We assess the performance of a new clustering method for Hierarchical Factor Classification of variables, which is based on the evaluation of the least differences among representative variables of groups, as defined by a set of two-dimensional Principal Components Analysis. As an additional feature the method gives at each step a principal plane where both grouped variables and units, as seen only by these variables, can be projected. We compare the method results with both single and complete linkage clustering, applied to simulated data with known correlation structure and we evaluate the results with a coherence measure based on the entropy between the expected partitions and those found by the methods. We found that the Hierarchical Factor Classification method performed as good as, and in some cases better than, both single and complete linkage clustering in detecting the known group structures in simulated data, with the advantage that the groups of variables and the units can be viewed on principal planes where usual interpretations apply.
Anderberg, M.R. 1973. Cluster Analysis for Applications . Academic Press, New York
Anderberg M.R. , '', in Cluster Analysis for Applications , (1973 ) -.
Camiz, S., J.J. Denimal and V.D. Pillar. 2006. Hierarchical factor classification of quantitative variables and count data. Community Ecology 7: 165–179.
Pillar V.D. , 'Hierarchical factor classification of quantitative variables and count data ' (2006 ) 7 Community Ecology : 165 -179 .
Denimal, J.J. 2001. Hierarchical Factorial Analysis . Proceedings of the 10 th International Symposiumon Applied Stochastic Models and Data Analysis. Compiègne, 12–15 Juin 2001.
Florek, K., J. Lukaszewicz, J. Perkal, H. Steinhaus and S. Zubrzycki. 1951. Sur la liason et la division des points d’un ensemble fini. Colloquium Mathematicae 2: 282–285.
Zubrzycki S. , 'Sur la liason et la division des points d’un ensemble fini ' (1951 ) 2 Colloquium Mathematicae : 282 -285 .
Ganeshanandam, S. and W.J. Krzanowski. 1990. Error-rate estimation in two-group discriminant analysis using linear discriminant function. Journal of Statistical Computation and Simulation 36: 157–175.
Krzanowski W.J. , 'Error-rate estimation in two-group discriminant analysis using linear discriminant function ' (1990 ) 36 Journal of Statistical Computation and Simulation : 157 -175 .
Gordon, A.D. 1999. Classification . 2nd ed. Chapman and Hall, London.
Gordon A.D. , '', in Classification , (1999 ) -.
Lance, G.N. and W.T. Williams. 1967. A general theory of classificatory sorting strategies. I. Hierarchical systems. Computer J . 9: 373–380.
Williams W.T. , 'A general theory of classificatory sorting strategies. I. Hierarchical systems ' (1967 ) 9 Computer J : 373 -380 .
Legendre, P. and L. Legendre. 1998. Numerical Ecology , 2nd English edition. Elsevier, Amsterdam.
Legendre L. , '', in Numerical Ecology , (1998 ) -.
Lerman, I.C. 1991. Foundations of the likelihood linkage analysis ( LLA ) classification method. Applied Stochastic Models and Data Analysis 7: 63–76.
Lerman I.C. , 'Foundations of the likelihood linkage analysis (LLA) classification method ' (1991 ) 7 Applied Stochastic Models and Data Analysis : 63 -76 .
Milligan, G.W. and M.C. Cooper. 1985. An examination of procedures for determining the number of clusters in a data set. Psychometrika 50: 159–179.
Cooper M.C. , 'An examination of procedures for determining the number of clusters in a data set ' (1985 ) 50 Psychometrika : 159 -179 .
Orlóci, L. 1991. Entropy and Information . SPB Academic Publishing, The Hague.
Orlóci L. , '', in Entropy and Information , (1991 ) -.
Peres-Neto, P.R. and D.A. Jackson. 2001. How well do multivariate datasets match? The advantages of a Procrustean superimposition approach over the Mantel test. Oecologia 129: 169–178.
Jackson D.A. , 'How well do multivariate datasets match? The advantages of a Procrustean superimposition approach over the Mantel test ' (2001 ) 129 Oecologia : 169 -178 .
Pillar, V.D. 1999. The bootstrapped ordination re-examined. J. Veg. Sci. 10: 895–902.
Pillar V.D. , 'The bootstrapped ordination re-examined ' (1999 ) 10 J. Veg. Sci. : 895 -902 .
Pillar, V.D. 2006. MULTIV: Multivariate Exploratory Analysis, Randomization Testing and Bootstrap Resampling, User’s Guide v. 2.4 . Universidade Federal do Rio Grande do Sul, Porto Alegre.
Pillar V.D. , '', in MULTIV: Multivariate Exploratory Analysis, Randomization Testing and Bootstrap Resampling, User’s Guide v. 2.4 , (2006 ) -.
Pillar, V.D. and L. Orlóci. 1996. On randomization testing in vegetation science: multifactor comparisons of relevé groups. J. Veg. Sci. 7: 585–592.
Orlóci L. , 'On randomization testing in vegetation science: multifactor comparisons of relevé groups ' (1996 ) 7 J. Veg. Sci. : 585 -592 .
Podani, J. 2000. Introduction to the Exploration of Multivariate Biological Data . Backhuys, Leiden.
Podani J. , '', in Introduction to the Exploration of Multivariate Biological Data , (2000 ) -.
SAS Institute. 1999. SAS Online Doc, Version 8 . SAS Institute Inc, Cary, North Carolina.
'', in SAS Online Doc, Version 8 , (1999 ) -.
Sneath, P.H.A. 1957. The application of computers to taxonomy. J. Gen. Microbiol. 17: 201–226.
Sneath P.H.A. , 'The application of computers to taxonomy ' (1957 ) 17 J. Gen. Microbiol. : 201 -226 .
Sørensen, T. 1948. A method for establishing groups of equal amplitude in plant sociology based on similarity of species content and its application to analyses of the vegetation on Danish commons. Biologiske Skrifter 5(4): 1–34.
Sørensen T. , 'A method for establishing groups of equal amplitude in plant sociology based on similarity of species content and its application to analyses of the vegetation on Danish commons ' (1948 ) 5 Biologiske Skrifter : 1 -34 .
Vigneau, E., E.M. Qannari, K. Sahmer and D. Ladiray. 2006. Classification de variables autour de composantes latentes. Rev. Statistique Appliquée 54(1): 27–45.
Ladiray D. , 'Classification de variables autour de composantes latentes ' (2006 ) 54 Rev. Statistique Appliquée : 27 -45 .
Ward, J.H. 1963. Hierarchical grouping to optimize an objective function. J. Amer. Stat. Assoc. 58: 236–244.
Ward J.H. , 'Hierarchical grouping to optimize an objective function ' (1963 ) 58 J. Amer. Stat. Assoc. : 236 -244 .