Generalized association plots: Information visualization via iteratively generated correlation matrices Given a p-dimensional proximity matrix D p×p , a sequence of correlation matrices, 𝐑=(R (1) ,R (2) ,⋯), is iteratively formed from it. Here R (1) is the correlation matrix of the original proximity matrix D and R (n) is the correlation matrix of R (n-1) , n>1. This sequence was first introduced by L. L. McQuitty [Multivariate Behav. Res. 3, 465-477 (1968)], and R. L. Breiger, S. A. Boorman and P. Arabie [J. Math. Psychol. 12, 328-383 (1975)] developed an algorithm, CONCOR, based on their rediscovery of its convergence. The sequence 𝐑 often converges to a matrix R (∞) whose elements are +1 or -1. This special pattern of R (∞) partitions the p objects into two disjoint groups and so can be recursively applied to generate a divisive hierarchical clustering tree. While convergence is itself useful, we are more concerned with what happens before convergence. Prior to convergence, we note a rank reduction property with elliptical structure: when the rank of R (n) reaches two, the column vectors of R (n) fall on an ellipse in a two-dimensional subspace. The unique order of relative positions for the p points on the ellipse can be used to solve seriation problems such as the reordering of a Robinson matrix. A software package, Generalized Association Plots (GAP), is developed which utilizes computer graphics to retrieve important information hidden in the data or proximity matrices.

References in zbMATH (referenced in 11 articles , 2 standard articles )

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  1. Hahsler, Michael: An experimental comparison of seriation methods for one-mode two-way data (2017)
  2. Adhikari, Prem Raj; Vavpetič, Anže; Kralj, Jan; Lavrač, Nada; Hollmén, Jaakko: Explaining mixture models through semantic pattern mining and banded matrix visualization (2016)
  3. Gosnell, Denise K.; Berry, Michael W.: Using semidiscrete decomposition and vector space models to identify users of social networks. (2015)
  4. Antoch, Jaromír; Prchal, Luboš; Sarda, Pascal: Combining association measures for collocation extraction using clustering of receiver operating characteristic curves (2013)
  5. Yao, Wei-Ting; Wu, Han-Ming: Isometric sliced inverse regression for nonlinear manifold learning (2013)
  6. Gloria, Antoine: Numerical homogenization: survey, new results, and perspectives (2012)
  7. Gatu, Cristian; McCullough, B. D.: Second special issue on statistical algorithms and software (2010)
  8. Wu, Han-Ming; Tien, Yin-Jing; Chen, Chun-Houh: GAP: a graphical environment for matrix visualization and cluster analysis (2010)
  9. Peltonen, Jaakko; Venna, Jarkko; Kaski, Samuel: Visualizations for assessing convergence and mixing of Markov chain Monte Carlo simulations (2009)
  10. Van der Laan, Mark J.; Pollard, Katherine S.: A new algorithm for hybrid hierarchical clustering with visualization and the bootstrap (2003)
  11. Chen, Chun-Houh: Generalized association plots: Information visualization via iteratively generated correlation matrices (2002)

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