The Structural Representation of Three -Way Proximity Data
Koehn, Hans F.
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https://hdl.handle.net/2142/82135
Description
Title
The Structural Representation of Three -Way Proximity Data
Author(s)
Koehn, Hans F.
Issue Date
2007
Doctoral Committee Chair(s)
Hubert, Lawrence J.
Department of Study
Psychology
Discipline
Psychology
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Psychology, Psychometrics
Language
eng
Abstract
Scaling and clustering techniques are well-established statistical methods for generating continuous and discrete structural representations of the relationships between the row and column objects of proximity matrices. Most commonly, the representational structure is fit to the observed data through minimizing the least-squares loss function; traditional implementations rely typically on gradient or sub-gradient optimization. Alternatively, scaling and clustering can be reformulated as combinatorial data analytic tasks, solvable through discrete optimization strategies. We develop generalizations of combinatorial algorithms for analyzing individual differences through scaling and clustering three-way data that consist of collections of proximity matrices observed on multiple sources. We propose an approach derived from a deviation-from-the-mean principle. Order-constrained matrix decomposition can be regarded as a combinatorial data analytic meta-technique, providing a unifying framework for evaluating the differential merits of continuous and discrete structural representations of proximity matrices. We introduce a generalization of order-constrained matrix decomposition to accommodate three-way proximity data. Multiobjective programming, as an alternative approach to modelling three-way data, is presented, accompanied by a survey of existing applications in the psychometric literature.
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