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A Library of Components for Classification Problem Solving

A Library of Components for Classification Problem Solving. Wenjin Lu and Enrico Motta Knowledge Media Institute. Four Main Goals. To carry out a knowledge-level analysis of classification To develop a practical resource to support the development of classification applications

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A Library of Components for Classification Problem Solving

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  1. A Library of Components for Classification Problem Solving Wenjin Lu and Enrico Motta Knowledge Media Institute

  2. Four Main Goals • To carry out a knowledge-level analysis of classification • To develop a practical resource to support the development of classification applications • To provide a concrete set of components to act as a test case for IBROW brokering system and IRS • To evaluate the UPML framework and the OCML modelling language on a non-trivial test-case

  3. UPML Framework

  4. Detailed Modelling in OCML • Supports domain, task and PSM specification • Large Library (>90 Ontologies) • Extensive experience (~20 projects, 5 years) • Robust Infrastructure • Both web-based and ‘vanilla’ development environments • Intg. of specification and operationalization is a good thing! • Rapid development and validation • Result = both analytical and engineering resource

  5. Amalgamating UPML and OCML • OCML Base Ontology was revised to comply with UPML • Tasks and PSMs become assumption-based

  6. Classification Classification can be seen as the problem of finding the solution (class), which best explains a set of known facts (observables), according to some criterion Observables Classification Candidate Sols. Solution Criterion

  7. Example Observables {background=green; area=china...} {chinese-granny, dutch-granny, etc..} Classification Candidate Sols. Solution {chinese-granny} Criterion Complete-coverage-criterion (every observable has to be explained)

  8. Observables Observables = set_of (Observable); Observable = {feature, value}. Well defined Observables (obs): ({f1, v1}  obs  {f1, v2}  obs) -> v1 = v2 ({f1, v1}  obs) -> legal_feature_value (f1, v1 )

  9. Solutions Solution = set_of (Feature_Spec); Feature_Spec = {Feature, Feature_value_spec} Feature_value_spec = Unary_Relation Well defined Solution (sol): {f1, s1}  sol  holds (s1, v1 ) -> legal_feature_value (f1, v1 )

  10. Matching Observable={f1, v1} matches Solution=sol iff: {f1, c}  sol  holds (c, v1 )

  11. Matching Sets of Obs to a Solution Sol: {{fsol1, c1}...{fsolm, cm}}; Obs: {{fob1, v1}...{fobn, vn}} Four possible cases: {fj, cj}  sol  {fj, vj}  obs  holds (cj, vj) -> Explained (fj) {fj, cj}  sol  {fj, vj}  obs  not holds (cj, vj) -> Inconsistent(fj) {fj, vj}  obs  {fj, cj}  sol -> Unexplained (fj) {fj, vj}  obs  {fj, cj}  sol -> Missing (fj)

  12. Default Match Criterion Match Score: Vector: <I, E, U, M> Match Comparison Relation S1 = (i1, e1, u1, m1); S2 = (i2, e2, u2, m2) S1 better_score than S2 iff: (i1 < i2)  (i2 = i1 e2 < e1)  (i2 = i1 e2 = e1 u1 < u2)  (i2 = i1 e2 = e1 u2 = u1  m1 < m2)

  13. Possible Solution Criteria • Positive Coverage • Some feature is explained and none is incosistent • Complete Coverage • All features are explained and none is incosistent

  14. Solution Criterion Hierarchy of Criteria Match Criterion Match Score Mechanism Match Score Comparison Rel Macro Score Mechanism Feature Score Mechanism

  15. Observables (def-class observables (set) ?obs "This is simply a set of observables. An important constraint is that there cannot be two values for the same feature in a set of observables" :iff-def (every ?obs observable) :constraint (not (exists (?ob1 ?ob2) (and (member ?ob1 ?obs) (member ?ob2 ?obs) (has-observable-feature ?ob1 ?f) (has-observable-feature ?ob2 ?f) (has-observable-value ?ob1 ?v1) (has-observable-value ?ob2 ?v2) (not (= ?v1 ?v2))))))

