Patterns for NextGeneration Database Systems PANDA A First
Patterns for Next-Generation Database Systems PANDA A First Attempt towards a Logical Model for the PBMS PANDA Meeting, Milano, 18 April 2002 National Technical University of Athens P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002
Overview • • • General Understanding of the PBMS Mathematical Background Meta. Model: Entities and Language The Software Engineering Perspective Conclusions P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002 2
Overview • • • General Understanding of the PBMS Mathematical Background Meta. Model: Entities and Language The Software Engineering Perspective Conclusions P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002 3
PBMS General Framework Meta_Pattern Type Meta-Pattern Type + Patter Types = PBMS Catalog Meta-Pattern Type Layer Language belong to Association Rule Type DBSCAN Cluster Type belong to Pattern Layer = PBMS Content Assoc. Rule n belong to Assoc. Rule 2 Assoc. Rule 1 Cluster 3 Cluster 2 Cluster 1 Decision Tree Type Pattern Type Layer belongs to Decision Tree 1 DBSCAN Cluster Algorithm Dec. Tree Ass. Rule Raw Data Algorithm. P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002 4
General Idea Meta-Pattern Type+ Language Relation + Language • a Name • a Condensed Expression • an Extension and Language • a Name • a Schema • an Extension and Relational Calculus Pattern Type Relational Table • Association. Rule. Type • head : - body • Buys • session_id, date, item, price • ext(Association. Rule. Type) • ext(Buys) Pattern Tuple Buys(x, _, beer, _): Buys(x, _, pampers, _) Buys(34, 4/4/2002, beer, 2) P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002 5
Overview • • • General Understanding of the PBMS Mathematical Background Meta. Model: Entities and Language The Software Engineering Perspective Conclusions P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002 6
Mathematical Background Assumptions from the definition: • There exists a data space and a pattern space. • There always exist M: N relationships among data and patterns. Data Space Pattern Space P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002 7
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(A 1)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(A 1)x…xdom(AM) • Proposal: all dom(x) are infinitely countable + DM is clearly finite. P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002 8
Statistical Measures The data-pattern relationship f. DP has: • participation measures for the relationship; • importance measures for a data item; • importance measures for a pattern. Data Space Pattern Space P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002 9
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 10
Overview • • • General Understanding of the PBMS Mathematical Background Meta. Model: Entities and Language The Software Engineering Perspective Conclusions P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002 11
PBMS General Framework Meta_Pattern Type Meta-Pattern Type + Patter Types = PBMS Catalog Meta-Pattern Type Layer Language belong to Association Rule Type DBSCAN Cluster Type belong to Pattern Layer = PBMS Content Assoc. Rule n belong to Assoc. Rule 2 Assoc. Rule 1 Cluster 3 Cluster 2 Cluster 1 Decision Tree Type Pattern Type Layer belongs to Decision Tree 1 DBSCAN Cluster Algorithm Dec. Tree Ass. Rule Raw Data Algorithm. P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002 12
Pattern Types • Intentional Description of a Pattern Type as follows: – PID – Explicit Relationship: f. DPi: DN→Di. M. – 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 13
Example Pattern Type Intentional Description [small part of] Pattern Type Extensional Description • PID • Explicit Relationship • Relationship Expression • PID 123 • f. DPi: DN→Di. M ={(PID 123, RID 124), …} • Buys(x, _, beer, _): Buys(x, _, pampers, _) • Coverage=80%, Confidence=90% • Statistical Measures P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002 14
PBMS General Framework Meta_Pattern Type Meta-Pattern Type + Patter Types = PBMS Catalog Meta-Pattern Type Layer Language belong to Association Rule Type DBSCAN Cluster Type belong to Pattern Layer = PBMS Content Assoc. Rule n belong to Assoc. Rule 2 Assoc. Rule 1 Cluster 3 Cluster 2 Cluster 1 Decision Tree Type Pattern Type Layer belongs to Decision Tree 1 DBSCAN Cluster Algorithm Dec. Tree Ass. Rule Raw Data Algorithm. P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002 15
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 16
Example Meta-Pattern Type Intentional Description • Name • Condensed Expression • [Meta]Statistical Measures • Schema Attributes? ? [small part of] Meta-Pattern Extensional Description • Association. Rule. Type • head : - body • Coverage: Float[0. . 1], Confidence: Float[0. . 1] • PID, Head, Body ? ? Pattern Type Intentional Description [small part of] Pattern Type Extensional Description • PID • Explicit Relationship • Relationship Expression • PID 123 • f. DPi: DN→Di. M ={(PID 123, RID 124), …} • Buys(x, _, beer, _): Buys(x, _, pampers, _) • Coverage=80%, Confidence=90% • Statistical Measures P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002 Type 17
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 result for non-linear constraints… P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002 18
Which language to choose? P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002 19
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 20
Overview • • • General Understanding of the PBMS Mathematical Background Meta. Model: Entities and Language The Software Engineering Perspective Conclusions P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002 21
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 22
How to build it? PBMS General Framework Generic Class Set of DDL/DML Languages ISA Meta-Pattern Type + Patter Types = PBMS Catalog Association Rule Class Cluster Class IN Pattern Layer = PBMS Content Assoc. Rule n IN Assoc. Rule 2 Assoc. Rule 1 Cluster 3 Cluster 2 Cluster 1 Decision Tree Class IN Decision Tree 1 P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002 23
Overview • • • General Understanding of the PBMS Mathematical Background Meta. Model: Entities and Language The Software Engineering Perspective Conclusions P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002 24
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 25
Thank you … P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002 26
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 patternrelated operations generating intentional information. P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002 27
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, multidimensionality, recursion, hierarchies, etc. ) P. Vassiliadis. PANDA Meeting, Milano, 18 April 2002 28
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 29
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 30
- Slides: 30