Tenth Midwest Artificial Intelligence and Cognitive Science Conference

April 23-25, 1999, 

Indiana University, Bloomington, Indiana

Spatial Representation of Semantic Information

John Old

School of Library and Information Science

Indiana University

Introduction

The goal - semantic "topographical landscapes"

•  Indiana University elevation surface derived from two-foot contours--a real-world topography.
•  Total population vs. population density of Native Americans by state--a "value-added" map formed by joining demographic data with geographic data. There are two dimensions to the data:
  • Height indicates number of Native Americans by State
  • Color density indicates population density, or concentration 
    •    [yellow indicates a selected area--Oklahoma]
•  Distribution (affiliation) vs total (mean-citation count) of the top 75 information scientists. 
  •  Non-geographic data is "spatialized" by Multi-dimensional Scaling (MDS). Distance (or proximity) is derived from mutual citation (co-citation), and implies similar interests or affiliation.
  • Elevations are extruded according to mean citation counts. 
•   A pretty but nonsensical topographical map of senses of the word "over"--no theoretical underpinning

Lexical semantics 

(Senses of the word "over" used throughout)

Source data--Graphs as Maps

• textual - Oxford English Dictionary (OED)

• OED Word overlaps: 
  • Shows all senses, linked by counts of words shared between the senses-only the most frequent words are displayed.
• OED Word links
  • Shows Head senses (categories) and words shared by those senses (parsed full text).

• relational Roget's Thesaurus (RIT)

• RIT hierarchy -- sub-trees of the full hierarchy
• Over senses - words plus categories  --
  • Is there a "central" sense?
  • Are there "main" words

• statistical (concordance/collocation; corpuses)

Methods of representation

• Matrices and graphs
• Multi-dimensional Scaling
  • MDS SPSS
  • GIS map from MDS ArcView
  • 3D MDS SPSS
• As 3D molecules - words as atoms

Some past methods

• T-Graphs, chains - Robert Bryan
  • equivalent to formal contexts, below.
• Brugman and Lakoff- Radial categories
  • ImageSchemes -- Trajectories and LandMarks
  • Radial categories - sense transforms - central sense?

Problems and ?Solutions

Complexity - limitations of software and hardware

Graph duals & Matrices

• RIT categories (senses, the other (dual) side of words)
• DUALS - two sides of the same coin - but more complex together. Galois connection models duality => Formal Concept Lattices
• Words and categories(senses) together - how to organize/arrange them?

Lattices -

• A latticeBoolean

Formal contexts

• A matrix - word/sense relation

Formal concepts

• Subset of "Over" synonyms as a lattice (automatic with 'Anaconda')
• throughout-related senses of over (by hand - with category labels)

Spatial Outputs

• Word-word relation with senses added - via MDS
• Sense-sense relation showing Word influence - via MDS
• Concept-centric - words AND senses per lattice - via MDS

Value Added?

• charts showing the numbers traditionally
• Toward spheres of Influence
• Tables may be displayed at the same time in GIS (concurrent views of data)
• MDS in 3 dimensions not so helpful - yet… MDS3d1.jpg MDS3d2.jpg MDS3d3.jpg
• synonymy of the senses (showing colour coding and ramping)

The Solution?

• Contours - the step before elevation surfaces
• wdcncptinfl. word-centric (influence3D_2.jpg)
• catcncptinfl sense-centric - showing the most influential senses
• wdcatnfl1 word-sense-centric
• cncptinfl.jpg concept-centric

Conclusion

• Without senses - VRML exports panoramic
• Same - Without over
• The final product? (sense 40:10:1 on the far side - a lot more work to go…)

Copyright L. John Old, April 1999