The Structural Representation of Three -Way Proximity Data

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Psychology

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Koehn, Hans F.

Contributors dc:contributor

• Hubert, Lawrence J.

• Psychology, Psychometrics

Language dc:language

eng

Identifier

(MiAaPQ)AAI3290276

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/82135