## Conclusion

After struggling with the problem of representing structure in similarity data for over 20 years, I find that a number of challenging problems still remain to be overcome—even in the simplest case of the analysis of a single symmetric matrix of similarity estimates. At the same time, I am more optimistic than ever that efforts directed toward surmounting the remaining difficulties will reap both methodological and substantive benefits. The methodological benefits that I forsee include both an improved efficiency and a deeper understanding of “discovery” methods of data analysis. And the substantive benefits should follow, through the greater leverage that such methods will provide for the study of complex empirical phenomena—perhaps particularly those characteristic of the human mind.

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Presidential address delivered before the annual meeting of the Psychometric Society at Stanford University on March 28, 1974 (in a somewhat revised form necessarily, for purposes of publication, with more words and fewer pictures). Much of the work surveyed in this paper was supported by the Bell Telephone Laboratories, during my eight years as a member of the technical staff there, and by grants (principally, GS-1302, GS-2283, and GB-31971X) from the National Science Foundation, during my subsequent eight years at Harvard and at Stanford. I wish to acknowledge, too, the important contributions to this work made by my many students and associates during these 16 years including, particularly, Doug Carroll, Jih-Jie Chang, Steve Johnson, and Joe Kruskal (at the Bell Laboratories) and Phipps Arabie, Glen Crawford, and Jim Cunningham (at Stanford). Finally, I am indebted to Sherry Huntsberger for suggestions and extensive help in connection with the preparation of the paper itself, and to Bert Green for useful editorial comments.

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Shepard, R.N. Representation of structure in similarity data: Problems and prospects.
*Psychometrika* **39, **373–421 (1974). https://doi.org/10.1007/BF02291665

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### Keywords

- Data Analysis
- Public Policy
- Statistical Theory
- Deep Understanding
- Similarity Data