Fractal reasoning

McGreggor, Brian Keith

Title:

Fractal reasoning

dc.contributor.advisor	Goel, Ashok K.
dc.contributor.author	McGreggor, Brian Keith
dc.contributor.committeeMember	Abowd, Gregory D.
dc.contributor.committeeMember	Corballis, Paul
dc.contributor.committeeMember	Essa, Irfan
dc.contributor.committeeMember	Thomaz, Andrea
dc.contributor.department	Interactive Computing
dc.date.accessioned	2014-01-13T16:48:52Z
dc.date.available	2014-01-13T16:48:52Z
dc.date.created	2013-12
dc.date.issued	2013-11-18
dc.date.submitted	December 2013
dc.date.updated	2014-01-13T16:48:52Z
dc.description.abstract	Humans are experts at understanding what they see. Similarity and analogy play a significant role in making sense of the visual world by forming analogies to similar images encountered previously. Yet, while these acts of visual reasoning may be commonplace, the processes of visual analogy are not yet well understood. In this dissertation, I investigate the utility of representing visual information in a fractal manner for computing visual similarity and analogy. In particular, I develop a computational technique of fractal reasoning for addressing problems of visual similarity and novelty. I illustrate the effectiveness of fractal reasoning on problems of visual similarity and analogy on the Raven’s Progressive Matrices and Miller’s Analogies tests of intelligence, problems of visual novelty and oddity on the Odd One Out test of intelligence, and problems of visual similarity and oddity on the Dehaene test of core geometric reasoning. I show that the performance of my computational model on these various tests is comparable to human performance. Fractal reasoning provides a new method for computing answers to such problems. Specifically, I show that the choice of the level of abstraction of problem representation determines the degree to which an answer may be regarded as confident, and that that choice of abstraction may be controlled automatically by the algorithm as a means of seeking that confident answer. This emergence of ambiguity and its remedy via problem re-representation is afforded by the fractal representation. I also show how reasoning over sparse data (at coarse levels of abstraction) or homogeneous data (at finest levels of abstraction) could both drive the automatic exclusion of certain levels of abstraction, as well as provide a signal to shift the analogical reasoning from consideration of simple analogies (such as analogies between pairs of objects) to more complex analogies (such as analogies among triplets, or larger groups of objects). My dissertation also explores fractal reasoning in perception, including both biologically-inspired imprinting and bistable perception. In particular, it provides a computational explanation of bistable perception in the famous Necker cube problem that is directly tied to the process of determining a confident interpretation via re-representation. Thus, my research makes two primary contributions to AI theories of visual similarity and analogy. The first contribution is the Extended Analogy By Recall (ABR*) algorithm, the computational technique for visual reasoning that automatically adjusts fractal representations to an appropriate level of abstraction. The second contribution is the fractal representation itself, a knowledge representation that add the notion of self-similarity and re-representation to analogy making.
dc.description.degree	Ph.D.
dc.format.mimetype	application/pdf
dc.identifier.uri	http://hdl.handle.net/1853/50337
dc.language.iso	en_US
dc.publisher	Georgia Institute of Technology
dc.subject	Analogy
dc.subject	Artificial intelligence
dc.subject	Knowledge representation
dc.subject	Fractals
dc.subject	Reasoning
dc.subject	Visual analogy
dc.subject.lcsh	Reasoning
dc.subject.lcsh	Artificial intelligence
dc.subject.lcsh	Similarity (Psychology)
dc.subject.lcsh	Fractal analysis
dc.title	Fractal reasoning
dc.type	Text
dc.type.genre	Dissertation
dspace.entity.type	Publication
local.contributor.advisor	Goel, Ashok K.
local.contributor.corporatename	College of Computing
local.contributor.corporatename	School of Interactive Computing
relation.isAdvisorOfPublication	986c5440-b322-4b1d-b6fe-fbc68f752f7f
relation.isOrgUnitOfPublication	c8892b3c-8db6-4b7b-a33a-1b67f7db2021
relation.isOrgUnitOfPublication	aac3f010-e629-4d08-8276-81143eeaf5cc
thesis.degree.level	Doctoral