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University of Waterloo

1. Kennedy, Ian. Distance Measures for Probabilistic Patterns.

Degree: 2020, University of Waterloo

Numerical measures of pattern dissimilarity are at the heart of pattern recognition and classification. Applications of pattern recognition grow more sophisticated every year, and consequently we require distance measures for patterns not easily expressible as feature vectors. Examples include strings, parse trees, time series, random spatial fields, and random graphs [79] [117]. Distance measures are not arbitrary. They can only be effective when they incorporate information about the problem domain; this is a direct consequence of the Ugly Duckling theorem [37]. This thesis poses the question: how can the principles of information theory and statistics guide us in constructing distance measures? In this thesis, I examine distance functions for patterns that are maximum-likelihood model estimates for systems that have random inputs, but are observed noiselessly. In particular, I look at distance measures for histograms, stationary ARMA time series, and discrete hidden Markov models. I show that for maximum likelihood model estimates, the L2 distance involving the information matrix at the most likely model estimate minimizes the type II classification error, for a fixed type I error. I also derive explicit L2 distance measures for ARMA(p, q) time series and discrete hidden Markov models, based on their respective information matrices.

Subjects/Keywords: pattern recognition; information matrix; distance measure; maximum likelihood; time series; hidden Markov model

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Kennedy, I. (2020). Distance Measures for Probabilistic Patterns. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/15419

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Kennedy, Ian. “Distance Measures for Probabilistic Patterns.” 2020. Thesis, University of Waterloo. Accessed January 25, 2020. http://hdl.handle.net/10012/15419.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Kennedy, Ian. “Distance Measures for Probabilistic Patterns.” 2020. Web. 25 Jan 2020.

Vancouver:

Kennedy I. Distance Measures for Probabilistic Patterns. [Internet] [Thesis]. University of Waterloo; 2020. [cited 2020 Jan 25]. Available from: http://hdl.handle.net/10012/15419.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Kennedy I. Distance Measures for Probabilistic Patterns. [Thesis]. University of Waterloo; 2020. Available from: http://hdl.handle.net/10012/15419

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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