Identifying Multiple Cluster Structures in a Data Matrix

References

• Arabie , P. and Carroll , J. D. 1980 . MAPCLUS: a mathematical programming approach to fitting the ADCLUS model . Psychometrika , 45 : 211 – 235 .
   Google Scholar
• Berry , K. J. 1982 . Algorithm AS 179. Enumeration of all permutations of multi-sets with fixed repetition numbers . Applied Statistics , 31 : 169 – 173 .
   Google Scholar
• Bowman , K. O. and Shenton , L. R. 1982 . “ Approximations to distributions ” . In Encyclopedia of Statistical Sciences Edited by: Kotz , S. and Johnson , N. L. Vol. 1 , 107 – 118 . New York : Wiley .
   Google Scholar
• Boyett , J. M. 1979 . Algorithm AS 144. Random R × C tables with given row and column totals . Applied Statistics , 28 : 329 – 332 .
   Google Scholar
• Brennan , R. L. and Light , R. J. 1974 . Measuring agreement when two observers classify people into categories not defined in advance . British Journal of Mathematical and Statistical Psychology , 27 : 154 – 163 .
   Google Scholar
• Brook , R. J. and Stirling , W. D. 1984 . Agreement between observers when the categories are not specified in advance . British Journal of Mathematical and Statistical Psychology , 37 : 271 – 282 .
   Google Scholar
• Carroll , J. D. and Arabie , P. 1983 . INDCLUS: an individual differences generalization of the ADCLUS model and the MAPCLUS algorithm . Psychometrika , 48 : 157 – 169 .
   Google Scholar
• Costanzo , C. M. , Hubert , L. J. and Golledge , R. G. 1983 . A higher moment for spatial statistics . Geographical Analysis , 15 : 347 – 351 .
   Google Scholar
• De Soete , G. , DeSarbo , W. S. and Carroll , J. D. 1985 . Optimal variable weighting for hierarchical clustering: an alternating least-squares algorithm . Journal of Classification , 2 : 173 – 192 .
   Google Scholar
• DeSarbo , W. S. , Carroll , J. D. , Clark , L. A. and Green , P. E. 1984 . Synthesized clustering: a method for amalgamating alternative clustering bases with differential weighting of variables . Psychometrika , 49 : 57 – 78 .
   Google Scholar
• Fisher , N. I. , Mammen , E. and Marron , J. S. 1994 . Testing for multimodality . Computational Statistics and Data Analysis , 18 : 499 – 512 .
   Google Scholar
• Fowlkes , E. B. , Gnanadesikan , R. and Kettenring , J. R. 1988 . Variable selection in clustering . Journal of Classification , 5 : 205 – 228 .
   Google Scholar
• Gnanadesikan , R. , Kettenring , J. R. and Tsao , S. L. 1995 . Weighting and selection of variables for cluster analysis . Journal of Classification , 12 : 113 – 136 .
   Google Scholar
• Gordon , A. D. 1990 . Constructing dissimilarity measures . Journal of Classification , 7 : 257 – 269 .
   Google Scholar
• Gordon , A. D. 1996 . “ Hierarchical classification ” . In Clustering and Classification Edited by: Arabie , P. , Hubert , L. J. and De Soete , G. 65 – 121 . Singapore : World Scientific .
   Google Scholar
• Gordon , A. D. 1999 . Classification. 2nd ed. Boca Raton : Chapman and Hall/CRC .
   Google Scholar
• Gordon , A. D. and Vichi , M. 1998 . Partitions of partitions . Journal of Classification , 15 : 265 – 285 .
   Google Scholar
• Green , P. E. , Carmone , F. J. and Kim , J. 1990 . A preliminary study of optimal variable weighting in k-means clustering . Journal of Classification , 7 : 271 – 285 .
   Google Scholar
• Hansen , P. and Jaumard , B. 1997 . Cluster analysis and mathematical programming . Mathematical Programming , 79 : 191 – 215 .
   Google Scholar
• Hansen , P. , Jaumard , B. and Sanlaville , E. 1994 . “ Partitioning problems in cluster analysis: a review of mathematical programming approaches ” . In New Approaches in Classification and Data Analysis Edited by: Diday , E. , Lechevallier , Y. , Schader , M. , Bertrand , P. and Burtschy , B. 228 – 240 . Berlin : Springer-Verlag .
