Association Rule Mining Using Revolution R for Market Basket Analysis

Transcription

1 Association Rule Mining Using Revolution R for Market Basket Analysis Veepu Uppal 1, Dr.Rajesh Kumar Singh 2 1 Assistant Professor, Manav Rachna University, Faridabad, INDIA 2 Principal, Shaheed Udham Singh college of Engineering, Tangori, INDIA Abstract The paper presents application of association rule mining techniques for deriving frequent patterns and their visualization in synthetic database of sales transactions. We explain fundamental steps in deriving association rules using Revolution R. Various pruning techniques are presented to determine significant rules. This paper presents the discovery and visualization of association rules using the revolution R. I. INTRODUCTION The task of association rule mining has received a great deal of attention. The mining of such rules is still the very popular pattern discovery methods in data mining area.frequent itemset mining is a focused area in data mining research and an important step in the analysis of data arising in a broad range of applications. Mining frequent itemsets and generation of meaningful association rules is a popular and well researched method for discovering interesting relations between variables in large databases. Initial research was largely motivated by the analysis of market basket data, the results of which allowed super markets to more understand the purchasing behavior of customers as a result; better managerial decisions can be made. For example, an insurance company, by finding a strong correlation between two policies A and B, of the form A B, indicating that customers that purchase policy A were also likely to hold policy B, so using this rule company can make decision to sell policy B to people who hold policy A.The R package arules presented in this paper provides a basic infrastructure for creating and manipulating input data sets and for analyzing the resulting itemsets and rules using [4] Transaction: Let I = {i 1, i 2 i m} be a set of literals, called items. Let D be a set of transactions, where each transaction T is a set of items such that T I.A transaction T contains X, a set of some items in I, if X T. Association Rule: An association rule is an implication of the form X Y, where X I, Y I, and X Y = Ø. The sets of items (for short itemsets) X and Y are called antecedent (left-hand-side or LHS) and consequent (right-hand-side or RHS) of the rule. Apriori: - Apriori is an algorithm for generating association rules. Apriori is designed to operate on databases containing transactions. It generates the association rules from given a set of item sets, the algorithm attempts to find subsets which are common to at least a minimum number candidate C of the item sets. Apriori uses a "bottom up" approach, where frequent subsets are extended one item at a time, and groups of candidates are tested against the data. The algorithm terminates when no further successful extensions are found. The purpose of the Apriori Algorithm is to find relations between different sets of data. It is sometimes referred to as "Market Basket Analysis". Each set of data has a number of items and is called a transaction. The output of Apriori is sets of rules that tell us how often items are contained in sets of data [3]. Apriori Principle: If a itemset is frequent then all of its subsets must be frequent. Support of association rule: A support determines how often a rule is applicable to a given data set. Support(x->Y)=count (XUY)/N Confidence of association rule: It determines how frequently items in Y appear in transaction those contain X. Confidence(x->Y )=count (XUY)/ X To illustrate the concepts, we use a small example from the supermarket domain. The set ofitems is I = {milk, bread, butter, beer} and a small database containing the items is shown infigure 1. An example rule for the supermarket could be {milk, bread} {butter} meaning that if milk and bread is bought,customers also buy butter. IJIRT INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 346

