x2d2 GROUP BY ?
R(f1, f2, ?)
What if a feature, say f2, is categorical? (e.g.
sex)
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LOCUS
SELECT ?, count() FROM R WHERE f1x1-d1 AND
f1x1d1 AND f2x2 GROUP BY ?
R(f1, f2, ?)
What if a feature, say f2, is categorical? (e.g.
sex)
Not a problem, since generally in practice

• Combinations of categorical and numeric
  features

• Categorical features have small domains

Hence, they do not contribute to sparsity
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Introduction
Motivation
LOCUS
Parallel Execution
Experimental Evaluation
Conclusions Future Work
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Introduction
Motivation
LOCUS
Parallel Execution
Experimental Evaluation
Conclusions Future Work
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Parallel Execution
R R1 ? R2 ? R3 ? R4
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Parallel Execution
Count distributive function
?1 23
?1 7
?1 5
?2 4
?2 1
?2 2
?1 6
?2 0
?1 5
?2 1
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Parallel Execution

• Small network traffic
• Load balancing
• Lightweight operations on the main server

?1 7
?1 5
?2 1
?2 2
?1 6
?2 0
?1 5
?2 1
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Introduction
Motivation
LOCUS
Parallel Execution
Experimental Evaluation
Conclusions Future Work
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Introduction
Motivation
LOCUS
Parallel Execution
Experimental Evaluation
Conclusions Future Work
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Experimental Evaluation

• LOCUS vs DTs and NNs (weka)
• Synthetic datasets
• Ten functions Agrawal et al., IEEE TKDE 1993
• D 9
• N ? 5?103, 5?106
• Real-world datasets
• UCI Repository

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Experimental Evaluation
Classification error rate (synthetic datasets, N
5?104)
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Experimental Evaluation
Effect of dataset size on classification error
rate of LOCUS (synthetic datasets, N ? 5?103,
5?106)
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Experimental Evaluation
Effect of dataset size on time scalability of
LOCUS (synthetic datasets, N ? 5?103, 5?106)
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Experimental Evaluation
Classification error rate (real-world datasets)
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Experimental Evaluation
Effect of dataset size on classification error
rate (dataset CovType, N ? 5?103, 5?105)
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Introduction
Motivation
LOCUS
Parallel Execution
Experimental Evaluation
Conclusions Future Work
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Introduction
Motivation
LOCUS
Parallel Execution
Experimental Evaluation
Conclusions Future Work
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Conclusions Future Work

• LOCUS
• Lazy (complex/dynamic datasets and models)
• Efficient (based on simple SQL queries)
• Reliable (converging to optimal)
• Parallelizable

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Conclusions Future Work

• Similar techniques for
• feature selection
• regression
• Implementation of a parallel version

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Questions?
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Thank you!