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 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

UPML Framework

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! ÝRapid development and validation ÝResult = both analytical and engineering resource

Amalgamating UPML and OCML OCML Base Ontology was revised to comply with UPML ÝTasks and PSMs become assumption-based

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 Candidate Sols. Criterion Classification Solution

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

Observables Observables = set_of (Observable); Observable = {feature, value}. Well defined Observables (obs): ({f 1, v 1 }  obs  {f 1, v 2 }  obs) -> v 1 = v 2 ({f 1, v 1 }  obs) -> legal_feature_value (f 1, v 1 )

Solutions Solution = set_of (Feature_Spec); Feature_Spec = {Feature, Feature_value_spec} Feature_value_spec = Unary_Relation Well defined Solution (sol): {f 1, s 1 }  sol  holds (s 1, v 1 ) -> legal_feature_value (f 1, v 1 )

Matching Observable={f 1, v 1 } matches Solution=sol iff: {f 1, c}  sol  holds (c, v 1 )

Matching Sets of Obs to a Solution Sol: {{fsol 1, c 1 }...{fsol m, c m }}; Obs: {{fob 1, v 1 }...{fob n, v n }} Four possible cases: {f j, c j }  sol  {f j, v j }  obs  holds (c j, v j ) -> Explained (f j ) {f j, c j }  sol  {f j, v j }  obs  not holds (c j, v j ) -> Inconsistent(f j ) {f j, v j }  obs  {f j, c j }  sol -> Unexplained (f j ) {f j, v j }  obs  {f j, c j }  sol -> Missing (f j )

Default Match Criterion Match Score: Vector: Match Comparison Relation S 1 = (i 1, e 1, u 1, m 1 ); S 2 = (i 2, e 2, u 2, m 2 ) S 1 better_score than S 2 iff: (i 1 < i 2 )  (i 2 = i 1  e 2 < e 1 )  (i 2 = i 1  e 2 = e 1  u 1 < u 2 )  (i 2 = i 1  e 2 = e 1  u 2 = u 1  m 1 < m 2 )

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

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

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))))))

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))))

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)))

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))))

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

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

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

Specific Classification Tasks Single-Solution Classification Task –Single-solution assumption Optimal Classification Tasks –Goal requires optimality

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

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

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))))

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)))))))

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

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

Task-Method Hierarchy

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!

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)))))

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))))

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 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))))))

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)))))))

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

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.

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

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