2 Table1: Set of Transactions Transaction ID Items 1 milk, bread 2 Bread,butter 3 Beers 4 Milk,bread,butter 5 Bread,Butter Representing collections of itemsets,from the definition of the association rule mining problem we see that transaction databases and sets of associations have in common that they contain sets of items (itemsets) together with additional information. For example, a transaction in the database contains a transaction ID and an itemset. A rule in a set of mined association rules contains two itemsets, one for the LHS and one for the RHS, and additional quality information, e.g., values for various interest measures. Collections of itemsets used for transaction databases and sets of associations can be represented as binary incidence matrices with columns corresponding to the items and rows corresponding to the itemsets. II. ASSOCIATION RULE GENERATION USING REVOLUTION R arules package in Revolution R Provides the facilities for representing, manipulating and analyzing transaction data and association rules generated from that data. Also provides interfaces to C implementations of the association mining algorithms apriori. To discover the rules first of all the arules package must be loaded. Any package R can be loaded using function library. Loading arules Package: library("arules") Preparation of dataset:-matrix function is used to design a matrix where we consider one represents the presence of item and 0 represents the absence.next we give names to rows and coloums.after that that matrix is converted to transactions. Itemset<matrix(c(1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1, 1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,1,0,1,0,1),ncol =5) Display the data.itemset Table Matrix displayed as rows and columns dim(itemset):this function displays the number of rows and coloumns in matrix. 9 5 Dimnames: function gives names to columns and rows. dimnames(itemset)<list(c("tarns1","trans2","trans3"," trans4","trans5","trans6","trans7","trans8","trans9"),c ("milk","bread","butter","jam","cofee")) Convert the matrix into transactions:next step is to change the itemset matrix into transactions.function trans is used to do this.the parameters of as are matrix that is to be converted and transaction.the return type of as function is transactions. trans<-as(itemset,"transactions") Display all transaction: inspect(trans):- Inspect transaction is used to display every transaction with transactionid and items contained in that transaction. Table 3: Transaction Set transactionid Items 1 {milk,butter,jam,cofee} 2 {bread, butter,jam} 3 {milk,butter,cofee} 4 {bread, butter} 6 {milk,butter,cofee} Calculate the items frequency: This function is used to display the frequency of every item. The frequency of an item is No. of transactions containing that item/total number of transactions mitemfrequency(trans) milk bread butter jam cofee IJIRT INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 347

3 Table 4: Association Rule itemfrequencyplot(trans):this functions give the frequency plot, which represents the frequency of every item.the transactions are passed as arguments forthisfunction. Fig 1: Item frequency Plot Generation of Association Rules: Rules function is used to generate association rules. We have to specify the minimum support and confidence for rules. The parameters for this function are transaction for which rules are to be generated and the minimum confidence and support. rules<apriori(trans,parameter=list(support=0.1,confid ence=0.6)) Function apriori takes the transaction name,the measures like support and confidence as parameters and generate the rules based on these. Display Rules inspect(rules):inspect function is used to display all the rules Pruning of duplicate rules IJIRT INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 348

4 After discovering all association rules the next step is to prune the duplicate rules. rules.sorted<- sort (rules, by="lift") subset.matrix<- is.subset (rules. sorted, rules.sorted) subset.matrix[lower.tri(subset.matrix,diag=t)]<-na redundant <- colsums(subset.matrix, na.rm=t) >= 1 rules.pruned<- rules.sorted[!redundant] first of all the rules rae sorted according to the lift measure then all the subset rules are removed. inspect(rules.pruned) Table 4: Pruned Association Rules To inspect the individual rule selecting the rule by clicking the inspect button. To inspect the set of rules select a rectangular region of the plot and click the inspect button Zooming into a selected region (zoom in/ zoom out buttons). Filtering rules using the measure used for shading by clicking the filter button and selecting a cut-off point in the color key. All rules with a measure lower than the cut-off point will be filtered [1]. III. VISUALIZATION OF ASSOCIATION RULES arulesviz Package in R is used to visualize and represent the association rules by different types of plots. This package contains the various functions to visualize the association rules in various forms[3] library (arulesviz) Sactter Plot: Scatter plot use two interest measures on the axes. The default method for plot() for association rules in arulesviz is a scatter plot using support and confidence on the axes. plot(rules.pruned,measure=c("support","lift"),shading ="confidence",interactive=true) The Parameters for this function are: Rules for which we are going to draw plot Measure of interestingness (e.g., "support", "confidence", "lift") used in the Visualization. Shading measure of interestingness used for the color of the points/arrows/nodes (e.g.,"support", "confidence", "lift"). The default is "lift". NA can be often used to suppress shading. Interactive features include: Fig2: Scatter Plot with interactive features enabled: Number of rules selected: 1 Association Rule support confidence lift {} => {butter} Graph-based technique: These techniques visualize association rules as vertices and edges where vertices typically represent items or itemsets and edges indicate relationship in rules. Interest measures are displayed on the plot as labels on the edges or by color or width of the arrows displaying the edges. plot(rules.pruned, method="graph") Fig 3: Graph Visualization of Rules IJIRT INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 349

