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A%20Library%20of%20Components%20for%20Classification%20Problem%20Solving

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Title: A%20Library%20of%20Components%20for%20Classification%20Problem%20Solving

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 (gt90 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
backgroundgreen areachina...
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) -gt v1 v2
(f1, v1 ? obs) -gt 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 ) -gt
legal_feature_value (f1, v1 )

10
Matching

Observablef1, v1 matches Solutionsol 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)
-gt Explained (fj)
fj, cj ? sol ? fj, vj ? obs ? not holds (cj,
vj) -gt Inconsistent(fj)
fj, vj ? obs ? fj, cj ? sol -gt Unexplained
(fj)
fj, vj ? obs ? fj, cj ? sol -gt Missing (fj)

12
Default Match Criterion

Match Score
Vector ltI, E, U, Mgt
Match Comparison Relation
S1 (i1, e1, u1, m1) S2 (i2, e2, u2, m2)
S1 better_score than S2 iff
(i1 lt i2) ?
(i2 i1 ? e2 lt e1) ?
(i2 i1 ? e2 e1 ? u1 lt u2) ?
(i2 i1 ? e2 e1 ? u2 u1 ? m1 lt 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
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 (gt (and (has-feature-name ?x ?f)
(has-feature-value-spec ?x
?spec))
(gt (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 (gt (and (solution-admissibility-crit
erion ?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)
(gt (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-crit
erion
solution-admissibility-criterion
((applies-to-match-score-type default-match-score
)
(has-solution-admissibility-relation
complete-coverage-admissibility-relation)))
(def-relation complete-coverage-admissibility-rela
tion (?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 -gt Obs
Refiners
Mechanism for specialising a solution
Refiner Sol -gt 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)
(gt (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-C
RITERIA
(forall (?sol ?task)
(gt (member ?sol (the-solution-space
?task))
(not (and (admissible-solution
?sol
(the-match-score ?sol)
(role-value
?task
'has-solution-admissibil
ity-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
(No Transcript)
32
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)))))

33
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))))

34
Sample Abstractor

(def-instance sugar-abstractor abstractor
((has-body '(lambda (?obs)
(in-environment
((?v . (observables-feature-value
?obs 'sugar)))
(cond ((gt ?v 70)
(list-of 'sweet-level
'high
(list-of
(list-of 'sugar ?v))))
((and (lt ?v 70) (gt ?v 40))
(list-of 'sweet-level
'medium
(list-of
(list-of 'sugar ?v))))
((lt ?v 40)
(list-of 'sweet-level
'low
(list-of
(list-of 'sugar ?v))))))))
(applicability-condition
(kappa (?obs) (member 'sugar
(all-features-in-observa
bles
?obs))))))

35
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)))))))

36
Evaluation/Results