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International Journal of Emerging Trends & Technology in Computer Science (IJETTCS) Web Site: www.ijettcs.org Email: editor@ijettcs.org, editorijettcs@gmail.com Volume 2, Issue 6, November – December 2013 ISSN 2278-6856 Mining Association Rule by Multilevel Relationship Algorithm: An Innovative Approach for Cooperative Learning D.A. Vidhate1, Dr. Parag Kulkarni2 1 Padmashri Dr. Vithalrao Vikhe Patil College of Engineering, Vilad Ghat, PO MIDC, Ahmednagar 2 EKLaT Research Lab, Pune Abstract: Mining the Data is also known as Discovery of to changing conditions which is user-friendly by adapting Knowledge in Databases is to get correlations, trends, to needs of their individual users, and also can improve patterns, anomalies from the databases which can help out to performance over time. make exact future decisions. However data mining is not the Association rule mining concept has been applied to natural. No one can assure that the decision will lead to good market domain and specific problem has been studied, the quality results. It only helps experts to understand the data management of some aspects of a shopping mall, and an and lead to good decisions. architecture that makes it possible to construct agents Association Mining is the discovery of relations or correlations among an item set. An objective is to make rules capable of adapting the association rules has been used. from given multiple sources of customer database A shopping mall is a cluster of independent shops, transaction. It needs increasingly deepening the knowledge planned and developed by one or several entities, with a mining process for finding refined knowledge from data. common objective. The size, commercial mixture, Earlier work is on mining association rules at one level. common services and complementary activities developed Though mining association rules at various levels is are all in keeping with their surroundings. A shopping necessary. Finding of interesting association relationship mall needs to be managed and, the management includes among large amount of data will helpful to decision building, solving incidents or problems in a dynamic environment. marketing, & business managing. As such, a shopping mall can be seen as a large dynamic For generating frequent item set we are using Apriori problem, in which the management required depends on Algorithm in multiple levels so called Multilevel Relationship the variability of the products, clients, opinions. Our aim algorithm (MRA). MRA works in first two stages. In third is to develop an open system, capable of incorporating as stage of MRA uses Bayesian probability to find out the dependency & relationship among different shops, pattern of many agents as necessary, agents that can provide useful sales & generates the rule for learning. This paper gives services to the clients not only in this shopping centre, but detail idea about concepts of association mining, also in any other environment such as the labor market, mathematical model development for Multilevel Relationship educational system, medical care, etc. algorithm, Implementation & Result Analysis of MRA and Data Mining refers to extracting knowledge from large performance comparison of MRA and Apriori algorithm. quantity of data. Interesting association can be discovered among a large set of data items by Association rule Keywords: Apriori Algorithm, Association rule, mining. The finding of interesting relationship among Bayesian Probability, Data mining, Multilevel learning large amount of business transaction records can help in many business decisions making process, such as catalog 1. INTRODUCTION plan, cross marketing and loss leader analysis [34]. The area of Machine Learning deals with the design of However, previous work has been focused on mining programs that can learn rules from data, adapt to association rules at a single concept level. There are changes, and improve performance with experience. In applications, which need to get associations at multiple addition to being one of the initial dreams of Computer concept levels. Science, Machine Learning has become crucial as Real world problem can be expressed in term of computers are expected to solve increasingly complex mathematical model and mathematical solutions can be problems and become more integrated into our daily lives. found out. Following stages represents the process for These include identifying faces in images, autonomous solving the real world problems. driving in the desert, finding relevant documents in a Study of basic concepts for mathematical modeling