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# Apriori Algorithm

, 10 Aug 2012 CPOL
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Implementation of the Apriori algorithm in C#.

## Introduction

In data mining, Apriori is a classic algorithm for learning association rules. Apriori is designed to operate on databases containing transactions (for example, collections of items bought by customers, or details of a website frequentation).

Other algorithms are designed for finding association rules in data having no transactions (Winepi and Minepi), or having no timestamps (DNA sequencing).

## Overview

The whole point of the algorithm (and data mining, in general) is to extract useful information from large amounts of data. For example, the information that a customer who purchases a keyboard also tends to buy a mouse at the same time is acquired from the association rule below:

Support: The percentage of task-relevant data transactions for which the pattern is true.

Support (Keyboard -> Mouse) =

Confidence: The measure of certainty or trustworthiness associated with each discovered pattern.

Confidence (Keyboard -> Mouse) =

The algorithm aims to find the rules which satisfy both a minimum support threshold and a minimum confidence threshold (Strong Rules).

• Item: article in the basket.
• Itemset: a group of items purchased together in a single transaction.

## How Apriori Works

1. Find all frequent itemsets:
• Get frequent items:
• Items whose occurrence in database is greater than or equal to the min.support threshold.
• Get frequent itemsets:
• Generate candidates from frequent items.
• Prune the results to find the frequent itemsets.
2. Generate strong association rules from frequent itemsets
• Rules which satisfy the min.support and min.confidence threshold.

## Example

A database has five transactions. Let the min sup = 50% and min con f = 80%.

## Solution

### Step 1: Find all Frequent Itemsets

#### Frequent Itemsets

`{A}   {B}   {C}   {E}   {A C}   {B C}   {B E}   {C E}   {B C E}`

## Lattice

Closed Itemset: support of all parents are not equal to the support of the itemset.

Maximal Itemset: all parents of that itemset must be infrequent.

Keep in mind:

Itemset {c} is closed as support of parents (supersets) {A C}:2, {B C}:2, {C D}:1, {C E}:2 not equal support of {c}:3.

And the same for {A C}, {B E} & {B C E}.

Itemset {A C} is maximal as all parents (supersets) {A B C}, {A C D}, {A C E} are infrequent.

And the same for {B C E}.

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Article Copyright 2010 by Omar Gameel Salem