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Global mapping analysis: stochastic approximation for multidimensional scaling
1Kazunori Yamaguchi Laboratory, Department of General Systems Studies, Graduate School of Arts and Sciences, The University of Tokyo, Japan. matsuda@graco.c.u-tokyo.ac.jp
Abstract:
In this paper, we propose global mapping analysis (GMA) as a new method to solve multidimensional scaling (MDS). By GMA, MDS is done by an online learning rule based on stochastic approximation. GMA need not directly calculate the disparity matrix for carrying out MDS, as Oja's PCA network do not calculate the correlation matrix. So, GMA is expected to be useful for multivariate data analysis on a large scale. Actually, it was verified by numerical experiments based on artificial data that GMA can work well even if the number of the attribute N is quite large (N=10,000.)