---
title: "Association Rules"
author: "Prof. Eric A. Suess"
date: "February 28, 2024"
format: 
  revealjs:
    self-contained: true
---

## Introduction

Do you ever make ''impulse purchases''?

Why is the product always ''nearby'' and ''easily available''?

On some of the online retailer websites there is the 
''wishlist'' or ''shopping cart''?

## Introduction

**Recommendation systems** have been based on subjective experience
of marketers.

With online retailers machine learning has been used to learn 
the patterns of **purchasing behavior**.

With barcode scanners, computerized inventory systems, and 
online shopping there is a lot of **transactional data** 
available for **data mining**.

## Introduction

Do you know what an [SKU](https://en.wikipedia.org/wiki/Stock_keeping_unit)
is?

Answer: **Stock Keeping Unit**

## Introduction

In this chapter we will learn about methods for identifying
associations among items in transactional data.

This is known as **market basket analysis**.

## Understanding association rules

The result of **market basket analysis** is a set of 
**association rules**.

For example,

    {peanut butter,jelly}  ->  {bread}
    
Association rules are learned from subsets of **itemsets**.
    
## Understanding association rules

Association rules were developed in the context of **Big Data**
and **database science** and **data mining** for 
**knowledge discovery** (KDD).  

*Looking for the needle in the haystack*.

Association rules are **unsupervised**, so there is **no
need** for the algorithm to be **trained**.

And there is no objective measure of performance for such
rule learners.

## Apriori algorithm

The complexity of transactional data is what makes association rule 
mining a challenging task.

**Transactional datasets** are typically **extremely large**, both in
terms of the **number of transactions** and the **number of features** 
or items for sale.

The potential itemsets grows with the number of items for sale.

The good thing is that many itemsets are rare.

By **igoring rare itemsets**, it is possible to limit the search for rules.

## Apriori algorithm

The most widely used algorithm is the **Apriori algorithm**.

It employs a simple *a priori* belief as a guideline for reducing 
the association rule space, *all subsets of a frequent itemset
must also be frequent*.  This is the **Apriori property**.

See the paper

[Fast algorithms for mining association rules](http://www.vldb.org/conf/1994/P487.PDF),
Agrawal and Srikant (1994).

Or

[A comparison of association rule discovery and bayesian network causal inference algorithms](https://www.semanticscholar.org/paper/A-Comparison-of-Association-Rule-Discovery-and-Bowes-Neufeld/1d943d6cf426f5c1b47c00bcf4d7dea7b8dddf6e/pdf), Bowes, et. al. 

## Measuring rule interest 

Whether or not an association rule is deemed **interesting**
is determined by two statistical measures:

- support 

  $P(X)$
    
- confidence 

  $P(Y|X)$
  
## Measuring rule interest 

By providing **minimum thresholds** for each of these metrics 
and applying the Apriori principle, it is easy to limit the
number of rules reported.
  
## Measuring rule interest - support

The **support** of an itemset measures how frequently it occurs
in the data.

$support(X) = \frac{count(X)}{N}$

where $N$ is the number of transactions in the database and
$count(X)$ is the number of transactions that contain 
the itemset $X$.

## Measuring rule interest - confidence

A rule's **confidence** is a measurement of its predictive power 
or accuracy.

It is defined as the support of the itemset containing both
$X$ and $Y$ divided by the support of the itemset containing
only $X$.

$confidence(X \rightarrow Y) = \frac{support(X,Y)}{support(X)}$

The confidence tells us the proportion of transactions where the
presence of item or itemset $X$ results in the presence of
item or itemset $Y$.

## Measuring rule interest - confidence

Note $X \rightarrow Y$ is not the same as $Y \rightarrow X$.

**Rules** that have **high support** and **high confidence**
are referred to as **strong rules**.

## Building a set of rules with the Apriori principle

The **Apriori principle** states that all subsets of a frequent
itemset must also be frequent.

The **Apriori algorithm** uses the **Apriori principle** to
exclude potential association rules prior to actually evaluating
them.

The **process of creating rules** occurs in two phases:

- find all itemsets that meet a minimum **support threshold**
- create rules from these itemsets that meet a minimum 
**confidence threshold**

## Example

The author gives an example of the use of Market Basket Analysis
using **transaction data** to identify frequently purchased groceries
with association rules.

**Recommendation system**

## Example

The example uses:

- **unstructured data**
- **nosql**
- **sparse matrix**

We will use the R packages

- [arules](https://www.jstatsoft.org/article/view/v014i15/v14i15.pdf)
- [arulesViz](https://journal.r-project.org/archive/2017/RJ-2017-047/RJ-2017-047.pdf)

## Example

**Lift** is a metric used to measure how much more likely one item
is to be purchased relative to its typical purchase rate, given
that you know another item has been purchased.

$lift(X \rightarrow Y) = \frac{confidence(X \rightarrow Y)}{support(Y)}$

Here

$lift(X \rightarrow Y) = lift(Y \rightarrow X)$