  16. Solutions (def-class solution () ?x "A solution is a set of feature definitions" :iff-def (every ?x feature-definition)) (def-class feature-definition () ?x ((has-feature-name :type feature) (has-feature-value-spec :type unary-relation)) :constraint (=> (and (has-feature-name ?x ?f) (has-feature-value-spec ?x ?spec)) (=> (holds ?spec ?v) (legal-feature-value ?f ?v))))

  17. Solution Criterion (def-class solution-admissibility-criterion () ?c ((applies-to-match-score-type :type match-score-type) (has-solution-admissibility-relation :type unary-relation)) :constraint (=> (and (solution-admissibility-criterion ?c) (has-solution-admissibility-relation ?c ?r) (domain ?r ?d)) (subclass-of ?d match-score)))

  18. Monotonicity of Admissibile Solutions (def-axiom admissibility-is-monotonic "This axiom states that the admissibility criterion is monotonic. That is, if a solution, ?sol, is admissible, then any solution which is better than ?sol will also be admissible" (forall (?sol1 ?sol2 ?obs ?criterion) (=> (and (admissible-solution ?sol1 (apply-match-criterion ?criterion ?obs ?sol1) ?criterion) (better-match-than ?sol2 ?sol1 ?obs ?criterion)) (admissible-solution ?sol2 (apply-match-criterion ?criterion ?obs ?sol2) ?criterion))))

  19. Complete Coverage (def-instance complete-coverage-admissibility-criterion solution-admissibility-criterion ((applies-to-match-score-type default-match-score) (has-solution-admissibility-relation complete-coverage-admissibility-relation))) (def-relation complete-coverage-admissibility-relation (?score) "a solution should be consistent and explain all features" :constraint (default-match-score ?score) :iff-def (and (= (length (first ?score)) 0) ;;no inconsistency (= (length (third ?score)) 0))) ;;no unexplained

  20. Classification Task Ontology • 42 Definitions • Provides both a theory of classification and a vocabulary to describe classification problems • Ontology is separated from task specifications

  21. Generic Classification Task • Input roles • Candidate Solutions, Match Criterion, Solution Criterion, Observables • Precondition • Both observables and candidate solutions have to be provided • Goal • To find a solution from the candidate solutions which is admissible with respect to the given observables, solution criterion and match criterion

  22. Specific Classification Tasks • Single-Solution Classification Task • Single-solution assumption • Optimal Classification Tasks • Goal requires optimality

  23. Problem Solving Library • Based on heuristic classification model • Supports both data-directed and solution-directed classification • Based on search paradigm • Supported by a method ontology

  24. Method Ontology: Main Concepts • Abstractors • Mechanism for performing abstraction on observables • Abstractor: Obs* -> Obs • Refiners • Mechanism for specialising a solution • Refiner: Sol -> Sol* • Candidate Exclusion Criterion • A criterion which is used to decide when a search path is a dead-end • Default criterion rules out inconsistent solutions

  25. Monotonicity of Exclusion Criterion (def-axiom exclusion-is-monotonic (forall (?sol1 ?sol2 ?obs ?criterion) (=> (and (ruled-out-solution ?sol1 (the-match-score ?sol1) ?criterion) (not (better-match-than ?sol2 ?sol1 ?obs ?criterion))) (ruled-out-solution ?sol2 (the-match-score ?sol2)?criterion))))

  26. Axiom of Congruence (def-axiom CONGRUENT-ADMISSIBILITY-AND-EXCLUSION-CRITERIA (forall (?sol ?task) (=> (member ?sol (the-solution-space ?task)) (not (and (admissible-solution ?sol (the-match-score ?sol) (role-value ?task 'has-solution-admissibility-criterion)) (ruled-out-solution ?sol (the-match-score ?sol) (role-value ?psm 'has-solution-exclusion-criterion)))))))

