Approximation of Frequent Itemsets

Synonyms

AFI

Definition

Consider an n × m binary matrix D. Each row of D corresponds to a transaction t and each column of D corresponds to an item i. The (t, i)-element of D, denoted D(t, i), is 1 if transaction t contains item i, and 0 otherwise. Let T₀ = {t₁, t₂,…,t_n} and I₀ = {i₁, i₂,…,i_m} be the set of transactions and items associated with D, respectively.

Let D be as above, and let ε_r, ε_c ∈ [0, 1]. An itemset I ⊆ I₀ is an approximate frequent itemset AFI(ε_r, ε_c), if there exists a set of transactions T ⊆ T₀ with | T | ≥ minsup | T₀ | such that the following two conditions hold:

• 1. $\forall i\in T,\frac{1}{\mid I\mid}\sum_{j\in I}D\left(i,j\right)\ge \left(1-{\upepsilon}_r\right);$

• 2. $\forall j\in I,\frac{1}{\mid T\mid}\sum_{i\in T}D\left(i,j\right)\ge \left(1-{\upepsilon}_c\right);$

Historical Background

Relational databases are ubiquitous, cataloging everything from market-basket data [1] to genomic data collected in biological experiments [2]. A binary matrix is one...