Page 226 - MATLAB Recipes for Earth Sciences

222 9 Multivariate Statistics

ity. However, in heterogenic data sets consisting of a number of different
types of variables, it should be replaced the following measure.

2. Manhattan distance – In the city of Manhattan, one must walk on per-
pendicular avenues instead of diagonal crossing blocks. The Manhattan
distance is therefore the sum of all differences:

3. Correlation similarity coefficient – Here we use Pearson·s linear product-
moment correlation coefficient to compute the similarity of two objects.

This measure is used if one is interested in ratios between the variables mea-
sured on the objects. However, Pearson·s correlation coeffi cient is highly
sensitive to outliers and should be used with care (see also Chapter 4).

4. Inner-product similarity index – Normalizing the data vectors to one and
computing the inner product of these yields another important similarity
index. This is often used in transfer function applications. In this example,

a set of modern flora or fauna assemblages with known environmental
preferences is compared with a fossil sample to reconstruct the environ-
mental conditions in the past.

The inner product similarity varies between 0 and 1. A zero value sug-
gests no similarity and a value of one represents maximum similarity.
Transfer functions describe the similarity between the fossil sample and
all modern samples. The modern samples with the highest similarities are
then used to compute an estimate of the environmental conditions during
the existence of the fossil organisms.