Biplots: a series of research papers culminated in the book with David
Hand, but the work continues. Recent developments include improvements in
representing scales on biplots axes for two-way tables and data matrixes.
A book is being written in collaboration with Niel LeRoux and Sugnet Gardner,
(University of Stallenbosch) on applications of a variety of biplots in many
fields of application.
Procrustes problems. Procrustes problems originated with factor rotation
but my interest is more concerned with matching two or more configurations.
Application areas are diverse including assessing responses of sensory
test panels, general comparisons in multivariate analysis, rather more
general than common principal components analysis and shape analysis. The first monograph (in collaboration with Garmt Dijksterhuis
University of Goningen) on Procrustes Problems has been published by Oxford University Press.
Distance methods. A long-standing interest which encompasses the general
area of multidimensional scaling. A book is planned in collaboration
with Michael Greenacre.
Generalized Canonical Correlation. A Procrustes form of generalized canonical correlation has been developed and synthesized with canonical variate analysis (in collaboration with Niel LeRoux and Sugnet Gardner, University of Stellenbosch).
Classification. Another long-standing interest recently renewed following a PhD examination in Leiden. Bart van Os and I are working on applications of dynamic programming algorithms for maximal predictive classification.
Gower, J.C. and Hand, D. J. (1996) Biplots. London: Chapman and Hall, 277 + xvi pp.
Gower, J.C. and Dijksterhuis, G. B. (2004) Procrustes Problems. Oxford University Press, 235 + xivpp.
Papers:
Denis, J-B., & Gower, J.C. (1994) Asymptotic covariances for the parameters of biadditive models. Utilitas Mathematica, 46, 193–205.
Gower, J.C. (1995) A general theory of biplots. In: Recent Advances in Descriptive Multivariate Analysis. Ed. W. J. Krzanowski. Oxford University Press. 283–303.
Gower, J.C. (1995) Distance-geometry and shape. In: Proceedings in Current Issues in Statistical Shape Analysis. Eds. K. V. Mardia and C. A. Gill. Leeds University Press, 11–17.
Gower, J.C. & Zielman B. (1998) Orthogonality and its approximation in the analysis of asymmetry. Linear algebra and its applications. 278, 183–193.
Gower, J.C. (1996) Multivariate and multidimensional analysis. In: Advances in Biometry. Eds. P. A. Armitage and H. A. David. J. A. Wiley, New York. 149–175.
Gower, J.C. and Harding S.A. (1998) Prediction regions for categorical variables. In: Vizualisation of Categorical Variables. Eds J. Blasius and M. J. Greenacre. Academic Press, London. 405–419.
Gower, J. C. (1997) Principal coordinates Analysis. In: Encyclopedia of Biostatistics. Eds. P. Armitage and T. Colton. J. A. Wiley, Chichester. 3514–8.
Gower, J. C. (1997) Similarity. In: Encyclopedia of Biostatistics. Eds. P. Armitage and T. Colton. J. A. Wiley, Chichester. 4097–100.
Gower, J. C. (1997) . Gower, J. C. (1998). Classification, Overview. In: Encyclopedia of Biostatistics. Eds. P. Armitage and T. Colton. J. A. Wiley, Chichester. 656–667.
Gower, J.C., Meulman, J. J., and Arnold, G. M. (1999). Non-metric linear biplots. Journal of Classification, 16, 181–196.
Gower, J.C., Hand, D. J. and Ngouenet, R.F. (1997). The development of interactive graphical software for a unified biplot methodology. Computing Science and Statisitics, 29, No. 2. Eds. E. J. Wegman and S. P. Azen. International Assosciation for Statistical Computing. Pasadena, California, 22–27.
Gower, J. C. (1998). The role of constraints in determining optimal scores. Statistics in Medicine. 17, 2709–2721.
Gower, J.C. and Krzanowski, W.J. (1998). Analysis of distance for structured multivariate data. Applied Statistics . 48, 505–519.
Gower, J.C. and Ross, G. J. S. (1998). Nonprobabilistic Classification. In: Advances in Data science and Classification. Eds. A. Rizzi, M. Vichi and H.-H. Bock. Springr, Berlin, 21–28.
Gower, J.C. (1999). Geometry Algebra and Data Analysis. The Mathematical Scientist, 24, 75–89.
Gower, J.C. (2000). Rank-one and rank-two departures from symmetry. Computational Statistics and Data Analysis. 33, 177–188.
