49
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

Studies in the robustness of multidimensional scaling: euclidean models and simulation studies

, &
Pages 273-296 | Received 05 Nov 1980, Published online: 20 Mar 2007

References

  • Anderson , A.J.B. 1971 . Ordination methods in ecology . Journal of Ecology , 59 : 713 – 726 .
  • Bartlett , M.S. 1964 . The spectral analysis of two-dimensional point processes . Biometrika , 51 : 299 – 311 .
  • Benzecri , J.P. 1964 . Analyse factorielle des proximités . Publications de Institute de statistique de Université de Paris , 1 ( 13 ) : 235 – 282 .
  • Bloxom , B. 1978 . Constrained Multidimensional Scaling in N Spaces . Psychometrika , 43 ( 13 ) : 397 – 408 .
  • Chang , C.L. and Lee , R.C.T. 1973 . A heuristic relaxation method for non-linear mapping in cluster analysis . I.E.E.E. Trans on Systems, Man and Cybernetrics , 43 ( 13 ) : 197 – 200 .
  • Cohen , H.S. and Jones , L.E. 1974 . The effects of random error and sub-sampling of dimensions on recovery of configurations by non-metric multidimensional scaling . Psychometrika , 39 ( 13 ) : 69 – 90 .
  • Fletcher , R. and Reeves , C.M. 1964 . Function minimization by conjugate gradients . Computer Journal , 7 ( 13 ) : 149 – 153 .
  • Gower , J.C. 1971b . A general coefficient of similarity and some of its properties . Biometrika , 27 ( 13 ) : 857 – 871 .
  • Gower , J.C. 1971b . “ Statistical methods of comparing different rnultivanate analyses of the same data ” . In Mathematics in the Archaeological and Historical Sciences , Edited by: Hodson , R. , Kendall , D.G. and Tautu , P. 138 – 149 . Edinburgh : University Press .
  • Gower , J.C. and Banfield , C.F. . Goodness of fit criteria for hierarchical classifications and their empirical distributions . Processing of fhe 8th International Biometric Conference . 1974 , Constanza, Romania. Edited by: Corsten , L.C.A. and Postelnicu , T. pp. 347 – 361 . Bucharest : Romanlan Academy of Sciences Press .
  • Green , P.J. and Sibson , R. 1978 . Computing Dirichlet tessellations in the plane . Compurer Journal , 21 : 168 – 173 .
  • Isaac , P.D. and Poor , D.D.S. 1974 . On the determination of appropriate dimensionality in data with error . Psychometrika , 39 : 91 – 109 .
  • Kendall , D.G. 1971 . Construction of maps from "odd bits of information" . Nature , 231 : 158 – 159 .
  • Kendall , D.G. 1974 . The recovery of structure from fragmentary information . Philosophical Transactions of The Royal Society A. Mathematical and Physical Sciences , 279 : 168 – 173 .
  • Kruskal , J.B. 1964a . Multidimensional scaling by optimizing goodness-of-fit to a nonmetric hypothesis . Psychometrika , 29 : 1 – 27 .
  • Kruskal , J.B. 1964b . Non-metric multidimensional scaling: a numerical method . Psychometrika , 29 : 115 – 129 .
  • Lingoes , J.C. and Roskam , E.E. 1973 . A mathematical and empirical analysis of two multidimensional scaling algorithms . Psychometrika , 38 : 1 – 93 . Monograph Supplement
  • McGinley , W.C. and Sibson , R. 1973 . Dissociated random variables . Math. Proc. Camb. Phil. Soc , 77 : 185 – 188 .
  • McGinley , W.C. 1977 . Some Optimisation Problems in Data Analysis , University of Cambridge . Ph.D. thesis
  • Mardia , K.V. 1970 . Familie of Bivariate Distributions , London : Griffin .
  • Miles , R.E. 1970 . On the homogeneous planar Poisson process . Mathematical Biosciences , 6 : 85 – 127 .
  • Sammon , J.W. 1969 . A nonlinear mapping for data structure analysis . I.E.E.E Trans. on Computers , 18 : 401 – 409 .
  • Shepard , R.N. 1966 . Metric Structures in Ordinal Data . Journal of Mathematical Psychology , 3 : 287 – 315 .
  • Shepard , R.N. 1966 . Metric Structures in Ordinal Data . Journal of Mathematical Psychology , 3 : 287 – 315 .
  • Shepard , R.N. 1974 . Representation of structure in similarity data problems and prospects . Psychometrika , 39 : 323 – 355 .
  • Sherman , C.R. 1972 . Nonmetric multidimensional scaling. A Monte Carlo studu of the basic parameterts . Psychometrika , 37 : 323 – 355 .
  • Sibson , R. 1972 . Order Invariant methods for data analysis . Journal of the Royal Statistical Society Series B (Methodological) , 34 : 311 – 349 .
  • Sibson , R. 1978 . Studies in the robustness of mulridimensional scaling: procrustes statistics . Journal of the Royal Statistical Society Series B (Methodological) , 40 : 234 – 238 .
  • Sibson , R. 1979a . Studies in the robustness of mulridimensional scaling: perturbational analysis of classical scaling . Journal of the Royal Statistical Society Series B (Methodological) , 41 : 217 – 229 .
  • Sibson , R. 1980 . The Dirichlet tessellation as an aid in data analysis . Scandination Journal of Statistical , 7 : 14 – 20 .
  • Silverman , B.W. 1976 . Limit theorems for dissoctated random variables . Advance in Applied Prabability , 8 : 806 – 819 .
  • Spaeth , H.J. and Gu hery , S.B. 1969 . The use and utility of sthe monotone criterion in multidimensional scaling . Multivariate Behavioural Research , 4 : 501 – 515 .
  • Spence , I. 1970 . Local Minimum Solutions in Nonmetric Multidemensional Scaling . Pro. of the Stats Section of the American Statistical Association , 13 : 365 – 367 .
  • Spence , I. 1972 . A Monte Carlo Evaluation of three Nonmetric Multidimensional Scaling Algorithms . Psychometrika , 37 : 461 – 486 .
  • Spence , I. and Ogilvie , J.C. 1973 . A Table of Expected Stress Values for random rankings in Nonmetric Multidimensional Scaling . Mutitiate Behavioural Research , 8 : 511 – 517 .
  • Spence , I. and Graef , J. 1974 . The determination of the underlying dimensionality of an empirally obtained matrix of Proximates . Multivariate Behavioural Research , 9 : 331 – 341 .
  • Stenson , H.H. and Knoll , R.L. 1969 . Goodness of fit for random rankings in Kruskals nonmetric Scaling Procedure . Psychological Bulletin , 71 : 122 – 126 .
  • Wagenaar , W.A. and Padmas , P. 1971 . Quantitative Interruption of series in Kruskals nonmetric Scaling technique . British JOurnal of Mathematical and Statistical Psychology , 24 : 101 – 110 .
  • Young , F.W. 1970 . Nonmetric Multidimensional Scaling recovery of Metric Information . Psychomerika , 35 : 455 – 473 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.