### Control point selection for dimensionality reduction by radial basis function

#### Abstract

This research deals with dimensionality reduction technique which is based on radial basis function (RBF) theory. The technique uses RBF for mapping multidimensional data points into a low-dimensional space by interpolating the previously calculated position of so-called control points. This paper analyses various ways of selection of control points (*regularized* *orthogonal least squares* method, *random* and *stratified* selections). The experiments have been carried out with 8 real and artificial data sets. Positions of the control points in a low-dimensional space are found by principal component analysis. We demonstrate that *random* and *stratified* selections of control points are efficient and acceptable in terms of balance between projection error (*stress*) and time-consumption.

DOI: 10.15181/csat.v4i1.1095

#### References

Amorim, E., Brazil, E., Nonato, L. & Samavati, F., 2014. Multidimensional projection with radial basis function and control points selection. Yokohama, pp. 209-216.

Bernatavičienė, J., Dzemyda, G., Kurasova, O. & Marcinkevičius, V., 2006. Strategies of selecting the basis vector set in the relative MDS. Technological and Economical Development of Economy, 12(4), pp. 283-288.

Bernatavičienė, J., Dzemyda, G. & Marcinkevičius, V., 2007. Conditions for optimal efficiency of relative MDS. Informatica, 18(2), pp. 187-202.

Borg, I. & Groenen, P., 2005. Modern Multidimensional Scaling: Theory and Applications. 2 ed. New York: Springer.

Chen, S., Cowan, C. & Grant, P., 1991. Orthogonal least squares learning algorithm for radial basis function networks.. IEEE Transactions on Neural Networks, 2(2), pp. 302-309.

de Silva, V. & Tenenbaum, J., 2004. Sparse multidimensional scaling using, Stanford.

Fodor, I. K., 2002. A survey of dimension reduction techniques.

Joia, P. et al., 2011. Local affine multidimensional projection. IEEE Transactions on Visualization and Computer Graphics, 17(12), pp. 2563-2571.

Naud, A. & Duch, W., 2000. Interactive data exploration using MDS. Proceedings of the Fifth Conference: Neural Networks and Soft Computing, pp. 255-260.

Paulauskienė, K. & Kurasova, O., 2014. Analysis of dimensionality reduction methods for various volume data (in Lithuanian). Information Technology. 19th Interuniversity Conference on Information Society and University Studies (IVUS 2014), pp. 114-121.

Paulovich, F. et al., 2011. Piecewise laplacian-based projection for interactive data exploration. Computer Graphics Forum, 30(3), pp. 1091–1100.

Paulovich, F. V., Silva, C. T. & Nonato, L. G., 2010. Two-phase mapping for projecting massive data sets. IEEE Transactions on Visualization and Computer Graphics, 16(6), pp. 1281-1290.

Sorzano, C., Vargas, J. & Pascual-Monato, A., Submitted on 12 Mar 2014. A survey of dimensionality reduction techniques. CoRR.

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