Skip to main content
SpringerLink
Log in

Marketing Applications of Sequencing and Partitioning of Nonsymmetric and/or Two-Mode Matrices

  • Conference paper
Data, Expert Knowledge and Decisions

Summary

Although various authors have provided improvements to the bond energy algorithm for seriation originally proposed by McCormick, Schweitzer, and White (1972), most of these approaches have limited the types of data that can be considered (e.g., by assuming only binary input). We return to the original algorithm, free of such restrictions, and demonstrate ways of markedly improving its computational efficiency as well as the solutions it produces. These improvements enable the algorithm to sequence survey data (e.g., respondents by products’ attributes) having several hundred columns and rows. Such runs require only a few hours on a personal computer. Following the successful sequencing of such matrices, it is straightforward to partition the rows and columns. We present a substantive application from marketing.

This work was supported by AT & T Information Systems through the Industrial Affiliates Program of the University of Illinois and a Fulbright Award to the first author, who was based while preparing this paper at the Department of Computer Science, University College Dublin.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Arabie P, Boorman SA (1982) Blockmodeling: Developments and Prospects, in: Hudson H (ed.) Classifying Social Data: New Applications of Analytic Methods for Social Science Research. Jossey-Bass, San Francisco, pp 177–198

    Google Scholar 

  • Arabie P, Carroll JD (1985) Product Positioning Via INDCLUS, an Individual Differences Approach to Overlapping Clustering. Paper presented at the ORSA/TIMS Marketing Science Conference, Nashville, TN

    Google Scholar 

  • Arabie P, Carroll JD, DeSarbo W, Wind J (1981) Overlapping Clustering: A New Method for Product Positioning. Journal of Marketing Research 18: 310–317

    Article  Google Scholar 

  • Arabie P, Soli SD (1982) The Interface Between the Types of Regression and Methods of Collecting Proximity Data, in: Golledge RG, Rayner JN (eds.) Proximity and Preference: Problems in the Multidimensional Analysis of Large Data Sets. University of Minnesota Press, MN, pp 90–115

    Google Scholar 

  • Bass FM, Pessemier EA, Lehmann DR (1972) An Experimental Study of Relationships Between Attitudes, Brand Preference, and Choice. Behavioral Science 17: 532–541

    Article  Google Scholar 

  • Bhat MV, Haupt A (1976) An Efficient Clustering Algorithm. IEEE Transactions on Systems, Man, and Cybernetics 6: 61–64

    Google Scholar 

  • De Soete G, DeSarbo WS, Furnas GW, Carroll JD (1984a) Tree Representations of Rectangular Proximity Matrices, in: Degreef E, van Buggenhaut J (eds.) Trends in Mathematical Psychology. North-Holland, Amsterdam, pp 377–392

    Chapter  Google Scholar 

  • De Soete G, DeSarbo WS, Furnas GW, Carroll JD (1984b) The Estimation of Ultrametric Path Length Trees from Rectangular Proximity Data. Psychometrika 49: 289–310

    Article  Google Scholar 

  • DeSarbo WS (1982) GENNCLUS: New Models for General Nonhierarchical Clustering Analysis. Psychometrika 47: 449–475

    Article  Google Scholar 

  • DeSarbo WS, De Soete G (1984) On the Use of Hierarchical Clustering for the Analysis of Nonsymmetric Proximities. Journal of Consumer Research 11: 601–610

    Article  Google Scholar 

  • Fumas GW (1980) Objects and their Features: The Metric Analysis of Two-Class Data. Unpublished doctoral dissertation, Stanford University, Stanford, CA

    Google Scholar 

  • Garcia H, Proth JM (1986) A New Cross-Decomposition Algorithm: The GPM. Comparison with the Bond Energy Algorithm. Control and Cybernetics 15: 155–165

    Google Scholar 

  • Gower JC, Ross GJS (1969) Minimum Spanning Trees and Single Linkage Cluster Analysis. Applied Statistics 18: 54–64

    Article  Google Scholar 

  • Green PE, Tull DS (1978) Research for Marketing Decisions ( 4th ed ). Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

  • Harshman RA, Green PE, Wind Y, Lundy ME (1982) A Model for the Analysis of Asymmetric Data in Marketing Research. Marketing Science 1: 205–242

    Article  Google Scholar 

  • Hartigan JA (1975) Clustering Algorithms. Wiley, New York

    Google Scholar 

  • Hubert L (1973) Min and Max Hierarchical Clustering Using Asymmetric Similarity Measures. Psychometrika 38: 63–72

    Article  Google Scholar 

  • Hubert L, Schultz J (1976) Quadratic Assignment as a General Data Analysis Strategy. British Journal of Mathematical and Statistical Psychology 29: 190–241

    Article  Google Scholar 

  • Hutchinson JW (1986) Discrete Attribute Models of Brand Switching. Marketing Science 5: 350–371

    Article  Google Scholar 

  • Kirkpatrick S, Gelatt CD Jr., Vecchi MP (1983) Optimization by Simulated Annealing. Science 220: 671–680

    Article  Google Scholar 

  • Koopmans TC, Beckmann M (1957) Assignment Problems and the Location of Economic Activities. Econometrica 25: 53–76

