By John A. Hartigan
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The rank profiles algorithm transforms the values of each variable to ranks and in this way solves the scaling problem. ) The second important decision is the positioning of the variables. For a given order of variables, define a crossing to take piace if A(I,J)> A(K, J) but A(I, J 1) < A(K, J 1). The total number of crossings for all I K (1 s I < K S M) and all J (1 S J < N) is a measure of complexity of the profiles. ] The algorithm orders the variables to minimize the total crossings. Maurer suggested some parts of this algorithm.
And CROMPTON, C. W. (1971). " Taxon 20, 739-749. Electromicroscopy is used to measure 16 characteristics of 42 species of pollen. There are twelve continuous variables measuring geometric properties of the trilobed grains and four discrete variables measuring presence or absence of patterns, etc. This poses an interesting difficulty in the combination of different types of data. STEARN, W. T. (1971). " Bull. Brit. Museum (Nat. ) Bot. 4, 261-323. Uses numerical taxonomy conservatively in a revision of the genera.
SiEP 2A. For each variable, plot the cases along a horizontal line, identifying each case by its symbol. If a number of cases have identical values, their symbols should be placed vertically over this value as in a histogram. sin, 2B. The horizontal scale for each variable is initially set so that the minima for different variables coincide and the maxima coincide, approximately. STEP 2c. The vertical positions of the horizontal scales for each variable are assigned so that "similar" variables are in adjacent rows.