database, finding patterns in large volumes of scientific Mathematical Modeling of the system (MRA) data, and adjusting internal parameters of systems to Implementation & Result analysis of MRA optimize performance. Alternatively methods that take The focus was on working on mathematical model labeled training data and then learn appropriate rules development for multilevel association rule mining. from the data seem to be the best approach to solve the Multilevel Apriori algorithm and bayesian probability problems. Furthermore, it needs a system that can adapt estimation is not combined in any of the previous work. It Volume 2, Issue 6 November – December 2013 Page 130 International Journal of Emerging Trends & Technology in Computer Science (IJETTCS) Web Site: www.ijettcs.org Email: editor@ijettcs.org, editorijettcs@gmail.com Volume 2, Issue 6, November – December 2013 ISSN 2278-6856 is the novel move towards the mining association rule. c is percentage in transactions in T containing X which Efficiency of original Apriori algorithm has been also increased due to multilevel architecture. contain Y. i.e Support (X Y) = P (XY) (2.2) 2. ASSOCIATION RULE Confidence (X Y) = P (Y|X) (2.3) Mining association rule is finding the interesting Rules that satisfy both minimum support threshold association or correlation relationship among large set of (min_sup) and a minimum confidence threshold data items. With massive amount of data continuously (min_conf) are called strong. being collected & stored in database, many industries are Itemset is nothing but set of items. If it contains n item is becoming interested in mining association rule from their a n-itemset. The set {shirt-Bombay ding, jeans-levis} is database. Relationship among the business traction 2 itemset. The occurrence of itemset is the number of records can help to design catalog, loss leader analysis, transactions that contain the itemset. This is known as cross marketing & other business decision making frequency or support count of the item set. It satisfies process. lowest amount of support if the occurrences frequency of The discovery of such association can help retailers to itemset is greater than or equal to the product of min_sup develop marketing strategies by gaining insight into & total no of transactions in T. If an itemset satisfy the which items are frequently purchased together by minimum support then it is frequent itemset. Association customers. Such information can lead to increased sale by mining has two steps process. In first step, find all helping retailers to do selective marketing & plan their frequent item sets. All of these item sets will arise at least shelf space. Motivating example for association rule as frequently as a pre-determined minimum support mining is marker basket analysis. count. In second step, generate strong association rules Market basket analysis can also help retailers to plan from the frequent item sets and must satisfy lowest which item to put on sale at reduced price. If customer amount of support and minimum confidence. The overall tends to purchase shirt of Bombay ding and jeans of Levis performance of mining association rule is determined by together, then having a sale on jeans may encourage the the first step. sale of shirt as well as jeans. Buying patterns reflects which items are frequent associated or purchased 2.1 Apriori Algorithm together. These patterns represented in the form of It employs an iterative approach known as a level-wise association rules. For example, customer who purchase search, where (k − 1) itemsets are used to explore k item shirt-Bombay ding also tends to buy jeans Levis at the sets. First, the set of frequent 1-itemsets is found by same time is represented in association rule (2.1) below. scanning the database to collect the count for each item & Shirt-Bombay ding jeans-levis collecting those items that satisfy minimum support. The [supp=2%, conf=60%] (2.1) outcome is denoted L1. Then L1 is used to find L2, which Rule support & confidence are two measure rules. They is then used to find L3, and so on, until no more frequent respectively reflect the usefulness and certainty of item sets can be got. Getting of each Lk requires one full discovered rules. A support of 2% for association rule scan of D. means that 2% of all transactions under analysis show To improve the efficiency of the level-wise generation of that shirt-Bombay ding and jeans-levis are purchased frequent itemsets, one takes advantage of the Apriori together. A confidence of 60% means that 60% of property: All nonempty subsets of a frequent itemset customers who purchased shirt-Bombay ding also bought must also be frequent. This property is based on the jeans Levis. Typically, association rule are considered following observation. If an itemset A does not satisfy the interesting if they satisfy both a minimum support minimum support threshold, min sup, then A is not threshold and a minimum assurance threshold. Such frequent; i.e. P (A) < min sup. If an item B is added to the threshold can be located by users or area expert. itemset A, then the resulting itemset AB cannot occur Let I= {i1, i2, i3…………id} set of all items in dataset more frequently than A. Therefore AB is not frequent T= {t1, t2, t3…....