Page 52 - Lungshan Pottery Lunshanoid Research 1977 Paper

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On the other hand, basing the analysis on a matrix

of correlation coefficients, the distance between two

points (data units) also can be scaled in several dimen-

sions. The distances among data units can be easily

expounded on a pair of coordinates (two dimensions). But,

when there are more than 3 characters (variables), the

scaling of the distance Ibetween two data units becomes

more and more complicated. In Euclidean hyperspace, the

distance between two points (i.e. data units) is determined

by all their dimensions (i.e. characters). Thus, the

distance between 2 points in four dimensional space is

defined as dJ=(W v-W^)+(X i-X^)%(Y 1-Y^)+(Z^-Z^j . In an
L
n-space, a hyperspace of n dimensions, therefore, the maxi-

mum distance will be n (based on characters with maximal
values of unity). These multidimensional distances are

scaled independently by each pair of dimensions. Sometimes
the distribution of data units in each separate configura-

tion based on two dimensions is helpful in interpreting
certain phenomena in archaeology.

Neither similarity coefficients nor multidimensional

scaling can be calculated by hand efficiently. Fortunately,

nowadays the well-developed computer can execute these

complicated processes in a few seconds.