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Greg Gibbon

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3 papers

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AIJ Journal 2001 Journal Article

A general formulation of conceptual spaces as a meso level representation

Janet Aisbett
Greg Gibbon

Representing cognitive processes remains one of the great research challenges. Many important application areas, such as clinical diagnosis, operate in an environment of relative magnitudes, counts, shapes, colours, etc. which are not well captured by current representational approaches. This paper presents conceptual spaces as a meso level representation for cognitive systems, between the high level symbolic representations and the subconceptual connectionist representations which have dominated AI. Conceptual spaces emphasize orders and measures and therefore naturally represent counts, magnitudes, and volumes. Taking Gärdenfors' decade-long investigation of conceptual spaces [Gärdenfors, Conceptual Spaces: The Geometry of Thought, MIT Press, 2000] as start point, the paper presents a formal foundation for conceptual spaces, shows how they are theoretically and practically linked to higher and lower representational levels, and develops dynamics which allow the orbits of states in the space to solve appropriate meso level reasoning tasks. Interpretations of conceptual spaces are given to illustrate the formal definitions and show the flexibility of the representation.

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AAAI Conference 1999 Conference Paper

Cognitive Classification

Janet Aisbett
Greg Gibbon
The University of Newcastle

Classification assigns an entity to a category on the basis of feature values encoded from a stimulus. Provided they are presented with sufficient training data, inductive classifier builders such as C4. 5 are limited by encoding deficiencies and noise in the data, rather than by the method of deciding the category. However, such classification techniques do not perform well on the small, dirty /or and dynamic data sets which are all that are available in many decision making domains. Moreover, their computational overhead may not be justified. This paper draws on conjectures about human categorization processes to design a frugal algorithm for use with such data. On presentation of an observation, case-specific rules are derived from a small subset of the stored examples, where the subset is selected on the basis of similarity to the encoded stimulus. Attention is focused on those features that appear to be most useful for distinguishing categories of observations similar to the current one. A measure of logical semantic information value is used to discriminate between categories that remain plausible after this. The new classifier is demonstrated against neural net and decision tree classifiers on some standard UCI data sets and shown to perform well.

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AIJ Journal 1994 Journal Article

A tunable distance measure for coloured solid models

Janet Aisbett
Greg Gibbon

People are willing to rank simple objects of different shape and colour on the basis of “similarity”. If machines are to reason about structure, this comparison process must be formalized. That is, a distance measure between formal object representations must be defined. If the machine is reasoning with information to be presented to a human, the distance measure needs to accord with human notions of object similarity. Since our perception of similarity is subjective and strongly influenced by situation, the measure should be tunable to particular users and contexts. This paper describes a distance measure between solid models which incorporates heuristics of the mental mappings humans use to compare objects. The first step is to formally represent objects in a way that reflects human visual segmentations. We use a modified boundary representation scheme in colour + physical space. The next step is to define a family of maps between these representations, motivated by considerations of how humans match shapes. The distance between two objects is essentially the cost of the lowest-cost map between them. The cost of a map incorporates a geometric measure of the smooth deformation required of edges and faces, a feature measure based on visually significant singular points, and a topological measure based on correspondence of visually significant vertices, edges and faces. Tunable features of the match are: the relative cost of ignoring parts of objects; the treatment of colour; and whether or not the distance measure is required to be rotation invariant. An important application for such distance measures is to the development of user-friendly query of CAD and image databases. Query-by-example depends on implementation of a concept of likeness between object models in the database which, to be useful, must reflect the user's concepts. Another important application for distance measures is in automatic recognition of objects into classes whose members are not identical, so that the concept that “this object is like object X” is required. In the common situation that classes are based on human perceptions of visual similarity, the distance measure between the class prototype and the object to be classified should reflect those human perceptions.

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