Visualizing Semantics

Semantics, as used here, means the "meanings of words." As meaning is mostly defined not by reference to the external world, but to other words, the relationships between words, when visualised graphically, gives insights into their semantics.

In case you disagree with meaning being defined in terms of relations between words -- What is the first thing you think of, given the word HOT? What is the first thing you think of given OVER? CAT? HOUSE? Clearly CAT stands for the familiar animal, but it is the associations we have with the concept of cat that give it its meaning.

This page illustrates methods of visualizing the semantics of word using graphs (networks and lattices). Definitions are given of the different types of graphs but are not necessary to view and interpret the graphs.

Semantic Neighbourhoods

Given a "topic" word (S1), what is or are the senses (G1) (there are usually several) or meaning of that word? We can gain an understanding of the meaning of a topic word by studying the relationships between the topic word and its senses, and between the topic word and related words. We can represent the relation between the topic word and its senses as S1 X G1; or just s1g1. As a topology, or network, this is just a [star]

The set of words (S2) which share senses with S1 are its neighbours and, along with the senses shared, make up its neighbourhood . As S1 is a member of the set S2 we can represent the neighbourhood of S1 as s2g1. Depending on the number of senses or synonyms of S1, this can have a very complex topology.

The neighbouring words of S1, in turn, have senses (G2) of their own. These overlap with the senses of S1 (G1 is a subset of G2). So a semantic neighbourhood can then be expanded to s2g2 [1]. Usually this neighbourhood is too complex to be easily represented visually.

Comparisons between lattice and network

The neighbourhoods illustrated graphically below [ 2 ] are taken from the lexicon, Roget's Thesaurus, which defines senses by sets of synonyms. This eliminates potentially distracting phrases used in dictionary definitions, such as "is a type of," "is part of ,""is found under the," "an archaic term used to," etc.

The graphics are of two types: lattices and networks. Networks are composed of nodes (vertices, or circles), which represent the senses and/or words, and of lines which represent the connections or relations between the senses and/or words. Lattices are (simply put) graphs based on an ordered set (see FCA: Formal Concept Analysis ). Instead of all words being given equal billing, they are ordered --for example by the senses they share. Likewise (dually and symmetrically), the senses are ordered.

Relation Type	Formal Concept Lattices	Networks (Pajek)
Neighbourhood
Word X Sense	over (s2g1:Sienna) test (s2g1:ConExp)	over test
Restricted Neighbourhood
R_Word X Sense	over test (s2g1R:Siena)	over test
Self-Referencing Relations
Word X Word	N/A	over test
Sense X Sense	N/A	N/A
R_Word X R_Word	N/A	over test
GenDiff Relation
Word_1 X Word_N	N/A	N/A
Word_1 X R_Word		over
R_Word_1 X R_Word	over (Anaconda)
Word Association
Cue X Target	N/A	over Cue and over Target
	over Cue over Target over	over Cue over Target over

Restricted Neighbourhood

A Restricted Neighbourhood is a neighbourhood restricted to only those words that occur in more than one sense of the topic word (s2g1R) -- similarly for senses.

Any word that has has more than one sense is polysemous. Any word that has only one sense is monosemous, and known as a Singleton. Because a neighbourhood is restricted to the senses of the topic word, a polysemous neighbour may, in this context, have only one sense; in this situation it is known as neighbourhood-monosemous .

A self-referencing relation is a relation on one set; Word X Word, or Sense X Sense. A Restricted Neighbourhood Self-Referencing Relation on words, is between the words-only of a Restricted Neighbourhood (i.e., R_Word X R_Word)-- similarly for senses.

Genus-Differentiae

A Genus-Differentiae (GenDiff ) Relation takes Singletons (monosemous words (polysemy =1)) as Word_1 and polysemous words as Word_N. Singletons differentiate a sense -- they occur only in that sense and are differentiae. Polysemous words occur in more than sense -- they are classifying or genus words. Word_1 X Word_N is a relation between all singletons and polysemous words which share senses.

Because a neighbourhood is a subset of the entire set of senses, some non-topic polysemous words may occur only once in the neighbourhood (i.e. occur in only one sense of the topic word). These single-instance neighbours appear to be (appear as) singletons -- they are neighbourhood-monosemous -- and actas differentiae for the semantic neighbourhood of the topic word. Words that occur in more than one sense of the topic word (R_Word) act as classifying words or genus for the neighbourhood of the topic word.

R_Word_1 X R_Word_N: is a relation between the sense-differentiating words of a neighbourhood that occur only in those senses ( excluding the neighbourhood-monosemous singletons) and those words that occur in more than one sense of the topic word (occur as synonyms of the topic word in more than one sense). R_Word_N is identical to the set of restricted neighbourhood words,R_Word. => R_Word_1 X R_Word

Eliminating neighbourhood monosemous singletons (words which themselves maybe highly polysemous in other neighbourhoods, or contexts) reduces the visual load and restricts the visualization to just those singletons that differentiate senses of the Topic word.

Word Association

Word association data is collected by supplying a word (Cue) to a subject then recording the response (Target). The relation is directed: Cue => Target (prompt word => subject response). Because targets of a topic word may not be directly related to cues of the topic word, a Word Association Neighbourhood is composed using: TOPIC => Cue or Cue => TOPIC or TOPIC =>Target or Target => TOPIC (TOPIC - Cue - TOPIC - Target - TOPIC). TOPIC is removed (and consequently doesn't show

Software

[1] The semantic neighbourhood of a word can be expanded indefinitely or until the complete connected partition is reached. This is defined formally, using the PLUS (+) operator, by Priss (1996).

[2] The graphics on this page were produced by the following software:

ConExp * (Formal Concept Analysis)
Siena*(an editor in ToscanaJ ; Formal Concept Analysis) and
Pajek * (networks). Generate your own files for Pajek, Conexp, or Anaconda.
Anaconda (Formal Concept Analysis)

*free

Tupleware (Formal Concept Analysis) can be used with any database output simply by saving (or cutting and pasting) a binary relation (two columns: objects and attributes) to a .tuples file e.g. NAME.tuples -- without the column names/headers.

Input files can be generated automatically online:
For networks use
http://www.roget.org/Pajekcat.htm
For lattices use
http://www.roget.org/Anacondacat.htm

References

Priss, U. (1996). Relational Concept Analysis: Semantic structures in dictionaries and lexical databases . (Doctoral Dissertation, Technical University of Darmstadt, 1998). Aachen, Germany: Shaker Verlag.