Gower, J.C. (1999). Discussion of contrast between Psychometric and Statistical approaches to Multiway Data-Analysis. Bulletin of the International Statistical Institute, Tome 58, Book 3,101–102.
Gower, J.C. (2001). Procrustes Analysis. In: International Encyclopedia of the Social and Behavioral Sciences. Eds. N. J. Smelser and P. B. Baltes. Pergamon: Amsterdam etc. pp12141 - 12143.
Gower, J.C. (2002). Categories and Quantities In: Eds. S. Nishisato, Y. Baba, H. Bozdogan and K. Kanefuji, Measurement and Multivariate Analysis. Tokyo: Springer, 1 - 12. (Keynote Address)
Gower, J.C. (2002). A unified approach to oblique Procrustes problems. In: Eds. S. Nishisato, Y. Baba, H. Bozdogan and K. Kanefuji, In: Eds. H. Yanai, A. Okada, K. Shigemasu, Y. Kano and J. J. Meulman, New Developments in Psychometrics, Proceedings of The International Conference on Measurement and Multivariate Analysis. Tokyo: Springer, 371 - 380.
Gower, J.C. and de Rooij, M. (2003). A comparison of the multidimensional scaling of triadic and dyadic distances. Journal of Classification, 20, 115 - 136.
de Rooij, M. and Gower, J.C. (2003). The geometry of triadic distances, Journal of Classification, 20, 181 - 220.
Gower, J. C. (2003). Unified biplot geometry. In: Eds. Anuska Ferligoj and Andrej Mrvar, Metodoloski zvezki, 19. Ljubljana: FDV. 3-22.
Gower, J. C. (2003) Visualisation in Multivariate and Multidimensional Data Analysis. Bulletin of the International Statistical Institute 54, 101-104.
Gower, J.C. (2004). The geometry of biplot scaling. Biometrika, 91 705-714.
Gower, J.C. and Ngouenet, R.F. (2005) Nonlinearity effects in multidimensional scaling. Journal of multivariate analysis (in press).
Gower, J.C., Gardner, S. and LeRoux, N.J. (2006). A Synthesis of Canonical Variate Analysis, Generalised Canonical Correlation and Procrustes Analysis. CSDA, Special issue: Matrix Computations and Statistics - Edited by J.L. Barlow, M.W. Berry, A. Ruhe and H.Zha, 50 pp 107-134.
Gower, J.C. (2005). An application of the modified Leverrier-Faddeev algorithm to the singular value decomposition of block-circulant matrices and the spectral decomposition of symmetric block-circulant matrices. CSDA, Special issue: Matrix Computations and Statistics - Edited by J.L. Barlow, M.W. Berry, A. Ruhe and H. Zha, 50/1 pp 89-106.
Gower, J.C. (2005) Biplot. Encyclopedia of Statistics in Behavioral Science. Volume 1. Eds. Brian S Everitt and David C. Howell. John Wiley and Sons Ltd, Chichester. 163-164.
Gower, J.C. and Blasius, J. (2005) Multivariate prediction with nonlinear principal components analysis (Methodology). Quality and Quantity, 39, 359-372.
Blasius, J. and Gower, J.C. (2005) Multivariate prediction with nonlinear principal components analysis (Application). Quality and Quantity 39, 373-390.
Gower, J.C. (2006) Divided by a Common Language. In :Multiple Correspondence Analysis and Related Methods, Eds. Joerg Blasius and Michael Greenacre. Boca Raton, Forida, Chapman and Hall. 77-105.
Gower, J.C. (2006) Statistica Data Analytica Est et Aliter. Statistica Neerlandica, 60, 124-134.
Arnold, G.M., Gower, J.C., Gardner, S. and LeRoux, N.J. (2007) Biplots of Free-Choice-Profile Data in Generalized Procrustes Analysis. Applied Statistics (in press)
Albers, C.J., Critchley, F. and Gower, J.C. (2007) Group average representation in Euclidean distance cones. Edwin Diday Festschrift. Springer
Gower, J.C. and Greenacre, M. J. Distance Analysis (In progress)
Gower, J.C., Gardner, S. and LeRoux, N.J. Examples of Biplots (Provisional title - in progress)
Gardner, S., Gower, J. C. and LeRoux, N. J. (200?) Biplots with Free Choice profiling in generalized Procrustes analysis.
Gower, J.C. and de Rooij (200?) Model terms in biometrics and psychometrics.
Constantine, A. G. & Gower, J.C. Australian interstate migration 1881-1981.
Go to Statistics Group home page
Go to Open University home page
Last Updated September 2007