    Article  Google Scholar 

  • Kusiak A, Vannelli A, Kumar KR (1986) Clustering Analysis: Models and Algorithms. Control and Cybernetics 15: 139–154

    Google Scholar 

  • Lattin JM (1987) A Model of Balanced Choice Behavior. Marketing Science 6: 48–65

    Article  Google Scholar 

  • Lattin JW, McAlister L (1985) Using a Variety-Seeking Model to Identify Substitute and Complementary Relationships Among Competing Products. Journal of Marketing Research 22: 330–339

    Article  Google Scholar 

  • Lenstra JK (1974) Clustering a Data Array and the Traveling-Salesman Problem. Operations Research 22: 413–414

    Article  Google Scholar 

  • MacQueen J (1967) Some Methods for Classification and Analysis of Multivariate Observations, in: Le Cam LM, Neyman J (eds.) Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability 1. University of California Press, Berkeley, pp 281–297

    Google Scholar 

  • McAlister L, Lattin JM (1984) Identifying Competitive Brand Relationships when Consumers Seek Variety. Marketing Science Institute (Tech. Rep. No. 84–105 ) Cambridge, MA

    Google Scholar 

  • McCormick WT Jr., Schweitzer PJ, White TW (1972) Problem Decomposition and Data Reorganization by a Clustering Technique. Operations Research 20: 993–1009

    Article  Google Scholar 

  • Moore WL, Pessemier EA, Lehmann DR (1986) Hierarchical Representations of Market Structures and Choice Processes through Preference Trees. Journal of Business Research 14: 371–386

    Article  Google Scholar 

  • Murtagh F (1985) Multidimensional Clustering Algorithms. Physica-Verlag, Vienna

    Google Scholar 

  • Novak TP, Stangor C (1987) Testing Competitive Market Structures: An Application of Weighted Least Squares Methodology to Brand Switching Data. Marketing Science 6: 82–97

    Article  Google Scholar 

  • Peay ER (1975) Grouping by Cliques for Directed Relationships. Psychometrika 40: 573–574

    Article  Google Scholar 

  • Punj G, Stewart DW (1983) Cluster Analysis in Marketing Research: Review and Suggestions for Application. Journal of Marketing Research 20: 134–148

    Article  Google Scholar 

  • Rao VR, Sabavala DJ (1981) Inference of Hierarchical Choice Processes from Panel Data. Journal of Consumer Research 8: 85–96.

    Article  Google Scholar 

  • Rao VR, Sabavala DJ, Zahorick AJ (1982) Market Structure Analysis Using Brand Switching Data: A Comparison of Clustering Techniques, in: Srivastava RK, Shocker A (eds.) Analytical Approaches to Product and Marketing Planning: The Second Conference. Marketing Science Institute, Cambridge, MA., pp 17–25

    Google Scholar 

  • Shepard RN, Arabie P (1979) Additive Clustering: Representation of Similarities as Combinations of Discrete Overlapping Properties. Psychological Review 86: 87–123

    Article  Google Scholar 

  • Sibson R (1973) SLINK: An Optimally Efficient Algorithm for the Single-Link Cluster Method. Computer Journal 16: 30–45

    Article  Google Scholar 

  • Slagle JR, Chang CL, Heller SR (1975) A Clustering and Data-Reorganizing Algorithm. IEEE Transactions on Systems, Man, and Cybernetics 5: 125–128

    Google Scholar 

  • Späth H (1980) Cluster Analysis Algorithms (U. Bull, Trans.). Ellis Horwood, Chichester, England

    Google Scholar 

  • Tucker LR (1964) The Extension of Factor Analysis to Three-Dimensional Matrices, in: Frederiksen N, Gulliksen H (eds.) Contributions to Mathematical Psychology. Holt, Rinehart, and Winston, New York, pp 109–127

    Google Scholar 

  • Wind Y (1978a) Introduction to Special Section on Market Segmentation Research. Journal of Marketing Research 15: 315–316

    Article  Google Scholar 

  • Wind Y (1978b) Issues and Advances in Segmentation Research. Journal of Marketing Research 15: 317–337

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University College Dublin, USA

    P. Arabie

  2. Department of Psychology, University of Illinois at Champaign, 603 E. Daniel St., Champaign, IL, 61820, USA

    S. Schleutermann, J. Daws & L. Hubert

Authors
  1. P. Arabie
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Schleutermann
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Daws
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. L. Hubert
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Entscheidungstheorie und Unternehmensforschung, Universität Karlsruhe (TH), Kollegiengebäude am Schloß, Bau III, 7500, Karlsruhe 1, Germany

    Wolfgang Gaul

  2. Institut für Informatik, Universität der Bundeswehr, Holstenhofweg 85, 2000, Hamburg 70, Germany

    Martin Schader

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Berlin · Heidelberg

About this paper

Cite this paper

Arabie, P., Schleutermann, S., Daws, J., Hubert, L. (1988). Marketing Applications of Sequencing and Partitioning of Nonsymmetric and/or Two-Mode Matrices. In: Gaul, W., Schader, M. (eds) Data, Expert Knowledge and Decisions. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73489-2_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-73489-2_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-73491-5

  • Online ISBN: 978-3-642-73489-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation