QUADRATIC ASSIGNMENT AS A GENERAL DATA ANALYSIS STRATEGY

TLDR

The quadratic assignment paradigm from operations research is a general approach to data analysis using proximity matrices, and problems are classified as static (testing a pre‑posed hypothesis) or non‑static (searching for relational structure without a prior conjecture). The paper aims to apply a general computational heuristic based on quadratic assignment to non‑static data‑analysis problems and to illustrate its relevance for behavioral science research tactics, particularly in psychology. The authors employ a search‑based heuristic for quadratic assignment, demonstrated through numerical examples in hierarchical clustering, homogeneous subset identification, linear and circular seriation, and discrete multidimensional scaling. The examples demonstrate the method’s ability to perform hierarchical clustering, identify homogeneous subsets, execute linear and circular seriation, and carry out discrete multidimensional scaling.

Abstract

The quadratic assignment paradigm developed in operations research is discussed as a general approach to data analysis tasks characterized by the use of proximity matrices. Data analysis problems are first classified as being either static or non‐static. The term ‘static’ implies the evaluation of a detailed substantive hypothesis that is posited without the aid of the actual data. Alternatively, the term ‘non‐static’ suggests a search for a particular type of relational structure within the obtained proximity matrix and without the statement of a specific conjecture beforehand. Although the static class of problems is directly related to several inference procedures commonly used in classical statistics, the major emphasis in this paper is on applying a general computational heuristic to attack the non‐static problem and in using the quadratic assignment orientation to discuss a variety of research tactics of importance in the behavioral sciences and, particularly, in psychology. An extensive set of numerical examples is given illustrating the application of the search procedure to hierarchical clustering, the identification of homogeneous object subsets, linear and circular seriation, and a discrete version of multidimensional scaling.