   Google Scholar
• Hartigan , J. A. and Hartigan , P. M. 1985 . The dip test of unimodality . The Annals of Statistics , 13 : 70 – 84 .
   Google Scholar
• Hartigan , P. M. 1985 . Algorithm AS 217. Computation of the dip test for unimodality . Applied Statistics , 34 : 320 – 325 .
   Google Scholar
• Hohenegger , J. 1986 . Weighted standardization. A general data transformation method preceding classification procedures . Biometrical Journal , 3 : 295 – 303 .
   Google Scholar
• Hubert , L. and Arabie , P. 1985 . Comparing partitions . Journal of Classification , 2 : 193 – 218 .
   Google Scholar
• Johnson , N. L. , Kotz , S. and Balakrishnan , N. 1995 . Continuous Univariate Distributions Vol. 2. , New York : Wiley .
   Google Scholar
• Krieger , A. M. and Green , P. E. 1999 . A generalized Rand-index method for consensus clustering of separate partitions of the same data base . Journal of Classification , 16 : 63 – 89 .
   Google Scholar
• Mielke , P. W. 1978 . Clarification and appropriate inferences for Mantel and Valand's nonparametric multivariate analysis technique . Biometrics , 34 : 277 – 282 .
   Google Scholar
• Mielke , P. W. 1979 . “ On asymptotic nonnormality of null distributions of MRPP statistics ” . In Communications in Statistics—Theory and Methods A8:1541–1550 (errata: 1981, A10, 1795 and 1982, A11, 847
   Google Scholar
• Mielke , P. W. , Berry , K. J. and Johnson , E. S. 1976 . “ Multi-response permutation procedures for a priori classifications ” . In Communications in Statistics—Theory and Methods 1409 – 1424 . A5
   Google Scholar
• Mielke , P. W. and Berry , K. K. 2001 . Permutation Methods. A Distance Function Approach New York : Springer-Verlag. .
   Google Scholar
• Milligan , G. W. 1989 . A validation study of a variable weighting algorithm for cluster analysis . Journal of Classification , 6 : 53 – 71 .
   Google Scholar
• Milligan , G. W. 1996 . “ Clustering validation: results and implications for applied analyses ” . In Clustering and Classification Edited by: Arabie , P. , Hubert , L. J. and De Soete , G. 341 – 375 . Singapore : World Scientific .
   Google Scholar
• Milligan , G. W. and Cooper , M. C. 1985 . An examination of procedures for determining the number of clusters in a data set . Psychometrika , 50 : 159 – 179 .
   Google Scholar
• Milligan , G. W. and Cooper , M. C. 1986 . A study of the comparability of external criteria for hierarchical cluster analysis . Multivariate Behavioral Research , 21 : 441 – 458 .
   Google Scholar
• Milligan , G. W. and Cooper , M. C. 1988 . A study of standardization of variables in cluster analysis . Journal of Classification , 5 : 181 – 204 .
   Google Scholar
• Mirkin , B. 1987 . Additive clustering and qualitative factor analysis methods for similarity matrices . Journal of Classification , 4 : 7 – 31 . (erratum: 1989, 6:271–272)
   Google Scholar
• Müller , D. W. and Sawitzki , G. 1991 . Excess mass estimates and tests for multimodality . Journal of the American Statistical Association , 86 : 738 – 746 .
   Google Scholar
• Patefield , W. M. 1981 . Algorithm AS 159. An efficient method of generating random R × C tables with given row and column totals . Applied Statistics , 30 : 91 – 97 .
   Google Scholar
• Rand , W. M. 1971 . Objective criteria for the evaluation of clustering methods . Journal of the American Statistical Association , 66 : 846 – 850 .
   Google Scholar
• Shepard , R. N. and Arabie , P. 1979 . Additive clustering representation of similarities as combinations of discrete overlapping properties . Psychological Review , 86 : 87 – 123 .
   Google Scholar
• Silverman , B. W. 1981 . Using kernel density estimation to investigate multimodality . Journal of the Royal Statistical Society B , 43 : 97 – 99 .
   Google Scholar
• Silverman , B. W. 1986 . Density Estimation for Statistics and Data Analysis London : Chapman and Hall. .
   Google Scholar
• Vichi , M. 1999 . One mode classification of a three way data matrix . Journal of Classification , 16 : 27 – 44 .
   Google Scholar