…...tn} set of all transactions either, that is P (AB) < min sup. A two-step process is used to find Lk from Lk−1 , for k ≥ 2: Each transaction ti contains a subset of items chosen from I. A transaction tj is said to contain an itemset X if X is 2.1.1 Join step: subset of tj. To find Lk, a set of candidate k−itemsets is generated by Association rule is an implication of the form of joining Lk−1 with itself. Candidate set is denoted by Ck. X Y, where X I, Y I & X ∩Y = Ф Suppose L1 and L2 be item sets in Lk−1 . The notation Li The rule X Y holds in the transaction set T with [j] refers to the jth item in Li. Thus in L1, the last item and support s, where s is percentage of transactions in T that the next to the last item are given respectively by L1 [k −1] contain X U Y. The rule X Y has confidence c in the and L1 [k −2]. Any two itemsets Lk−1 are joined if their transaction set T if first (k −2) items are in frequent. Then members L1 and L2 are joined if Volume 2, Issue 6 November – December 2013 Page 131 International Journal of Emerging Trends & Technology in Computer Science (IJETTCS) Web Site: www.ijettcs.org Email: editor@ijettcs.org, editorijettcs@gmail.com Volume 2, Issue 6, November – December 2013 ISSN 2278-6856 (L1[1] = L2 [1]) ^ (L1 [2] = L2 [2]) ^ . . . ^ Table 2.3: Transaction 1-itemset L1 support 2 (L1[k − 2] = L2[k − 2]) ^ (L1 [k − 1] < L2 [k − 1]) L1 Itemset Support count The condition L1[k − 1] < L2 [k − 1] ensures that no SH-A 06 duplicates are created. The outcome of itemset formed by SH-B 07 joining L1 and L2 is {L1[1], L1[2]. ………. . L1[k − 2], L1[k − TSH-P 06 1], L2[k − 1]} TSH-Q 02 J-X 02 2.1.2 Prune step: Set Ck is a superset of Lk, because although all the To discover the set of frequent 2-itemsets, L2, the frequent k-itemsets are included in Ck, its members may algorithm joins L1 with itself to generate a candidate set or may not be frequent. One could scan the database to of 2-itemsets, C2. Note that no candidates are removed determine the count of each candidate in Ck and eliminate from C2 during the pruning step since each subset of the any itemset that does not meet the minimum support candidates is also frequent. threshold. This would then give Lk. However, Ck can be huge, and so this could be very time-consuming. Table 2.4: Transaction 2-itemset C2 To eliminate the infrequent itemsets, the Apriori property C2 itemset is used as follows. Any (k−1)-itemset that is not frequent (SH-A)-(SH-B) cannot be a subset of a frequent k-itemset. Hence, if any (SH-A)-(TSH-P) (k−1) itemset of a candidate k-itemset is not in Lk−1, then (SH-A)-(TSH-Q) the candidate cannot be frequent either and so can be (SH-A)-(J-X) removed from Ck. This subset testing can be done quickly (SH-B)-(TSH-P) by maintaining a hash tree of all frequent itemsets. We (SH-B)-(TSH-Q) illustrate the use of the Apriori algorithm for finding (SH-B)-(J-X) frequent itemsets in our transaction database, D. (TSH) (TSH) Table 2.1: Transaction data set (TSH) Transaction Transaction ID Items ID Items T1 SH A,SH 3. MULTILEVEL RELATIONSHIP T2 SH B,TSH ALGORITHM T3 SH B, TSH Multilevel Relationship algorithm works in three stages. T4 SH A, SH In first two stages it utilizes apriori algorithm for finding T5 SH A, TSH out frequent itemsets. Third stage of MRA uses bayesian T6 SH B,TSH probability to find out the dependency & relationship T7 SH A, TSH amongst different shops and generates the rules for learning. T8 SH A, SH Let the system S be represented as T9 SH A, SH S = {I, O, fs | s } In the first iteration of the algorithm, each item is a I = Input Datasets member of the set of candidate’s 1-itemsets, C1. The O = Output Patterns algorithm simply scans all the transactions in order to O = fs(I) s count the number of occurrences of each item. fs : I O be ONTO function Objective was to find out pattern of sale from given Table 2.2: Transaction 1-itemset C1 with count dataset of three different shops for particular time period. C1 Itemset Support count Input dataset I = {X,Y,Z} such that X = {x1,x2,x3} , SH-A 