5 Matrix based Visualization: In matrix graph Antecedents of association rule are shown as numbers for rows and Itemsets in Consequent (rhs) are shown as numbers in columns and the complete item sets are printed to the terminal for look-up. Itemsets in Antecedent (LHS) [1] "{cofee}" [2] "{bread,cofee}" [3] "{milk,bread}" [4] "{bread}" [5] "{jam}" [6] "{}" Itemsets in Consequent (RHS) [1] "{milk}" [2] "{jam}" [3] "{cofee}" [4] "{butter}" plot(rules.pruned, method="matrix", interactive=true) By opening the matrix in interactive mode we can explore the rules by clicking on the colored box in the matrix.the corresponding rule will be displayed in terminal with its support count. Fig 4:Matrix visualization of rules Group Matrix: To visualize the grouped matrix we use a balloon plot with antecedent groups as columns and consequents as rows. The color of the balloons represents the aggregated interest measure in the group with a certain consequent and the size of the balloon shows the aggregated support. The default aggregation function is the median value in the group. The number of antecedents and the most important (frequent) items in the group are displayed as the labels for the columns. plot(rules, method="grouped",interactive=true) Fig 5: Group Matrix visualization of Rule with interative enabled The selected rule is displayed in console. The rule is selected and then inspect button is pressed.then the corresponding rule is displayed as below. Association Rule support confidence lift 1 {jam} => {cofee} {jam} => {milk} Parallel coordinate Plot Parallel coordinates plots are used to visualize multidimensional data where each dimension is displayed separately on the x-axis and the y-axis. Each data point is represented by a line connecting the values for each dimension. Parallel coordinates plots display the items on the y-axis as nominal values and the x-axis represents the positions in a rule. Instead of a simple line an arrow is used where the head points to the consequent item. Arrows only span enough positions on the x-axis to represent all the items in the rule, i.e., rules with less items are shorter arrows. Fig 6: Parallel coordinate Plot of association Rules IJIRT INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 350

6 IV. CONCLUSION Association rule mining algorithms generate a large number of association rules which are very difficult to analyze and understand the rules. In this paper we presented how to use arules package of Revolution R to generate and prune the rules. And to use arulesviz to explore the rules. Future development will focus on enhancing the visualizing techniques with advanced interactive features using for example iplots which supports selection and zooming with brushing and linking between different plots. REFERENCES [ 1 ] Michael Hahsler, Sudheer Chelluboina,. Visualizing Association Rules: Introduction to the R-extension Package arulesviz, iz/vignettes/arulesviz.pdf [ 2 ] MichaelHahsler,SudheerChelluboina,.Package arulesviz, ages/arulesviz/arulesviz.pdf [ 3 ] Hahsler M, Buchta C, Gr un B, Hornik K (2010). arules: Mining Association Rules and Frequent Itemsets. R package version , URL [ 4 ] Agrawal R, Imielinski T, Swami A (1993). \Mining Association Rules between Sets of Items in Large Databases." In Proceedings of the 1993 ACM SIGMOD International Conference on Management of Data, pp. 207{216. ACM Press. URL [ 5 ] Bayardo, Jr RJ, Agrawal R (1999). \Mining the most interesting rules." In KDD '99: Proceedings of the _fth ACM SIGKDD international conference on Knowledge discovery and data mining, pp. 145{154. ACM. IJIRT INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 351