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Association Rules. Spring 2010. Data Mining: What is it?. Two definitions: The first one, classic and well-known, says that data mining is the nontrivial extraction of implicit, previously unknown, and potentially useful information from data (W. Frawley)

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Association Rules

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Association rules

Association Rules

Spring 2010

Data mining what is it

Data Mining: What is it?

  • Two definitions:

    • The first one, classic and well-known, says that data mining is the nontrivial extraction of implicit, previously unknown, and potentially useful information from data (W. Frawley)

    • The second one, spark and rebel, says that data mining is nothing else than torturing the data until it confesses… and if you torture it enough, you can get it to confess to anything (Fred Menger).

Data mining techniques

Data mining techniques

  • Association Rules

  • Classification

  • Prediction

  • Clustering

What is association mining

What is Association mining?

Finding frequent patterns, associations, or casual structures among sets of items or objects in transaction databases, relational databases, and other information repositories.

Searches for relationships between variables. For example a supermarket might gather data on customer purchasing habits. Using association rule learning, the supermarket can determine which products are frequently bought together and use this information for marketing purposes. This is sometimes referred to as market basket analysis.


Basket Data Analysis


Catalog design

Introduction to association rules ar

Introduction to Association Rules (AR)

  • Ideas came from the market basket analysis (MBA)

  • What do customers buy?

  • Which products are bought together?


  • Find association and correlations between the different items that customers place in their shopping basket.

Some definitions in ar

Some definitions in AR


  • A particular data behavior, arrangement or form that might be of a business interest


  • A set of items, a group of elements that represents together a single entity. It is actually a type of pattern.

Some definitions in ar cntd

Some definitions in AR (cntd.)

  • Transaction database T

    • A set of transactions T = {T1 ,T2,…, Tn }

  • Itemset

    • Each transaction contains a set of items I(Itemset)

    • An Itemset is a collection of items I = {I1, I2, ..., In}

Ar general aim

AR General Aim

  • Find frequent/interesting patterns, associations, correlations, or casual structures among set of items or elements in databases or other information repositories.

  • An AR is an implication of two itemsets:

  • X => y

Ar contd

AR (contd.)

Frequent itemsets: items that frequently appear together.


  • Bread => peanut-butter

  • I = {bread, peanut-butter}

An interesting rule

An Interesting Rule

  • Support count (σ):

    • Frequency of occurrence of an itemset

    • σ {bread, peanut-butter} = 3

  • Support:

    • Fraction of transactions that contain an itemset

    • S {bread, peanut-butter} = 3/5

Ar contd1

AR (contd.)

The two most used measures of interest:

  • Support(s): the occurring frequency of the rule, i.e. the number of transactions that contain both X and Y

    • S = σ (X union Y) / # of transactions

  • Confidence(s): the strength of the association, i.e. measures of how often items in Y appear in transactions that contain X.

    • C = σ (X union Y) / σ (X)

Ar contd2

AR (contd.)

Types of ar

Types of AR

  • Binary Association Rules

  • Quantitative Association Rules

  • Fuzzy Association Rules

    Let’s start from the beginning:

  • Binary Association Rules, A-priori

A priori algorithm

A-priori algorithm

  • Priori is the most influential AR miner

  • It consist of two steps:

    • Generate all frequent itemsets whose support >= minimum support.

    • Use frequent itemsets to generate association rules.

A priori contd

A-priori (contd.)

  • Key Idea:

    • Downward closure property:

      • Any subsets of a frequent itemset are also frequent itemsets.

    • The algorithm iteratively does:

      • Create itemsets

      • Only continue exploration of those whose support >= minimum support

Back to our example minsup 3

Back to our example (minsup = 3)

Example minsup 2

Example (minsup = 2)

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