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A First Attempt towards a Logical Model for the PBMS

Pa tterns for N ext-Generation Da tabase Systems PANDA. A First Attempt towards a Logical Model for the PBMS. PANDA Meeting, Milano , 18 April 2002 National Technical University of Athens. Overview. General Understanding of the PBMS Mathematical Background

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A First Attempt towards a Logical Model for the PBMS

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  1. Patterns for Next-Generation Database Systems PANDA A First Attempt towards a Logical Model for the PBMS PANDA Meeting, Milano, 18 April2002 National Technical University of Athens

  2. Overview • General Understanding of the PBMS • Mathematical Background • MetaModel: Entities and Language • The Software Engineering Perspective • Conclusions P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  3. Overview • General Understanding of the PBMS • Mathematical Background • MetaModel: Entities and Language • The Software Engineering Perspective • Conclusions P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  4. PBMS General Framework Meta-Pattern Type Layer Meta_Pattern Type Language Meta-Pattern Type + Patter Types = PBMS Catalog belong to Pattern Type Layer Association Rule Type DBSCAN Cluster Type Decision Tree Type belong to belong to belongs to Pattern Layer = PBMS Content Cluster 2 Assoc. Rule 2 Cluster 3 Decision Tree 1 Assoc. Rule n Cluster 1 Assoc. Rule 1 DBSCAN Cluster Algorithm Ass. Rule Algorithm Dec. Tree Algorithm Raw Data P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  5. General Idea P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  6. Overview • General Understanding of the PBMS • Mathematical Background • MetaModel: Entities and Language • The Software Engineering Perspective • Conclusions P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  7. Data Space Pattern Space Mathematical Background Assumptions from the definition: • There exists a data space and a pattern space. • There always exist M:Nrelationships among data and patterns. P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  8. Characteristics of data and pattern space • Each data item is characterized by a finite number of features N. • dom(x) the domain of each feature. • Data space DNdom(A1)x…xdom(AN) • Proposal: all dom(x) are infinitely countable + consider cases for DN (whether it is finite or not). • Each pattern is characterized by a finite number of features M. • Pattern space DMdom(A1)x…xdom(AM) • Proposal: all dom(x) are infinitely countable + DM is clearly finite. P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  9. Data Space Pattern Space Statistical Measures The data-pattern relationship fDP has: • participation measures for the relationship; • importance measures for a data item; • importance measures for a pattern. P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  10. Statistical Measures • Richness of representation = relationships captured by the condensed representation total number of relationships • Compactness of the representation = size(DM)*M size(DN)*N P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  11. Overview • General Understanding of the PBMS • Mathematical Background • MetaModel: Entities and Language • The Software Engineering Perspective • Conclusions P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  12. PBMS General Framework Meta-Pattern Type Layer Meta_Pattern Type Language Meta-Pattern Type + Patter Types = PBMS Catalog belong to Pattern Type Layer Association Rule Type DBSCAN Cluster Type Decision Tree Type belong to belong to belongs to Pattern Layer = PBMS Content Cluster 2 Assoc. Rule 2 Cluster 3 Decision Tree 1 Assoc. Rule n Cluster 1 Assoc. Rule 1 DBSCAN Cluster Algorithm Ass. Rule Algorithm Dec. Tree Algorithm Raw Data P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  13. Pattern Types • Intentional Description of a Pattern Type as follows: • PID • Explicit Relationship: fDPi:DN→DiM. • Relationship Expression • Statistical Measures. • Extensional Description (or Pattern Extension) of a Pattern Type : a finite set of patterns • Data extension of of a Pattern Type: a countable? set of data items P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  14. Example P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  15. PBMS General Framework Meta-Pattern Type Layer Meta_Pattern Type Language Meta-Pattern Type + Patter Types = PBMS Catalog belong to Pattern Type Layer Association Rule Type DBSCAN Cluster Type Decision Tree Type belong to belong to belongs to Pattern Layer = PBMS Content Cluster 2 Assoc. Rule 2 Cluster 3 Decision Tree 1 Assoc. Rule n Cluster 1 Assoc. Rule 1 DBSCAN Cluster Algorithm Ass. Rule Algorithm Dec. Tree Algorithm Raw Data P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  16. Meta-Pattern Types • Intentional Description of a Pattern Type as follows: • Name • Condensed Expression • [Meta]Statistical Measures. • ?? Schema Attributes ?? • Extensional Description of a Meta-Pattern Type : a finite set of