ISSN: 2277 – 9043                              International Journal of Advanced Research in Computer Science and Electron...
ISSN: 2277 – 9043                                  International Journal of Advanced Research in Computer Science and Elec...
ISSN: 2277 – 9043                              International Journal of Advanced Research in Computer Science and Electron...
ISSN: 2277 – 9043                            International Journal of Advanced Research in Computer Science and Electronic...
ISSN: 2277 – 9043                            International Journal of Advanced Research in Computer Science and Electronic...
ISSN: 2277 – 9043                                   International Journal of Advanced Research in Computer Science and Ele...
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  1. 1. ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering Volume 1, Issue 5, July 2012 Concise Representation of Multi-level Association Rules using MinMaxExact Rules R. Vijaya Prakash, A. Govardhan, SSVN.Sarma In this paper, we present a Reliable basis representation of Abstract— Association Rule mining plays an important role non-redundant Association Rules. We then look into thisin the discovery of knowledge and information. Association hierarchical redundancy and propose an approach fromRule mining discovers huge number of rules for any dataset for which more non-redundant rules can be derived. We use thedifferent support and confidence values, among this many ofthem are redundant, especially in the case of multi-level same definition of non-redundant rules in single leveldatasets. Mining non-redundant Association Rules in datasets, but to this definition we add a requirement thatmulti-level dataset is a big concern in field of Data mining. In considers the different levels of the item(s) in determining thethis paper, we present a definition for redundancy and a concise redundancy rule. By doing so, more redundant Associationrepresentation called Reliable Exact basis for representing Rules can be eliminated. We also show that it is possible tonon-redundant Association Rules from multi-level datasets. The derive all of the Association Rules, without lose ofgiven non-redundant Association Rules are loss lessrepresentation for any datasets. information. The paper is organized as follows. Section 2 briefly Index Terms—Association Rules, Itemsets, Non-Redundant discusses some related work. In Section 3, we first discussReliable Rules. the algorithms for generating frequent patterns in multilevel datasets and then we present the definition of hierarchical redundancy and introduce our approach for deriving I. INTRODUCTION multilevel non-redundant exact basis rules. In Section 4, we The huge amount of the extracted rules is a big problem for discuss the redundancy in Association Rules and present aAssociation Rule mining. Especially, many of the extracted definition to redundant rules. Experiments and results arerules are considered redundant since they produce the same presented in Section 5. Finally, Section 6 concludes themeaning to the user or extracted rules can be replaced by paper.other rules. Many efforts have been made on reducing thesize of the extracted rule set. There are number ofrepresentations of frequent patterns have been proposed, one II. RELATED WORKof them, is the closed itemsets, is of particular interest as they The approaches proposed in [13, 18] make use of thecan be applied for generating non-redundant rules [10,12,18]. closure of the Galois connection [4] to extract non-redundantThe use of frequent closed itemsets presents a clear promise rules from frequent closed itemsets instead of from frequentto reduce the number of extracted rules [13, 17, 19]. itemsets. One difference between the two approaches is the However, these approaches have only dealt with definition of redundancy. The approach proposed in [18]redundancy in single level datasets. Multi-level datasets in extracts the rules with shorter antecedent and shorterwhich the items are not all at the same concept level contain consequent as well among rules which have the sameinformation at different abstract levels. The approaches used confidence, while the method proposed in [13] defines thatto find frequent itemsets in single level datasets miss the non-redundant rules are those which have minimalinformation, as they only look at one level in the dataset. antecedents and maximal consequents. The definitionThus techniques that consider all the levels are needed [6, 7 proposed in [17] is similar to that of [13]. However, the8,9]. requirement to redundancy is relaxed, and the lesser However, rules derived from multi-level datasets can have requirement makes more rules to be considered redundantthe same issues with redundancy as those from a single level and thus eliminated. Most importantly, [17] proved that thedataset. While approaches used to remove redundancy in elimination of such redundant rules increase the belief to thesingle level datasets [13, 17, 19] can be adapted for use in one extracted rules and the capacity of the extractedrule at a given level gives the same information as another non-redundant rules for solving problems. However, therule at a different level. work mentioned above has only focused on datasets where all items are at the same concept level. Thus they do not need to Manuscript received June 15, 2012. consider redundancy that can occur when there is a hierarchy R. Vijaya Prakash, Department of Informatics, Kaktiya University, among the items.