By Fielding A
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Additional info for Clusterand Classification Techniques for the Biosciences
0). The loadings, or weights, of each variable control the contributions that they make to the component scores. Because the variables share the same scale it is easy to interpret their relative importance. For example, v4 and v5 make only minor contributions to the ﬁrst component, and more major contributions to the second component. The variables making the most important contribution to each component have their loading shown in bold. 3 are considered important. In a real example the next stage would be an attempt to assign some name to the combination of variables associated with a component.
The following examples attempt to explain the importance, and role, of eigen values and eigen vectors using a mainly graphical description. Imagine what a three-dimensional scatter plot of three uncorrelated variables (x, y and z) would look like. If the three variables share the same measurement scale the points would form a circular cloud (the shape of a tennis ball). 1) has three dimensions that are all the same length (the diameter of the cloud). 1 Three-dimensional scatter plot of three uncorrelated variables.
One of the main aims of these analyses is to discover if there is some underlying structure to the data, perhaps represented by clusters of cases. They also offer the opportunity to identify relationships between cases that possibly represent recognisable temporal patterns such as those found in developmental pathways or species changes following changes to ecological management practices. g. cities), but in reduced dimensions (typically two or three). This is achieved by ﬁnding a conﬁguration of points, in Euclidean space, such that the distance matrix (Dc) of this new conﬁguration is a reasonable match to Dm.
Clusterand Classification Techniques for the Biosciences by Fielding A