Classifying token frequencies using angular Minkowski $p$-distance

TL;DR

This paper explores the use of angular Minkowski p-distance for classifying token frequency data, demonstrating it can outperform cosine dissimilarity with proper parameter tuning.

Contribution

It introduces angular Minkowski p-distance as an alternative to cosine dissimilarity for token frequency classification and evaluates its effectiveness on the 20-newsgroups dataset.

Findings

Higher classification accuracy with suitable p values

Performance depends on hyperparameters like p, k, and weights

Angular Minkowski p-distance can outperform cosine dissimilarity

Abstract

Angular Minkowski $p$-distance is a dissimilarity measure that is obtained by replacing Euclidean distance in the definition of cosine dissimilarity with other Minkowski $p$-distances. Cosine dissimilarity is frequently used with datasets containing token frequencies, and angular Minkowski $p$-distance may potentially be an even better choice for certain tasks. In a case study based on the 20-newsgroups dataset, we evaluate clasification performance for classical weighted nearest neighbours, as well as fuzzy rough nearest neighbours. In addition, we analyse the relationship between the hyperparameter $p$, the dimensionality $m$ of the dataset, the number of neighbours $k$, the choice of weights and the choice of classifier. We conclude that it is possible to obtain substantially higher classification performance with angular Minkowski $p$-distance with suitable values for $p$ than with classical cosine dissimilarity.