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Extending fuzzy and probabilistic clustering to very large data sets. (English) Zbl 1157.62435

Summary: Approximating clusters in very large (VL=unloadable) data sets has been considered from many angles. The proposed approach has three basic steps: (i) progressive sampling of the VL data, terminated when a sample passes a statistical goodness of fit test; (ii) clustering the sample with a literal (or exact) algorithm; and (iii) non-iterative extension of the literal clusters to the remainder of the data set. Extension accelerates clustering on all (loadable) data sets. More importantly, extension provides feasibility-a way to find (approximate) clusters-for data sets that are too large to be loaded into the primary memory of a single computer. A good generalized sampling and extension scheme should be effective for acceleration and feasibility using any extensible clustering algorithm. A general method for progressive sampling in VL sets of feature vectors is developed, and examples are given that show how to extend the literal fuzzy (\(c\)-means) and probabilistic (expectation-maximization) clustering algorithms onto VL data. The fuzzy extension is called the generalized extensible fast fuzzy \(c\)-means (geFFCM) algorithm and is illustrated using several experiments with mixtures of five-dimensional normal distributions.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
65C60 Computational problems in statistics (MSC2010)
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