(e-mail: vijprak@hotmail.com),Warangal, India, 9951332996 Dr. A Govardhan, Department of Computer Science and Engineering , A multi-level dataset is the one which has an implicitJNT University, Hyderabad, India, (e-mail: givardhan_cse@yahoo.co.in). taxonomy or concept tree, like shown in Figure 1. The items Prof. SSVN.Sarm, Department of Computer Science and Engineering , in the dataset exist at the lowest concept level but are part of aVaagdevi College of Engineering, Warangal, India, (e-mail: hierarchical structure and organization.ssvn.sarma@gmail.com). 44 All Rights Reserved © 2012 IJARCSEE
  2. 2. ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering Volume 1, Issue 5, July 2012 Food multi-level dataset. It is designed for use on single level datasets. But, it has been adapted for multi-level datasets. One adaptation of Apriori to multi-level datasets is the ML_T2L1 algorithm [5, 6]. The ML_T2L1 algorithm uses a transaction table that has the hierarchy information encoded into it. Each level in the dataset is processed individually. Milk Bread Fruit Firstly, level 1 (the highest level in the hierarchy) is analyzed for large 1-itemsets using Apriori. The list of level 1 large 1- itemsets is then used to filter and prune the transaction dataset of any item that does not have an ancestor in the level 1 large 1-itemset list and remove any transaction which has 2 percent Skimmed White Wheat Apple Banana no frequent items (thus contains only infrequent items when assessed using the level 1 large 1-itemset list). From the level Figure 1 A Simple example of product taxonomy 1 large 1-itemset list, level 1 large 2-itemsets are derived (using the filter dataset). Then level 1 large 3-itemsets are Thus for level of the taxonomy but it also belongs to the derived and so on, until there are no more frequent itemsets toexample, ‘Old Mills’ is an item at the lowest higher concept discover at level 1. Since ML_T2L1 defines that only thecategory of ‘bread’ and also the more refined category ‘white items that are descendant from frequent items at level 1bread’. (essentially they must descend from level 1 large 1-itemsets) Because of the hierarchical nature of a multi-level dataset, can be frequent themselves, the level 2 itemsets are deriveda new approach to finding frequent itemsets for multi-level from the filtered transaction table. For level 2, the largedatasets has to be considered. Work has been done in 1-itemsets are discovered, from which the large 2-itemsetsadapting approaches originally made for single level datasets are derived and then large 3-itemsets etc. After all theinto techniques usable on multi-level datasets. The paper in frequent itemsets are discovered at level 2, the level 3 large[5][7] shows one of the earliest approaches proposed to find 1-itemsets are discovered (from the same filtered dataset) andfrequent itemsets in multi-level datasets and later was so on. ML_T2L1 repeats until either all levels are searchedrevisited in [6]. This work primarily focused on finding using Apriori or no large 1-itemsets are a found at a level.frequent itemsets at each of the levels in the dataset and did As the original work shows [5,6], ML_T2L1 does not findnot focus heavily on cross-level itemsets (those itemsets that cross-level frequent itemsets. We have added the ability for itare composed of items from two or more different levels). to do this. At each level below 1 (so starting at level 2) whenReferring to Figure 1 for an example, the frequent itemset large 2-itemsets or later are derived the Apriori algorithm is{Dairyland-2%-milk, white-bread} is a cross-level itemset not restricted to just using the large n-1-itemsets at the currentas the first item is from the lowest level, while the second level, but can generate combinations using the large itemsetsitem is from a different concept level. In fact the cross-level from higher levels. The only restrictions on this are that theidea was an addition to the work being proposed. Further derived frequent itemset(s) can not contain an item that haswork proposed an approach which included finding an ancestor-descendant relationship with another item withincross-level frequent itemsets [15]. This later work also the same itemset and that the minimum support thresholdperforms more pruning of the dataset to make finding the used is that of the current level being processed (which isfrequent itemsets more efficient. However, even with all this actually the lowest level in the itemset).work the focus has been on finding the frequent itemsets as A second, more recent adaptation