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.
Keywords for this software
References in zbMATH (referenced in 7 articles , 2 standard articles )
Showing results 1 to 7 of 7.
- Antoch, Jaromír; Prchal, Luboš; Sarda, Pascal: Combining association measures for collocation extraction using clustering of receiver operating characteristic curves (2013)
- Yao, Wei-Ting; Wu, Han-Ming: Isometric sliced inverse regression for nonlinear manifold learning (2013)
- Gatu, Cristian; McCullough, B.D.: Second special issue on statistical algorithms and software (2010)
- Wu, Han-Ming; Tien, Yin-Jing; Chen, Chun-Houh: GAP: a graphical environment for matrix visualization and cluster analysis (2010)
- Peltonen, Jaakko; Venna, Jarkko; Kaski, Samuel: Visualizations for assessing convergence and mixing of Markov chain Monte Carlo simulations (2009)
- van der Laan, Mark J.; Pollard, Katherine S.: A new algorithm for hybrid hierarchical clustering with visualization and the bootstrap (2003)
- Chen, Chun-Houh: Generalized association plots: Information visualization via iteratively generated correlation matrices (2002)
Further publications can be found at: http://gap.stat.sinica.edu.tw/Software/GAP/#References