www.nomencurator.org what name can do alone an application of formal concept analysis with rough set...

www.nomencurator.org

What name can do alone An Application of Formal Concept Analysis with Ro

ugh Set Approximation to Multiple Hierarchies

Visualisation by TaxoNote Comparator Nozomi Ytow1, David R. Morse2, Akira Sato1, David McL. Roberts4

1 University of Tsukuba, Japan2 Open University, UK

3 The Natural History Museum, UK©2003 team Nomencurator. All rights reserved.


Multiple taxonomiesSimilar data models accept multiple

taxon concepts, multiple hierarchiesWe also need a method to compare

concepts and hierarchiesPrometheus/II: specimen/character basedLITCHI, MoReTaX: rule based Nomencurator: annotation captures

historical relationships, but need more

Does set theory help us?


Two Major Set Theories

Axiomatic set theoryExplicit list of elements in the set

Naïve set theoryCollection of items satisfies

conditions


Axiomatic Set TheoryLogically well-establishedDefines a set as an explicit list of

elements, e.g. specimen or taxaAddition of a new identified

specimen modifies the set, and hence the concept represented by the set?

Too stiff for taxonomy, because it requires a complete list


Naïve set theory

Collection of items satisfying conditions

Flexible than axiomatic setToo flexible, e.g. Russell's paradox,

or,Too stiff, with Russell's type theory

Theoretically more problematic than axiomatic set theory, but sounds better as taxon concept


Elements of taxon “set”

Axiomatic set theory assumes specimen or lower taxa as elements

Naïve set theory uses not only “ordinary” elements but a list of conditions to be satisfied; it is an implicit set of character states

Trick: using two sets to capture a concept


Formal concept analysis

Axiomatic set theoryextensional set

Naïve set theoryintensional set (of objects)

Formal conceptDefined as a pair of its

extension and intension sets


Taxon concept and name

Specimen circumscription

“Character” circumscription

Taxon Conceptcircumscription


Rough set theoryNot a genuine set theory, but an

application of set theoryUses two sets to approximate a

concept; positive and negative setsSet to be included in the conceptSet to be excluded from the concept

Boundary between these two sets gives a flexibility


Concept approximation


Rough comparison of concepts

Cross evaluation


Comparison of hierarchies

A taxonomy looks like a tree…A tree can be divided into nodes and

linkages between nodes

Can a taxonomy divided as in tree?Looks like inseparableA taxon concept closely relate to its

members, i.e. links included in a node

Rough set enables the separation


From Taxon to Taxonomy

A hierarchy of names works as whole


Difference in concepts

Rough set detects difference in concepts


Difference in hierarchies

Separation of concept and hierarchy


Hierarchies of compatible concepts


Hierarchies of incompatible concepts


Team NomencuratorDavid McL RobertsZoological DepartmentThe Natural History Museum

David M. MorseFaculty of Mathematics and ComputingThe Open University, UK

Akira SatoInformation Processing CenterUniversity of Tsukuba, Japan


AcknowledgementInitial exploration of the problem domain was made by Dr

Marion Edwards, generously supported by The Cadbury Trust.

Development of Nomencurator and its specification (so called Mk II) was initiated as part of a foreign scholarship funded by the Ministry of Education, Culture, Sports Science and Technology of Japan (November 1998 - November 1999) to one of us (NY).

It's development was partly funded by University of Tsukuba (2000) and by the Ministry of Education, Culture, Sports Science and Technology of Japan (Grant-in-Aid for Exploratory Research, 13878069, 2001-2003 to NY and Science and Technology Special Coordination Funds to NY with Juno Shimura at NIES).

Travel has been partly supported by the National Institute of Environmental Sciences, Japan, as part of collaboration of NY with Junko Shimura at NIES focusing on GBIF.

The Nomencurator website is hosted under name of www.nomencurator.org by courtesy of University of Tsukuba


Revisiting nameA name is not a stringName is the relationship between

a string and the designated objectA tag removed from the object is not

the tag anymore

Name (and hence database) can not manage object directlyGiving a name to a set containing

single object enables unified management both specimen and taxa


Nested subsets, not members

Treat each specimen as a sat

Each lower taxon is not a member of lower taxa, but a subset


Common Data Structure


Revisiting nameA name is not a stringName is the relationship between

a string and the designated objectA tag removed from the object is not

the tag anymore

Name (and hence database) can not manage object directlyGiving a name to a set containing

single object enables unified management both specimen and taxa

www.nomencurator.org what name can do alone an application of formal concept analysis with rough set...

Documents