Statistical Papers

, Volume 60, Issue 3, pp 903–931 | Cite as

Classification with the pot–pot plot

  • Oleksii PokotyloEmail author
  • Karl Mosler
Regular Article


We propose a procedure for supervised classification that is based on potential functions. The potential of a class is defined as a kernel density estimate multiplied by the class’s prior probability. The method transforms the data to a potential–potential (pot–pot) plot, where each data point is mapped to a vector of potentials. Separation of the classes, as well as classification of new data points, is performed on this plot. For this, either the \(\alpha \)-procedure (\(\alpha \)-P) or k-nearest neighbors (k-NN) are employed. For data that are generated from continuous distributions, these classifiers prove to be strongly Bayes-consistent. The potentials depend on the kernel and its bandwidth used in the density estimate. We investigate several variants of bandwidth selection, including joint and separate pre-scaling and a bandwidth regression approach. The new method is applied to benchmark data from the literature, including simulated data sets as well as 50 sets of real data. It compares favorably to known classification methods such as LDA, QDA, max kernel density estimates, k-NN, and DD-plot classification using depth functions.


Kernel density estimates Bandwidth choice Potential functions k-Nearest-neighbors classification \(\alpha \)-Procedure DD-plot \(DD\alpha \)-classifier 

Mathematics Subject Classification

62H30 62G07 



We are grateful to Tatjana Lange and Pavlo Mozharovskyi for the active discussion of this paper. The work of Oleksii Pokotylo is supported by the Cologne Graduate School of Management, Economics and Social Sciences.

Supplementary material

362_2016_854_MOESM1_ESM.pdf (253 kb)
Supplementary material 1 (pdf 253 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Statistics and EconometricsUniversität zu KölnCologneGermany

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