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Blurred, helping the human brain to recognize the face more easily. So patterns are frequently overlayed, and this also happens in ecosystems, where it is actually the rule. One of the aims of pattern recognition is in fact to separate superimposed patterns by partitioning the data in an appropriate way. A well-known application of pattern recognition is (vegetation) mapping. The usually inhomogeneous and complex vegetation cover of an area is reduced to a limited number of types. 2 shows the centre of a peat bog in the Bavarian Pre-Alps.
1 Notations in contingency tables. a, b, c and d are frequency counts. 1. Name Formula Distance measure property Jaccard SJ = a a+b+c DJ = 1 − SJ metric Soerensen SS = 2a 2a+b+c DS = 1 − SS semimetric Simple maching SSM = DSM = 1 − SSM metric Dχ 2 = 1 − χ 2 metric Chi squared χ2 = a+d a+b+c+d ad−bc √ (a+b)(c+d)(a+c)(b+d) 2 The second is the Soerensen coefficient SS . This differs from the Jaccard coefficient in that common species have double weight. 667. e. the triangular unequality is violated), limiting its application in some methods.
The variance, however, remains unchanged. 4 EXAMPLE: TRANSFORMATION OF PLANT COVER DATA 23 Normalizing is a different method of transformation. Each element of the vector is divided by its (Euclidean) length. 0. 2, the vectors become more similar in many ways while the variances still differ. A most rigorous transformation is standardizing. This is a combination of centring and normalizing. 0. The length of the vector is equal to the square root of the number of elements. Standardization is used to compare different scaled measurements, such as temperature and the height of trees, for example.