pattern types P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  17. Example P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  18. Which language to choose? • Relational Calculus, Datalog and Stratified Datalog? • Powerful but not elegant for all the patterns that we might want to express… • Constraint database approach? • We cannot guarantee a finite representation of the resultfor non-linear constraints… P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  19. Which language to choose? P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  20. Which language to choose? • Remove recursion ? • Cannot express interesting patterns like transitive closure… • Only linear constraints? • Cannot express interesting patterns like cyclic clusters… • Approximation of polynomials through sets of linear constraints ? Not elegant… • Forget constraints and describe every pattern type as a simple predicate ? • Loss of all the declarative information on the nature of the pattern type … • So, what to do? Possible dead-end due to the paradigm? P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  21. Overview • General Understanding of the PBMS • Mathematical Background • MetaModel: Entities and Language • The Software Engineering Perspective • Conclusions P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  22. How to build it? • Each of the pattern types implemented as a Class. • The different pattern types defined as specializations of a Generic Pattern Class. • Treat pattern types as predicates, with semantics computed by a computationally complete procedural language [e.g., PL/SQL, C++, …]? • Instead of fundamental research we turn to feasibility issues… • What about behavior? P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  23. How to build it? General Framework PBMS Generic Class Set of DDL/DML Languages ISA Meta-Pattern Type + Patter Types = PBMS Catalog Association Rule Class Cluster Class Decision Tree Class IN IN IN Cluster 2 Pattern Layer = PBMS Content Assoc. Rule 2 Cluster 3 Decision Tree 1 Assoc. Rule n Cluster 1 Assoc. Rule 1 P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  24. Overview • General Understanding of the PBMS • Mathematical Background • MetaModel: Entities and Language • The Software Engineering Perspective • Conclusions P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  25. Conclusions • Followed the Datalog paradigm (need for deductive capabilities) enhanced with constraints (need for elegance) • Reduced the problem to the specification of a proper language for the description of pattern types • Fundamental language limitations when considered constraints • Dilemma: • Change paradigm? • Stick with this paradigm and focus on engineering issues? • …Any other suggestions ?… P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  26. Thank you … P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  27. Definitions from the minutes of Athens meeting • Pattern is a compact and rich in semantics representation of raw data. • A Pattern-Based Management System (PBMS) is a system for handling (storing / processing / retrieving) patterns extracted from raw data in order to efficiently support pattern matching and to exploit pattern- related operations generating intentional information. P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  28. Issues around the pattern definition • The mapping from original raw data space to less populated (compact) pattern space is always possible preserving (or, documenting) as much knowledge as possible from raw data space (rich in semantics). • A M:N mapping between raw data space and pattern space is permitted • Perhaps, several levels of representation / abstraction exist (different levels of granularity, multi-dimensionality, recursion, hierarchies, etc.) P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  29. Issues around the PBMS definition • A PBMS will cooperate with a DBMS storing raw data; • A PBMS processes different kinds of queries (because of different user needs) on raw data and returns more intuitive results to users; • A PBMS is useful in order to process those queries more efficiently than a normal DBMS would do; • A PBMS will have its own mechanisms for representing and storing its entries (patterns), posing and processing queries, efficiently retrieving its entries. P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

  30. Query Language Issues • Given a datum, which pattern does it refer to? Which are the data that correspond to this pattern? • Zoom-in, zoom-out a pattern. Pattern union, difference. • Composition of patterns (i.e., if A  B and B  C, then derive A  C). • What are values of the statistical measures for this pattern? Which patterns fulfill a certain constraint on a statistical measure? • Which are the patterns in the PBMS catalog? Which are the attributes or the statistical measures for this pattern type? Which pattern types relate to a certain statistical measure? • Closed Form of the Language. P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002

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