Classification with the pot–pot plot
- 106 Downloads
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.
KeywordsKernel density estimates Bandwidth choice Potential functions k-Nearest-neighbors classification \(\alpha \)-Procedure DD-plot \(DD\alpha \)-classifier
Mathematics Subject Classification62H30 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.
- Chang C-C, Lin C-J (2011) LIBSVM: a library for support vector machines. ACM Trans Intell Syst Technol 2: 27:1–27:27. Software available at http://www.csie.ntu.edu.tw/~cjlin/libsvm
- Cuesta-Albertos JA, Febrero-Bande M, de la Fuente MO (2016) The DD\(^G\)-classifier in the functional setting. arXiv:1501.00372
- Dutta S, Chaudhuri P, Ghosh AK (2012) Classification using localized spatial depth with multiple localization. Mimeo, New YorkGoogle Scholar
- Pokotylo O, Mozharovskyi P, Dyckerhoff R (2016) Depth and depth-based classification with R-package ddalpha. arXiv:1608.04109
- Serfling R (2006) Depth functions in nonparametric multivariate inference. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol 72Google Scholar