 
Summary: lanern Recognition. Vol. 24. No. 6. pp. 543553. l99l
Printed in Great Britain
I. INTRODUCTION
The mapping of multidimensional data is con
sidered as an important problem in data analysis.(l)
In general, mapping consists of finding a trans
formation h:R"+R2 that optimizes the criterion
J(*r, xz, X7r, I t, !2, . . . , ! u). The latter depends
on the given sample set of real vectors xr i = I,Z,
. . . , N in the ndimensional space Rn, &S well as on
their projections li,i: 1,2, . .. , N into R2. Due to
the fact that the planar images lr, i  1 ,2, .. . , N of
the data can be analysed by a hurnan observer the
mapping procedures are used as a tool for the inter
active exploratory data analysistesting the struc
tural similarity of data sets, cluster analysis and
designing the pattern classifiers.
The mapping transformations may be grouped
into linear and nonlinear. The nonlinear trans
formations(2'3) allow complicated mappings, but
