Q mode distance coefficients

Distance coefficients are functions which take their maximum values (often 1) for two objects that are entirely different, and 0 for two objects that are identical over all descriptors. Distances, like similarities, (Section 7.3), are used to measure the Metric association between objects. Distance coefficients may be subdivided in three groups. properties The first group consists of metrics which share the following four properties:

4) triangle inequality: D (a, b) + D (b, c) > D (a, c). In the same way, the sum of two sides of a triangle drawn in Euclidean space is necessarily equal to or larger than the third side.

The second group of distances are the semimetrics (or pseudometrics). These coefficients do not follow the triangle inequality axiom. These measures cannot directly be used to order points in a metric or Euclidean space because, for three points (a, b and c), the sum of the distances from a to b and from b to c may be smaller than the distance between a and c. A numerical example is given is Subsection 2. Some authors prefer to talk about dissimilarity coefficients as the general expression and use the term distance only to refer to coefficients that satisfy the four metric properties.

Table 7.2 Some properties of distance coefficients calculated from the similarity coefficients presented in Section 7.3. These properties (from Gower & Legendre, 1986), which will be used in Section 9.2, only apply when there are no missing data.

Similarity

D = 1 - 5

D = 1 - S

D = V1 - S D

= J1 - S

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