06 Y = {y1,y2,y3} and Z = {z1,z2,z3} SH-B 07 Success output O = {P(X0|Y0), P(X0|Z0), P(X1|Y1), TSH-P 06 P(Y1|Z1)……….. } TSH-Q 02 J-X 02 Multilevel Relationship Algorithm is applied on given J-Y 01 input dataset i.e. I={X,Y,Z} where X = {x1,x2,x3}, Y = {y1,y2,y3} and Z = {z1,z2,z3}. First stage gives Level 1 association amongst items in the The set of frequent 1-itemsets, L1, consists of the same shop using knowledge base. It is called as local candidate itemsets satisfying the minimum support count frequent itemsets generated in first phase. of 2. Thus all the candidates in C1, except for {J-Y}, are During second stage it uses individual knowledge base in L1. and level 1 association that was generated in stage I from Volume 2, Issue 6 November – December 2013 Page 132 International Journal of Emerging Trends & Technology in Computer Science (IJETTCS) Web Site: www.ijettcs.org Email: editor@ijettcs.org, editorijettcs@gmail.com Volume 2, Issue 6, November – December 2013 ISSN 2278-6856 same shops to find out the frequent item sets i.e. x1(0), 5. Similarly the algorithm is applied on Jewelry shop(Y) x2(3), x3(1)……etc. It is called as global frequent & Footwear shop(Z) to determine frequent itemset on itemsets. different items. 6. First Level output of Apriori algorithm provided Stage 1: internal association amongst the items i. e. At first stage it found out Level 1 association amongst y1(0) y1(1),y2(0) y2(1),y3(0) y3(1) & items in the same shop i.e. internal relationship between z1(0) z1(1), z2(0) z2(1), z3(0) z3(1)......etc for the same item types i. e. x1(0…….n), x2(0………n), Jewelry & Footwear shop respectively. x3(0……..n) within the Cloth shop (X) i.e. O = fs(X) 7. Second level input of Apriori algorithm provided from Internal relationship between the same item types i. e. newly generated individual knowledge base, the y1(0…….n), y2(0………n), y3(0……..n) within the frequent item sets i.e. y1(0), y2(3), y3(1), z1(1), z2(5), Jewelry shop (Y) i.e. O = fs(Y) z3(6)…… Internal relationship between the same item types i. e. 8. It gives with sets of frequent item sets for the Jewelry & z1(0…….n), z2(0………n), z3(0……..n) within the Footwear shop for different items i.e. Fy & Fz. Footwear shop (Z) i.e. O = fs(Z) 9. The context is generated under uncertainty in the form of frequent item sets Fx, Fy & Fz. System constraints Stage 2: applied here are sale of items in a day, week, month or During second stage it uses individual knowledge base any particular season. This context is refereed as Fi and level 1 association is generated in stage 1 of same which is not constant, i.e. it changed seasonably. shop to find out the frequent item sets i.e. x1(0), x2(3), 10. Hence it is necessary to determine dynamic behavior x3(1)……etc is called as global frequent itemsets. of Fi for particular season. It gives sets of frequent item sets for the Cloth shop for 11. External Dependencies amongst Items different items i.e. Fx as O = fs(x1,x2,x3) Xi Yi….Xn Yn is found with Bayesian It gives sets of frequent item sets for the Jewelry shop for probability. different items i.e. Fy as O = fs(y1,y2,y3) 12. New patterns are generated by Bayesian probability It gives with sets of frequent item sets for the Footwear though which learning rules could be predicted & shop for different items i.e. Fz as O = fs(z1,z2,z3) interpreted. Stage 3: It is necessary to determine dynamic behavior of Fi for 4 ARCHITECTURE OF MRA particular season. External Dependencies amongst Items Xi Yi……... Xn Yn has been found with Bayesian probability. New patterns are generated by Bayesian probability through which learning rules are predicted & interpreted. 3.1 Working of Multilevel Relationship Algorithm Let the sale of Item X at Cloth shop affects sale of item Y at Jewelry shop and item Z at Footwear. 1. Apriori association mining algorithm is applied on each item in cloth shops separately i.e. Jean(X0), Figure 1 : MRA Architecture Diagram Tshirt(X1), Shirt(X2) and so on from the given large item sets. It was applied at two levels / phases in the Figure 1 shows the flow diagram which depicted the same shop. development of Multilevel Relationship Algorithm 2. After applying Apriori algorithm at first level for (MRA). Multilevel Relationship algorithm worked in different support value it provide with the internal three stages. dependency amongst individual items & generate the In first two stages it utilized association rule mining individual knowledge base i.e. x1(0) x1(1), x2(0) algorithm for finding out frequent itemsets. Datasets of x2(1), x3(0) x3(1) …....etc. It is called as local three shops i.e. Cloth, Jewelry & Footwear were given as