Abstract
A technique for cluster analysis, known as the moment preservation method is found primarily in the engineering literature. The method appears to be motivated by mixture models. A brief description of this technique is as follows. If q clusters are to be determined, then 2q − 1 linearly independent functions of the data are calculated. (In many of the applications that I have encountered, these are the first 2q − 1 sample moments.) For univariate data, the values of these functions are used to determine thresholds. The thresholds are chosen so that these moments are preserved. For multivariate data, the thresholds are replaced by their natural analogue, linear manifolds. The theoretical properties of this process can be determined from a substantial body of mathematical analysis, known as the “Reduced Moment Problem”. These properties facilitate determining the solutions sets and their properties, including the determination of optimal solutions.
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Harris, B. (2003). The Moment Preservation Method of Cluster Analysis. In: Schwaiger, M., Opitz, O. (eds) Exploratory Data Analysis in Empirical Research. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55721-7_11
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DOI: https://doi.org/10.1007/978-3-642-55721-7_11
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