Johnson J H, 1981, "Q-discrimination analysis" Environment and Planning B 8(4) 419 – 434
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J H Johnson
Received 5 September 1981
Abstract. The Q-analysis algorithm is sometimes used as a clustering procedure, sometimes inappropriately. The data for clustering a set of elements in terms of a set of descriptors are assumed to be weighted in a scale. This paper shows the scale requires no structure beyond an ordinal order relation to allow a refinement of the q-connected component partitions by q-discrimination analysis. This requires a clear understanding of the meaning of the scale values when data are being collected, and gives a precise meaning to the slicing procedure of q-analysis. The relevant definitions of Q-analysis are presented through examples and the paper is mathematically self-contained. It concludes with two illustrative examples and discusses the questions they raise. Q-discrimination analysis is presented as part of the methodology of q-analysis, and to the extent that clustering is essentially concerned with set definition its application represents the beginning of a scientific enquiry rather than an end result.
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