A novel framework for quantifying nominal outlyingness

TL;DR

This paper introduces a new framework for measuring how outlying nominal data points are, using association rule ideas, which improves interpretability and performs well compared to existing methods.

Contribution

It provides a formal definition of nominal outlyingness and a novel, interpretable scoring framework based on association rule mining for outlier detection.

Findings

Framework performs comparably to state-of-the-art algorithms.

Outperforms existing methods in certain datasets.

Enhances interpretability of outlyingness scores.

Abstract

Outlier detection is an important data mining tool that becomes particularly challenging when dealing with nominal data. First and foremost, flagging observations as outlying requires a well-defined notion of nominal outlyingness. This paper presents a definition of nominal outlyingness and introduces a general framework for quantifying outlyingness of nominal data. The proposed framework makes use of ideas from the association rule mining literature and can be used for calculating scores that indicate how outlying a nominal observation is. Methods for determining the involved hyperparameter values are presented and the concepts of variable contributions and outlyingness depth are introduced, in an attempt to enhance interpretability of the results. The proposed framework is evaluated on both synthetic and publicly available data sets, demonstrating comparable performance to state-of-the-art frequent pattern mining algorithms and even outperforming them in certain cases. The ideas presented can serve as a tool for assessing the degree to which an observation differs from the rest of the data, under the assumption of sequences of nominal levels having been generated from a Multinomial distribution with varying event probabilities.