of Apriori for use inefficiently as possible and the issue of quality and/or multi-level datasets is a top-down progressive deepeningredundancy in single level datasets. Some brief work method by [15]. This approach was developed to findpresented by [6] discusses removing rules which are level-crossing Association Rules by extending existinghierarchically redundant, but it relies on the user giving an multi-level mining techniques and uses reduced support andexpected confidence variation margin to determine refinement of the transaction table at every hierarchy level.redundancy. There appears to be a void in dealing with This algorithm works very similarly to ML_T2L1 presentedhierarchical redundancy in Association Rules derived from previously in that it uses a transaction table which has themulti-level datasets. This work attempts to fill that void and hierarchy encoded into it and each level is processedshow an approach to deal with hierarchical redundancy individually, one at a time. Initially, level 1 is processed,without losing any information. followed by level 2, 3 and so on until the lowest level is reached and processed, or a level generates no large 1-itemsets. At each level, the large 1-itemsets are first derived III. MINING FREQUENT PATTERNS and are then used to filter / prune[11] the transaction table (as From the beginning of Association Rule mining in [1][3], described for ML_T2L1). This filtering happens at everythe first step has always been to find the frequent patterns or level, not just level 1, like in ML_T2L1. Then largeitemsets. The simplest way to do this is through the use of the 2-itemsets, 3-itemsets etc are derived from the filtered table.Apriori algorithm [2]. However, Apriori is not designed to When it comes to level 2 and lower, the itemsets are notwork on extracting frequent itemsets at multiple levels in a restricted to just the current level, but can include itemsets 45 All Rights Reserved © 2012 IJARCSEE
  3. 3. ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering Volume 1, Issue 5, July 2012from large itemset lists of higher levels. This is how level multiple levels and include cross-level rules (due to crosscrossing Association Rules will be found. For the itemsets level frequent itemsets). The ReliableExactRule approachthat span multiple levels, the minimum support threshold of can remove redundant rules, but as we will show, it does notthe lowest level in the itemset is used as the threshold to remove hierarchy redundancy. The rules given in Table 4 aredetermine whether the itemset is frequent / large. derived from the closed itemsets and generators in Table 3 when the minimum confidence threshold is set to 0.5 or 50% (Table 4). IV. GENERATION OF NON-REDUNDANT Table 3. Frequent closed itemsets and generators derived from MULTI-LEVEL ASSOCIATION RULES the frequent itemsets in Table 2. The use of frequent itemsets as the basis for Association Closed Itemsets GeneratorsRule mining often results in the generation of a large number [1-*-*] [1-*-*]of rules. This is a widely recognized problem. More recent [1-1-*] [1-1-*]work has demonstrated that the use of closed itemsets and [1-1-1] [1-1-1]generators can reduce the number of rules generated [14,16, [1-*-*, 2-2-*] [2-2-*]17,18,20]. This has helped to greatly reduce redundancy in [2-*-*, 1-1-*] [2-*-*, 1-1-*]the rules derived from single level datasets. Despite this, [1-1-*, 1-2-*] [1-2-*]redundancy still exists in the rules generated from multi-level [1-1-*, 2-2-*] [2-2-*]datasets even when using some of the methods designed to [1-*-*, 2-2-1] [2-2-1]remove redundancy. This redundancy we call hierarchical [2-*-*, 1-1-1] [2-*-*, 1-1-1]redundancy. Here in this section we first introduce [1-2-*, 1-1-1] [1-2-*, 1-1-1]hierarchical redundancy in multi-level datasets and then we [1-*-*, 2-1-*, 2-2-*] [2-1-*]detail our work to remove this redundancy without losing [2-*, 1-1-*, 1-2-*] [2-*-*, 1-2-*]information. [1-1-*, 1-2-*, 2-2-*] [1-2-*, 2-2-*] [1-1-*, 2-1-*, 2-2-*] [2-1-*] A. Hierarchical Redundancy [1-*-*, 2-1-1, 2-2-*] [2-1-1]Whether a rule is interesting and/or useful is usually [1-1-*, 2-1-1, 2-2-*] [2-1-1]determined through the support and confidence values that it [1-1-*, 2-2-1, 1-2-*] [2-2-1]has. However, this does not guarantee that all of the rules that [2-1-*, 1-1-1, 2-2-*] [2-1-*] [2-2-*, 1-1-1]have a high enough support and confidence actually convey [2-2-*, 1-1-1, 2-1-1] [2-1-1] [2-2-*, 1-1-1]new information. Following is an example transaction tablefor a multi-level dataset (Table 1). Table 4. Exact basis Association Rules derived from closed itemsets and generators in Table 3. Table 1. Simple multi-level transaction dataset. No Rule Supp Transaction ID Items . 