Matrix comparison, Part 1: Motivation and important issues for measuring the resemblance between proximity measures or ordination results

Jesper W. Schneider and Pia Borlund

Journal of the American Society for Information Science and Technology, 2007, vol. 58, issue 11, 1586-1595

Abstract: The present two‐part article introduces matrix com‐parison as a formal means of evaluation in informetric studies such as cocitation analysis. In this first part, the motivation behind introducing matrix comparison to informetric studies, as well as two important issues influencing such comparisons, are introduced and discussed. The motivation is spurred by the recent debate on choice of proximity measures and their potential influence upon clustering and ordination results. The two important issues discussed here are matrix generation and the composition of proximity measures. The approach to matrix generation is demonstrated for the same data set, i.e., how data is represented and transformed in a matrix, evidently determines the behavior of proximity measures. Two different matrix generation approaches, in all probability, will lead to different proximity rankings of objects, which further lead to different ordination and clustering results for the same set of objects. Further, a resemblance in the composition of formulas indicates whether two proximity measures may produce similar ordination and clustering results. However, as shown in the case of the angular correlation and cosine measures, a small deviation in otherwise similar formulas can lead to different rankings depending on the contour of the data matrix transformed. Eventually, the behavior of proximity measures, that is whether they produce similar rankings of objects, is more or less data‐specific. Consequently, the authors recommend the use of empirical matrix comparison techniques for individual studies to investigate the degree of resemblance between proximity measures or their ordination results. In part two of the article, the authors introduce and demonstrate two related statistical matrix comparison techniques the Mantel test and Procrustes analysis, respectively. These techniques can compare and evaluate the degree of monotonicity between different proximity measures or their ordination results. As such, the Mantel test and Procrustes analysis can be used as statistical validation tools in informetric studies and thus help choosing suitable proximity measures.

Date: 2007
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