By Leonard Kaufman
An creation to the sensible program of cluster research, this article provides a variety of tools which jointly can take care of such a lot purposes. those tools are selected for his or her robustness, consistency and common applicability. Discusses the most ways to clustering and gives counsel in settling on among the on hand tools. additionally discusses quite a few different types of info, together with interval-scaled and binary variables in addition to similarity info and explains how those should be reworked sooner than clustering. comprises a variety of workouts.
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Extra info for Finding groups in data: an introduction to cluster analysis
In the Rogers and Tanimoto (1960) formulas, the disagreements ( b c) carry twice the weight of the agreements ( a + d ) . On the other hand, Sokal and Sneath (1963) doubly weight the agreements. However, there is a simple monotone relation between all three coefficients, because the Rogers-Tanimoto dissimilarity can be written as a monotone function of the simple matching dissimilarity: + + + 2(b c) ( a + d ) + 2(b + c) = 2 1/((b + c)/(a + b + c + d ) ) + 1 (17) and the same holds for the dissimilarity coefficient proposed by Sokal and Sneath: b+c 2/((b 2 ( a + d ) + ( b + C) 1 + c)/(u + b + c + d)) - 1 (18) Therefore, it often makes little difference which of these three coefficients is used (especially if one applies a clustering algorithm that only depends on the ranks of the dissimilarities, such as the single linkage method discussed later).
The fifth column says whether the plant thrives best in dry (l),normal (2), or humid (3) soil. This is an ordinal variable, the states being ranked according to increasing moisture. The sixth column is someone’s preference ranking, going from 1 to 18. The code 18 next to the red rose indicates that this flower is best liked, whereas the code 1 is assigned to the plant least liked. This ordinal variable possesses many states, but each state occurs only once. The last columns list the height of the plants and the distances that should be left between them, both expressed in centimeters.
U s(i, j ) = - P and d ( i , j ) = P-U - P (Sokal and Michener, 1958). Here, u is the number of matches, that is, the number of variables for which objects i and j happen to be in the same TYPES OF DATA AND HOW TO HANDLE THEM 29 state. As before, p is the total number of variables (or, in a situation with missing values, the number of variables that are available for both i and j). Therefore, simple matching has exactly the same meaning as in the preceding section. For instance, it is invariant with respect to different codings of the variables because this does not affect the number of matches.
Finding groups in data: an introduction to cluster analysis by Leonard Kaufman