frequent itemsets generated in first phase. an input to the stage I and Level 1 association between 3. At second level Apriori algorithm was applied on individual items had been found out. Level 1 association newly generated individual knowledge base to find out between individual items was given as an input to stage II the frequent item sets i.e. x1(0), x2(3), x3(1)……etc. It and frequent itemsets had been found out. These frequent is called as global frequent itemsets. itemsets had generated new sale context. In stage III it 4. It provided with sets of frequent item sets for the Cloth used bayesian probability to find out the external shop for different items i.e. Fx. dependency & relationship amongst different shops, pattern of sale and generated the rules for cooperative learning. The algorithm consists of three sub modules: Volume 2, Issue 6 November – December 2013 Page 133 International Journal of Emerging Trends & Technology in Computer Science (IJETTCS) Web Site: www.ijettcs.org Email: editor@ijettcs.org, editorijettcs@gmail.com Volume 2, Issue 6, November – December 2013 ISSN 2278-6856 MRA Stage I, MRA stage II, Interdependency Module Xi Yi……Xn Yn is found with Bayesian probability. New patterns are generated by Bayesian MRA Stage I: probability through which learning rules are predicted & At first stage it finds Level 1 association amongst items in interpreted. Dependency between itemsets of Cloth shop the same shop i.e. (Fx) and Jewelry shop (Fy) is found out as Internal relationship between the same item types i. e. x1(0…….n), x2(0………n), x3(0……..n) within the P (Y | X ) P ( X ) P( X | Y ) Cloth shop (X) i.e. P (Y ) O = fs(X) = fstage_I_algorithm_apriori (X) O=fstage_I_algorithm_apriori{x1(….n)}={x1(0) x1(1), x1(3) x1(2)…} O=fstage_I_algorithm_apriori{x2(0…n)}={x2(2) x2(4), x2(2) x2(4)…} O=fstage_I_algorithm_apriori{x3(0…n)}={x3(0) x3(3), x3(1) x3(5)…} Dependency between itemsets of Jewelry shop (Fy) and Internal relationship between the same item types i. e. Footwear shop (Fz) is found out as y1(0…….n), y2(0………n), y3(0……..n) within the Jewelry shop (Y) P ( Z | Y ) P (Y ) P (Y | Z ) O = fs(Y) = fstage_I_algorithm_apriori(Y) P (Z ) O=fstage_I_algorithm_apriori{y1(0…n)}={y1(1) y1(3), y1(2) y1(5)…} O= fstage_I_algorithm_apriori{y2(0…n)}={y2(0) y2(1), y2(3) y2(7)…} O= fstage_I_algorithm_apriori{y3(0.n)}={y3(2) y3(3), y3(1) y3(4)…...} Internal relationship between the same item types i. e. Dependency between itemsets of Footwear shop (Fz) and z1(0…….n), z2(0………n), z3(0……..n) within the Cloth shop (Fx) is found out as Footwear shop (Z) P ( X | Z )P (Z ) P(Z | X ) O = fs(Z) = fstage_I_algorithm_apriori(Z) P(X ) O= fstage_I_algorithm_apriori{z1(0…..n)} = {z1(0) z1(2), z1(2) z1(4)…} O= fstage_I_algorithm_apriori{z2(0….n)} = {z2(1) z2(4), z2(1) z2(3)…} O= fstage_I_algorithm_apriori{z3(0….n)} = {z3(0) z3(3), z3(2) z3(5)…} Three cases are possible for the system to find out MRA Stage II: interdependencies and for the correct prediction of During second stage it uses individual knowledge base learning rules. and level 1 association is generated in stage 1 of same shop to find out the frequent item sets i.e. x1(0), x2(3), Case 1: Sale of items in Footwear shop (Z) depends on x3(1)……etc is called as global frequent itemsets. sale of items in Jewelry shop(Y) and it is in turn depends It gave sets of frequent item sets for the Cloth shop for on sale of items in Cloth shop (X). That means, X is a different items i.e. Fx as below. cause of Y and Y is a cause of Z. Result is an increase in O = fs(x1,x2,x3) sale of items in Cloth shop (X) causes increase in sale of O=fphase_II_algorithm_apriori{x1,x2,x3}={x1(0) x2(1),x2(3) x3( items in Jewelry shop (Y) which in turn cause increase in 2), x3(0) x2(2)…} sale of items in Footwear shop (Z)[11]. It gives sets of frequent item sets for the Jewelry shop for different items i.e. Fy as below Case 2: Sale of items in Footwear shop (Z) & Jewelry O = fs(y1,y2,y3) shop (Y) depends on sale of items in Cloth shop (X). That O=fphase_II_algorithm_apriori{y1,y2,y3}={y1(0) y2(1),y2(3) y3( 2), y3(0) y2(2)……} means X is a cause of Y and Z. Two child nodes are independent given the parent. Y & Z are independent It gives with sets of frequent item sets for the Footwear given the parent node X. Result is increase in sale of shop for different items i.e. Fz as below items in Cloth shop (X) cause increase in sale of items in O = fs(z1,z2,z3) O= fphase_II_algorithm_apriori{z1,z2,z3} = {z1(0) z2(1), both the shops i.e. Jewelry shop (Y) & Footwear shop (Z) z2(3) z3(2), z3(0) z2(2)…} [11]. MRA Stage 3: Case 3: Sale of items in Footwear shop (Z) depend on Interdependency by