Dissertation Information for George Furnas
- George Furnas
- (Alias) George W. Furnas
- Stanford University (USA) (1980)
MPACT Status: Incomplete - Inspected
Title: OBJECTS AND THEIR FEATURES: THE METRIC REPRESENTATION OF TWO-CLASS DATA
Abstract: "This dissertation concerns the structural representation of Objects and their Features. If the co-occurrence of features mirrors the structure of object to object relationships, it should be possible to embed both objects and features in a single representation. Thus efforts here investigated tree and dimensional spaces for jointly representing object interrelationships, feature co-occurrence and object feature associations. In the resulting structures, objects would be placed close to their related features, as well as to similar objects.
Mathematical treatment consisted of focusing on the general problem of representing two distinct classes of entities (here, Objects and Features) from between-class data alone (the Object-Feature relationships.) Following this formulation, the current work can be seen as an extension of the Unfolding theory of Coombs (1950, 1964) to non-dimensional structures. Necessary and Sufficient conditions were derived for the representability of a between-class, or ""two-class"", proximity measure in various metric spaces (General Metric space, Ultrametric space, and Additive Tree space). The uniqueness of possible representations was also investigated.
Methods were then introduced for constructing Multidimensional, Ultrametric, and Additive tree representations from real two-class data. Consideration was also given to ways of constructing single representations from simultaneous use of independent sets of within and between class data.
Finally, the methods were demonstrated on two categories: COLORS and BIRDS. For both categories, Multidimensional Scaling, Hierarchical Clustering and Additive Tree analyses were done on three types of relevant data: Object-to-Object proximity, coming from judged similarity; Feature-to-Feature data, based on judged co-occurrence; and Object-to-Feature relationships, indicated by the frequency that a feature was listed for an object. Scaling solutions produced pure feature structures that seemed to mirror the pure inter-object structures. The two-class scalings, in part using methods developed here, seemed to resemble and synthesize both pure class structures. Primary discussion of results focused on the representational implications of common and distinctive features."
MPACT Scores for George Furnas
A = 2
C = 3
A+C = 5
T = 2
G = 1
W = 2
TD = 2
TA = 0
calculated 2010-09-27 21:46:11
Advisors and Advisees Graph