Market basket Analysis

Few terminologies:

Transaction is a set of items (Itemset).

Confidence : It is the measure of uncertainty or trust worthiness associated with each discovered

pattern.

Support : It is the measure of how often the collection of items in an association occur together as percentage of all transactions

Frequent itemset : If an itemset satisfies minimum support,then it is a frequent itemset.

Strong Association rules: Rules that satisfy both a minimum support threshold and a minimum

confidence threshold

In Association rule mining, we first find all frequent itemsets and then generate strong association rules from the frequent itemsets

Apriori algorithm is the most established algorithm for finding frequent item sets mining.

The basic principle of Apriori is “Any subset of a frequent itemset must be frequent”.

We use these frequent itemsets to generate association rules.

Association rule mining

Finding frequent patterns, associations, correlations, or causal structures among sets of items in transaction databases

Understand customer buying habits by finding associations and correlations between the different items that customers place in their “shopping basket”

Applications: Basket data analysis, cross‐marketing, catalog design, loss‐leader analysis, web log analysis, fraud detection  (supervisor‐>examiner)

Rule form

Antecedent →Consequent [support, confidence]

(support and confidence are user defined measures of interestingness)

Let the rule discovered be {Jamun,...} → {Potato Chips}

Potato chips as consequent => Can be used to determine what should be done to boost its sales

Jamun in the antecedent => Can be used to see which products would be affected if the store discontinues selling Jamun

Jamun in antecedent and Potato chips in the consequent =>  Can be used to see what products should be sold with Jamun to promote sale of Potato Chips

Find all itemsets that have high support,These are known as frequent itemsets. Generate association rules from frequent itemsets

Let us see an example

:

 Finding the support, confidence and lift of i) shirts and ties, ii) trousers and ties.

Transaction  Id	Shirts	Trousers	Ties
001	1	1	1
002	0	1	0
003	1	0	1
004	1	0	1
005	1	1	0

For our data there are 3 transactions with both shirts and ties (shirts ∩ ties) out of total 5 transactions.

Support =3/5 =0.6 or 60%

Confidence for association is calculated using the following formula:

In our example, there are 3 transaction for both shirts and ties together out of 4 transactions for shirts. The calculation for confidence for our dataset is:

Confidence =3/4 =0.75 or 75 %

A third useful metric for association analysis is lift; it is defined as:

Expected confidence in the above formula is presence of ties in the overall dataset i.e. there are 4 instances of ties purchase out of 5.

The value for lift, 125%, shows that purchases of the ties improve when the customers buy shirts. The point to note   here is that if the customer buys a shirt, does his chance of buying ties go up i.e. value of lift above 100

Lift= confidence / expected confidence = P( ties | shirts) / P(ties)

Expected confidence in the above formula is presence of ties in the overall dataset i.e. there are 4 instances of ties purchase out of 5.

Lift = (3/4) / ( 3/5) = 15/12 =1.25 or 125%

Similarly for the trousers and ties

Support: 1/5

Confidence: 1/3

Lift= ( 1/3 )/ (3/5)= 5/9 or 55.6%