Bayesian Probability sale of items in Cloth shop (X) and Jewelry shop (Y). It is necessary to determine dynamic behavior of Fi for That means X & Y are the causes of Z. A node has two particular season. External Dependencies amongst Items parents that are independent unless child is given i.e. an Volume 2, Issue 6 November – December 2013 Page 134 International Journal of Emerging Trends & Technology in Computer Science (IJETTCS) Web Site: www.ijettcs.org Email: editor@ijettcs.org, editorijettcs@gmail.com Volume 2, Issue 6, November – December 2013 ISSN 2278-6856 event may have independent causes. Result is increase in sale of items in Cloth shop (X) & Jewelry shop (Y) cause increase in sale of items in the Footwear shop (Z) provided sale of items in Cloth shop & Jewelry shop does not depend on each other [11]. 5. EXPERIMENTAL RESULTS The experimental results that have been obtained through implementing MRA and Apriori algorithm are presented in this section. Multilevel relationship algorithm applied for finding the frequent itemset and external dependency amongst them. It comes up with pattern which can be further useful for leaning in cooperative system. Performance of Apriori and MRA has compared for various factors i.e. strength, support and interdependency. Graphs show the result comparison between Apriori and MRA. Figure 8: Percentage Interdependency among the three shops Simple Apriori algorithm shows only the frequent itemsets in each shop independently. It does not provide the internal dependency amongst individual items and cannot find out local frequent itemsets. Due to this, external dependencies are not found out between different shops and become unable to find out the learning rules Volume 2, Issue 6 November – December 2013 Page 135 International Journal of Emerging Trends & Technology in Computer Science (IJETTCS) Web Site: www.ijettcs.org Email: editor@ijettcs.org, editorijettcs@gmail.com Volume 2, Issue 6, November – December 2013 ISSN 2278-6856 and pattern of sale. Hence, there is need to develop [6] Rakesh Agrawal, Tomasz Imielinski and Arun modified approach which would enable to give internal & Swami “Database mining: A performance external dependencies along with the learning rules. perspective” published in IEEE Transactions on Multilevel Apriori algorithm and bayesian probability Knowledge and Data Engineering, 5(6):914 925, estimation gives the expected results. December 1993. Special Issue on Learning and Discovery in Knowledge-Based Databases. CONCLUSION [7] Aaron Ceglar & John F. Roddick “Association The classical apriori algorithm widely used for Mining” in ACM Computing Surveys, Vol. 38, No. association rule mining, this having important factors i.e. 2, Article 5, Publication date: July 2006. prediction rate and runtime. This system increase the [8] Baoqing Jiang,WeiWang and Yang Xu “The Math efficiency of generating association rules based on these Background of Apriori Algorithm” analysis and research. The new algorithm Multilevel [9] Jiawei Han & Micheline Kamber “Data Mining: Relationship Algorithm is better than the apriori Concepts & Techniques” Second Edition, Elsevier algorithm. Through this algorithm is good to find the publication. frequent item sets with minimum support.New pattern are [10] Pang-Ning Tan, Vipin Kumar & Michael Steinbach generated by Bayesian probability though which learning “Introduction to Data Mining” by Pearson Education rules are predicted and interpreted. Multilevel Apriori Inc. algorithm and Bayesian probability estimation is not [11] Ethem Alpaydin “Introduction to Machine Learning” combined in any of the previous work. This is novel move Second Edition, MIT Press by PHI. towards the mining association rule. Efficiency of original [12] Tom Mitchell “Machine Learning” McGraw Hill algorithm has been increased due to multilevel International Edition. architecture. Two passes of algorithm has been performed [13] Kishor S. Trivedi “Probability & Statistics with for more accuracy and efficiency. This multilevel Reliability, Queuing and Computer Science approach is especially beneficial when efficiency required Applications” by PHI. is important such as in computationally intensive [14] Liviu Panait Sean Luke “Cooperative Multi-Agent applications that must be run frequently. 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International Journal of Emerging Trends & Technology in Computer Science (IJETTCS)
Web Site: www.ijettcs.org Email: editor@ijettcs.org, editorijettcs@gmail.com
Volume 2, Issue 6, November – December 2013 ISSN 2278-6856, Impact Factor: 2.524 ISRA:JIF

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