A Library of Components for Classification Problem Solving
Wenjin Lu and Enrico MottaKnowledge 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
TaskRefiner
Task
PSMRefiner
PSM
Ontol.Refiner
Ontologies
DomainRefiner
DomainModel
PSM-TaskBridge
PSM-DomainBridge
Task-DomainBridge
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
Amalgamating UPML and OCML
• OCML Base Ontology was revised to comply with UPML Tasks 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):
({f1, v1} obs {f1, v2} obs) -> v1 = v2
({f1, v1} obs) -> legal_feature_value (f1, v1 )
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 )
Matching
Observable={f1, v1} matches Solution=sol iff:
{f1, c} sol holds (c, v1 )
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)
Default Match Criterion
Match Score:Vector: <I, E, U, M>
Match Comparison RelationS1 = (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)
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 MechanismFeature 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
abstraction
heuristic-classification-psm
classification
rank-solutions refinement
basic-heuristic-matchselect-abstractor one-step-abstraction collect-refiners apply-refiners
abstraction-psm refinement-psmrank-solutions-psm
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!
Classification TaskOntology
Heuristic ClassificationOntology
Apple Heuristic ClassificationApplication
Classification TaskSpecification
Classification-to-Class-RepresentationMapping Ontology
AppleDomain Model
Heuristic ClassificationPSMs
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 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))))))
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