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Modeling and Language Support for the management of PBMS

Manolis TerrovitisPanos Vassiliadis

Spiros SkiadopoulosElisa Bertino

Barbara CataniaAnna Maddalena

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Outline

IntroductionModeling of data and patternsQuery operatorsSummary and future work

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Motivation

Huge amounts of data are produced.Interesting knowledge has to be detected

and extracted.Knowledge extraction techniques (i.e.,

Data Mining) are not sufficient: Huge amounts of results (clusters, association

tules, decision trees etc) Arbitrary modeling of results

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Motivation (con’t)

We need to be able to manipulate the knowledge discovered!

The basic requirements: A generic and homogenous model for patterns. Well defined query operators. Efficient storage.

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The Patterns and PBMS [Rizzi et. al. ER 2003]

Patterns are compact and rich in semantics representations of raw data. Clusters, association rules, decision trees e.t.c.

Pattern Base Management System Patterns are treated as first class citizens Pattern-based queries Approximate mapping between patterns and

raw data

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Contributions

We formally define the logical foundations for pattern management

We present a pattern specification language

We introduce queries and query operators

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Outline

IntroductionModeling of data and patternsQuery operatorsSummary and future work

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PBMS architecture

Pattern Space: Pattern Types Pattern Classes Patterns

Intermediate Results

Data Space

PatternClasses

PatternTypes

Patterns

Member of Instanceof

DataMining

Algorithms

PatternRecognitionAlgorithms

DataSpace

PatternSpace

IntermediateMappings

DB1 DB2

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The patterns

Patterns hold information for: the data source the structure of the pattern The relation between the structure and the

source, in an approximate logical formula.

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Pattern - Cluster Example

Pid 337

Structure [CENTER: [X: 21, Y: 1200], RAD: 12 ]

Data EMP: {[Age, Salary]}

Formula (t.Age - 21)2 + (t.Salary - 1200)2 ≤ 12 2 where t EMP

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Pattern type - example

Name Disk

Structure Schema [CENTER: [X:real, Y: real], RAD: real ]

Data Schema REL: {[X: real, Y: real]}

Formula Schema (t.X - CENTER.X)2 + (t.Y - CENTER.Y )2 ≤RAD2

where t REL

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The formula

An intentional description of the pattern-data relation pros:

Efficiency, more intuitive results cons:

Accuracy

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Intentional vs. Extensional

Salary

30

30 31

AGE

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The formula (con’t)

The formula is a predicate:

fp(x,y) where x Source,y Structure Expressiveness.

Functions and predicates

Safety. Range restriction.

Queries employing the formula are n-depth domain independent.

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Outline

IntroductionModeling of data and patternsQuery operatorsSummary and future work

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Query Operators

Query operator classes: Database operators Pattern Base operators Crossover database operators Crossover pattern base operators

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Crossover Operators

PID

data

structure

formula

PatternSpace

DataSpace

Exact

Exact

Approximation

Exact evaluation, via the intermediate mappings

Approximate evaluation, via the formula

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Crossover Operators

Database Drill-Through: Which data are represented by

these patterns? Data-Covering: Which data from this dataset

can be represented by this pattern?

Pattern Base Pattern-Covering: Which of these patterns

represent this dataset?

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Query Example

Salary

AGE p

q

Drill-through(

{ p |

p intersects q})

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Outline

IntroductionModeling of data and patternsQuery OperatorsSummary and future work

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Summary

Formal specification of basic PBMS concepts

Investigation on the representation of the pattern-data relation

Formal definition of query operators

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Future Work

Query languageGeneric similarity measuresEfficient implementation of intermediate

mappingsStatistical measures for the patterns.