Interpoint Distance Classification of High Dimensional Discrete Observations

Abstract

Summary Classification is a multivariate technique that is concerned with allocating new observations to two or more groups. We use interpoint distances to measure the closeness of the samples and construct new rules for high dimensional classification of discrete observations. Applicable to high dimensional data, the new method is non‐parametric and uses test‐based classification with permutation testing. We propose a modification of a test‐based rule to use relative values with respect to the training samples baseline. We compare the proposed rule with parametric methods, such as likelihood ratio rule and modified linear discriminate function, and non‐parametric techniques such as support vector machine, nearest neighbour and depth‐based classification, under multivariate Bernoulli, multinomial and multivariate Poisson distributions.

Interpoint distances: Applications, properties, and visualization

“…which is the same as the marginal distribution in Equation (20). We obtain different multivariate distributions by using different values for a, a, and n. Table 2 shows the four prominent members of this family.…”

“…Moreover, IPDs provide a method of dealing with high‐dimensional problems. These applications include classification, 20 tests of equality of distribution functions, 1 and tests of mixture distributions 6 . Guo and Modarres 21 offer tests of the equality of distribution functions for matrix distributions based on the Frobenius norm.…”

“…The observation Z is classified as π x if PV 1 <PV 2 . Guo and Modarres 20 utilize IPDs to measure the closeness of the samples and construct new rules for high‐dimensional classification of discrete observations. Applicable to high‐dimensional data, their method is nonparametric and uses test‐based classification with permutation testing.…”

Graphical Comparison of High‐Dimensional Distributions

“…Song and Modarres (2019) use IPDS to test for the homogeneity of multivariate mixture models. (Guo & Modarres, 2018) use IPDs to classify high dimensional discrete observations. These tests are all based on the IPDs and applicable when because IPDs are always one‐dimensional irrespective of the value of .…”

Interpoint Distance Test of Homogeneity for Multivariate Mixture Models

“…Baringhaus & Franz (2004), Rosenbaum (2005) and Jurecková & Kalina (2012) utilise IPDs to construct tests for the general two-sample problem. Guo & Modarres (2018) use IPDs to classify high dimensional discrete observations.…”