Abstract
Widely-used cluster analysis methods such as K-means and spectral clustering require some measures of (pairwise) distance on the multivariate space. Unfortunately, distances are often dependent on the scales of the variables. In applications, this can become a crucial point. Here we propose an accelerated K-means technique that consists of two steps. First, an appropriate weighted Euclidean distance is established on the multivariate space. This step is based on univariate assessments of the importance of the variables for the cluster analysis task. Here, additionally, one gets a crude idea about what the number of clusters K is at least. Subsequently, a fast K-means step follows based on random sampling. It is especially suited for the purpose of data reduction of massive data sets. From a theoretical point of view, it looks like MacQueen’s idea of clustering data over a continuous space. However, the main difference is that our algorithm examines only a random sample in a single pass. The proposed algorithm is used to solve a segmentation problem in an application to ecology.
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Mucha, HJ., Bartel, HG. (2012). An Accelerated K-Means Algorithm Based on Adaptive Distances. In: Gaul, W., Geyer-Schulz, A., Schmidt-Thieme, L., Kunze, J. (eds) Challenges at the Interface of Data Analysis, Computer Science, and Optimization. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24466-7_5
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DOI: https://doi.org/10.1007/978-3-642-24466-7_5
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