  27. Three Heuristic Classification PSMs • Two Data-directed • Admissible Solution Classifier • Finds one admissible solution according to the given criteria • Uses backtracking hill climbing • Optimal Classifier • Performs complete search looking for optimal solution • Uses best-first strategy • Uses candidate exclusion criterion to prune search space • One Solution-directed • Goes down the solution hierarchy, acquiring observables as needed • Ask for observables with max discrimination power

  28. Four Assumptions in Main PSMs • No cycles in abstraction hierarchy • No cycles in refinement hierarchy • At least one class in the solution space is an admissible solution • The solution refinement hierarchy is consistent with the candidate exclusion criterion. That is if sol is ruled out, all refinements of sol can also be ruled out

  29. Task-Method Hierarchy

  30. Example • Apple Domain • Originally developed in Amsterdam • Solutions = Apple Types = {granny, noble, delicious...} • Hierarchy of Apple Types • Features = {bkg-colour, fg-colour, rusty....} • Pretty trivial really!

  31. Mapping Solutions and Obs to Apples (def-relation-mapping solution :up ((solution ?x) if (or (= ?x apple) (subclass-of ?x apple)))) (def-relation-mapping observable :up ((observable ?x) if (or (== ?X (?f ?v ?obs)) (== ?x (?f ?v)))))

  32. More Relation Mappings (def-relation-mapping has-observable-feature :up ((has-observable-feature ?x ?f) if (or (== ?X (?f ?v ?obs)) (== ?x (?f ?v))))) (def-relation-mapping has-observable-value :up ((has-observable-value ?x ?v) if (or (== ?X (?f ?v ?obs)) (== ?x (?f ?v))))) (def-relation-mapping directly-abstracts-from :up ((directly-abstracts-from ?ob ?obs) if (== ?ob (?f ?v ?obs))))

  33. Sample Abstractor (def-instance sugar-abstractor abstractor ((has-body '(lambda (?obs) (in-environment ((?v . (observables-feature-value ?obs 'sugar))) (cond ((>= ?v 70) (list-of 'sweet-level 'high (list-of (list-of 'sugar ?v)))) ((and (< ?v 70) (> ?v 40)) (list-of 'sweet-level 'medium (list-of (list-of 'sugar ?v)))) ((<= ?v 40) (list-of 'sweet-level 'low (list-of (list-of 'sugar ?v)))))))) (applicability-condition (kappa (?obs) (member 'sugar (all-features-in-observables ?obs))))))

  34. Generic (reusable) Refiner (def-instance refinement-through-subclass-of-links refiner "If the solution space is specified by means of classes arranged in a subclass-of hierarchy, then this is a good refiner to use" ((has-body '(lambda (?sol) (setofall ?sub (direct-subclass-of ?sub ?sol)))) (applicability-condition (kappa (?sol) (and (class ?sol) (exists ?sub (direct-subclass-of ?sub ?sol)))))))

  35. Evaluation/Results • All PSMs successfully tested on the apple domain • Assumptions also successfully tested in the domain • Library available online in WebOnto

  36. Next Tasks • Start work on Internet Reasoning Service • Approach: Ever increasing levels of intelligent support • Browsing/Navigation/Manual PSM Configuration • Intelligent Assistant • Semi-automated component selection/configuration • Intelligent Broker • Multiple libraries/multiple platforms/symbol-level interoperability • Application to more complex domains • Scientific Classification, Selection of Manufacturing Tech.

  37. Possible Platforms for IRS • Specialized WebOnto Configuration • Protégé • Intg. Protégé with OCML Library • Collaboration with Stanford (i.e., Monica) • Dedicated Tabs to support PSM selection/reuse • New Java/Lisp Tool • Java Applets interfaced with library sitting on Lisp server

  38. Classification Library in OCML (at the end of IBROW 1) • Task spec (TaskSpec1) • Flat classification PSM (GenPSM1) • Applied to apple and Rocky-III domains

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