LCM from FCA Point of View: A CbO-style Algorithm with Speed-up Features

TL;DR

This paper reinterprets the LCM algorithm for frequent closed itemset enumeration within the framework of Formal Concept Analysis, revealing it as a variant of the Close-by-One algorithm with specific speed-up features for sparse data.

Contribution

It provides a formal FCA perspective on LCM, highlighting its similarities with Close-by-One and analyzing its speed-up features compared to related FCA algorithms.

Findings

LCM is essentially a Close-by-One variant with speed-up features

Speed-up features improve performance on sparse data

Comparison shows LCM's advantages over similar FCA algorithms

Abstract

LCM is an algorithm for enumeration of frequent closed itemsets in transaction databases. It is well known that when we ignore the required frequency, the closed itemsets are exactly intents of formal concepts in Formal Concept Analysis (FCA). We describe LCM in terms of FCA and show that LCM is basically the Close-by-One algorithm with multiple speed-up features for processing sparse data. We analyze the speed-up features and compare them with those of similar FCA algorithms, like FCbO and algorithms from the In-Close family.