ERIC Number: ED205551
Record Type: RIE
Publication Date: 1980-Feb
Reference Count: 0
Extracting Undimensional Chains from Multidimensional Datasets: A Graph Theory Approach.
Yamomoto, Yoneo; Wise, Steven L.
An order-analysis procedure, which uses graph theory to extract efficiently nonredundant, unidimensional chains of items from multidimensional data sets and chain consistency as a criterion for chain membership is outlined in this paper. The procedure is intended as an alternative to the Reynolds (1976) procedure which is described as being exhaustive in the number of computer calculations it requires for chain extraction. Order analysis concepts are discussed and graphically represented before the general consistency index used in the procedure is introduced and defined. Procedures for chain extraction follow, in which it is stated that the dominance matrix can be reconsidered as a labeled digraph. From this digraph, all subgroups with perfect consistency are generated, and these in turn are used as starting points in the chain extraction process. The original dominance digraph is then reduced until the chain is found from each subgraph. The graph-theoretic algorithm may be carried out using a series of matrix manipulations performed on the dominance matrix. An illustrative example of the method is provided. In conclusion, possible extensions of the method are suggested. (Author/AEF)
Publication Type: Reports - Research
Education Level: N/A
Sponsor: Office of Naval Research, Arlington, VA. Personnel and Training Research Programs Office.
Authoring Institution: Illinois Univ., Urbana. Computer-Based Education Research Lab.
Identifiers: Data Sets; Graph Theory; Internal Consistency; Matrix Operations; Order Analysis