Chapter 2

Metrics, similarity, and sets

Abstract

In this chapter we cover an introduction to set theory, with common operations such as subset, intersection, union, set difference, complement and symmetric difference with examples from cybersecurity data. Set functions are also discussed, which leads us directly to the definition of a metric. We cover the variations of metric, including pseudometric, quasimetric, and semimetric. Similarities are also discussed. We then illustrate the metric on various sets, including strings, sets, Internet and cybersecurity specific metrics.

Keywords

Sets; Set operations; Functions; Metric; Similarity

The human eye can discern differences between two objects, but cannot necessarily quantify that difference. ...

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