Association Rules Presented by: Anilkumar Panicker Presented by: Anilkumar Panicker

What is Data Mining?? Search for valuable information in large volumes of data. A step in knowledge discovery in databases. It enables companies to focus on customer satisfaction, corporate profits, and determining the impact of various parameters on the sales.

Association Rule Association rules are used to show the relationships between data items. Association rules detect common usage of data items. E.g. The purchasing of one product when another product is purchased represents an association rule.

Example 1 Grocery store. Association rules have most direct application in the retail businesses. Association rules used to assist in marketing, advertising, floor placements and inventory control.

From the transaction history several association rules can be derived. E.g. 100% of the time that PeanutButter is purchased, so is bread. 33% of the time PeanutButter is purchased, Jelly is also purchased.

Example 2 A Telephone Company. A telephone company must ensure that all calls are completed and in acceptable period of time. In this environment, a potential data mining problem would be to predict a failure of a node. This can be done by finding association rules of the type X  Failure.

If these types of rules occur with a high confidence, Failures can be predicted. Even though the support might be low because the X condition does not frequently occur.

Association rule Given a set of items I = {I 1,I 2,….I m } and a database of transactions D = {t 1,t 2,….t m } where t i = { I i1,I i2,….I ik } and I iJ € I, an association rule is an implication of the form X  Y where X,Y C I are sets of items called itemsets and X∩Y =ø.

Support (s): The support (s) for an association rule X  Y is the percentage of transactions in the database that contain X U Y. E.g. If bread along with peanutbutter occurs in 60% of the total transactions, then the support for bread  peanutbutter is 60%

Confidence or Strength (α): The confidence or strength (α) for an association rule X  Y is the ratio of the number of transactions that contain X U Y to the number of transactions that contain X. Eg.if support for bread  peanutbutter is 60% and bread occurs in 80% of total transactions then confidence for bread  peanutbutter is 75%.

Selecting Association rules The selection of association rules is based on Support and Confidence. Confidence measures the strength of the rule, Whereas support measures how often it should occur in the database. Typically large confidence values and a smaller support are used. Rules that satisfy both minimum support and minimum confidence are called strong rules.

Association Rule Problem Given a set of Items I = {I 1,I 2,….I m } and a database of transactions D = {t 1,t 2,….t n } where t i = { I i1,I i2,….I ik } and I iJ € I. The association rule problem is to identify all association rules X  Y with a minimum support and confidence. These values (s,α) are given as input to the problem.

Large Itemsets A Large Itemset / frequent Itemset is an itemset whose number of occurrences is above a threshold, s (Support) Finding large Itemsets generally is quite easy but very costly. The naive approach would be to count all itemsets that appear in any transaction. Given a set of items of size m, there are 2 m subsets. Ignoring the empty set we are still left with 2 m – 1 subsets.

For e.g. In the retail store example if have set of items of size 5, i.e the store sells 5 products. Then the possible number of itemsets is 2 5 – 1 = 31. If the 5 products sold are bread,peanutbutter,milk,beer and jelly. then the 31 possible itemsets are

Bread Peanutbutter Milk Beer Jelly Bread,peanutbutter Bread,milk Bread,beer Bread,jelly Peanutbutter,milk Peanutbutter,beer Peanutbutter,jelly Milk,beer Milk,jelly Beer, jelly Bread,peanutbutter,milk Bread, Peanutbutter, beer and so on.

For m = 30 the number of potential itemsets become The challenge in solving an association problem is hence to efficiently determining all large itemsets. Most association rule algorithms are based on smart ways to reduce the number of itemsets to be counted.

Large Itemsets The most common approach to finding association rules is to breakup the problem into two parts 1.Finding large Itemsets and 2.Generating rules from these itemsets.

Subset of any large itemset is also large. Once the large Itemsets have been found, we know that any interesting association rule, X  Y,must have X U Y in this set of frequent itemsets. When all large itemsets are found, generating the association rules is straightforward.

Apriori Algorithm Apriori algorithm is the most well known association rule algorithm. Apriori algorithm is used to efficiently discover large itemsets. Apriori algorithm uses the property that any subset of a large itemset must be large. Inputs: Itemsets, Database of transactions, support and the output is large itemsets.

Apriori Algorithm Example T.I.D.Items 1001,3,4 2002,3,5 3001,2,3,5 4002,5 ITEM SET SUPPORT {1}2 {2}3 {3}3 {4}1 {5}3

Support threshold = 2 ITEM SETSUPPORT {1}2 {2}3 {3}3 {5}3 ITEM SET {1,2} {1,3} {1,5} {2,3} {2,5} {3,5}

Threshold Support = 2 ITEM SETSUPPORT {1,2}1 {1,3}2 {1,5}1 {2,3}2 {2,5}3 {3,5}2 ITEM SETSUPPORT {1,3}2 {2,3}2 {2,5}3 {3,5}2

ITEM SET {2,3,5} ITEM SETSUPPORT {2,3,5} 2

References Data Mining by Margaret Dunham. Wikipedia

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