1 [1-1-1, 1-2-1, 2-1-1, 2-2-1] 1 [2-2-*] ==> [1-*-*] 0.571 2 [1-1-1, 2-1-1, 2-2-2, 3-2-3] 2 [1-2-*] ==> [1-1-*] 0.571 3 [1-1-2, 1-2-2, 2-2-1, 4-1-1] 3 [2-2-*] ==> [1-1-*] 0.571 4 [1-1-1, 1-2-1] 4 [2-2-1] ==> [1-*-*] 0.428 5 [1-1-1, 1-2-2, 2-1-1, 2-2-1, 4-1-3] 5 [2-1-*] ==> [1-*-*, 2-2-*] 0.428 6 [1-1-3, 3-2-3, 5-2-4] 6 [2-1-*] ==> [1-1-*, 2-2-*] 0.428 7 [1-3-1, 2-3-1] 7 [2-1-1] ==> [1-*-*, 2-2-*] 0.428 8 [3-2-3, 4-1-1, 5-2-4, 7-1-3] 8 [2-1-1] ==> [1-1-*, 2-2-*] 0.428 This simple multi-level transactional dataset has 3 levels 9 [2-2-1] ==> [1-1-*, 1-2-*] 0.428with each item belonging to the lowest level. The item ID in 10 [2-1-*] ==> [1-1-1, 2-2-*] 0.428the table store/holds the hierarchy information for each item. 11 [2-2-*, 1-1-1] ==> [2-1-*] 0.428Thus the item 1-2-1 belongs to the first category at level 1 12 [2-1-1] ==> [2-2-*, 1-1-1] 0.428and for level 2 it belongs to the second sub-category of the 13 [2-2-*, 1-1-1] ==> [2-1-1] 0.428first level 1 category. Finally at level 3 it belongs to the first The ReliableExactRule algorithm lists all of the rules (insubcategory of the parent category at level 2. From this Table 4) as important and non-redundant. However, we arguetransaction set we use the ML_T2L1 algorithm with the cross that there are still redundant rules. This type of redundancy islevel add-on and a minimum support value of 4 for level 1 beyond what the ReliableExactRule algorithm was designedand 3 for levels 2 and 3. We used the ML_T2L1 algorithm to for. Looking at the rules in Table 4 we claim that rule 4 isdiscover frequent itemsets. From these frequent itemsets, the redundant to rule 1, rule 7 is redundant to rule 5, rule 8 isclosed itemsets and generators are derived (Table 3). The redundant to rule 6 and rule 12 is redundant to rule 10. Foritemsets, closed itemsets and generators come from all three example, the item 2-2-1 (from rule 4) is a child of the morelevels. general/abstract item 2-2-* (from rule 1). Thus rule 4 is in Finally from the closed itemsets and generators the fact a more specific version of rule 1. Because we know thatAssociation Rules can be generated. In this example we use rule 1 says 2-2-* is enough to fire the rule with consequent C,the ReliableExactRule approach presented in [17,18] to whereas rule 4 requires 2-2-1 to fire with consequent C, anygenerate the exact basis rules. The discovered rules are from item that is a descendant of 2-2-* will cause a rule to fire with 46 All Rights Reserved © 2012 IJARCSEE
  4. 4. ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering Volume 1, Issue 5, July 2012consequent C. It does not have to be 2-2-1. Thus rule 4 is Thus the algorithms to extract non-redundant multi-levelmore restrictive. Because 2-2-1 is part of 2-2-* having rule 4 rules using either MinmaxExactHR or ReliableExactHR aredoes not actually bring any new information to the user, as given as follows:the information contained in it is actually part of the Algorithm 1: MinmaxExactHR()information contained in rule 1. Thus rule 4 is redundant. We Input: C: a set of frequent closed itemsets G: a set of minimaldefine hierarchical redundancy in exact Association Rules generators. For g G , g.closure is the closed itemset of g.through the following definition. Output: A set of non-redundant multilevel rules. Definition 1: Let R1 = X1 => Y and R2 = X2 => Y be two 1. MinMaxExact := exact Association Rules, with exactly the same itemset Y as 2. for each k=1 to vthe consequent. Rule R1 is redundant to rule R2 if (1) the 3. for each k-generator g Gkitemset X1 is made up of items where at least one item in X1 4. nonRedundant = trueis descendant from the items in X2 and (2) the itemset X2 is 5. if g g closureentirely made up of items where at least one item in X2 is an 6. for all g′  Gancestor of the items in X1 and (3) the other non-ancestor 7. if (g ′ ≠ g)items in X2 are all present in itemset X1. 8. if ( g′ is ancestor set of g ) and ((c′ =c) or ( g= g ′)) and (g′ is not ancestor set of c′)From this definition, if for an exact Association Rule X1 => 9. then nonRedundant = falseY1 there does not exist any other rule X2 => Y2 such that at 10. breakleast one item in X1 shares an ancestor-descendant 11. end ifrelationship with X2 containing the ancestor(s) and all other 12. end ifitems X2 are present in X1, then X1 => Y1 is a 13. end fornon-redundant rule. To test for redundancy, we take this 14. if nonRedundant = truedefinition and add another condition for a rule to be 15. insert { (g c), g.supp} in MinMaxExact 16. end ifconsidered valid. A rule X => Y is valid if it has no 17. end ifancestor-descendant relationship between any items in 18. end foritemsets X and Y. Thus for example 1-2-1 => 1-2-* is not a 19. end forvalid rule, but 1-2-1 => 1-1-3 is a valid rule. If this condition 20. return MinMaxExactis not met by any rule X2 => Y2 when testing to see if X1 => Algorithm 2: ReliableExactHR()Y1 is redundant to X2 => Y2, then X1 => Y1 is a Input: C: a set of frequent closed itemsets G: a set of minimalnon-redundant rule as X2 => Y2 is not a valid rule.Submit generators. For g G, g.closure is the closed itemset of g.your manuscript electronically for review. Output: A set of non-redundant multilevel rules. 1. ReliableExact :=  B. Generating Exact Basis Rules 2. for all c CAs previous work has shown [14, 17, 18] using frequent 3. for all g Gcclosed itemsets in the generation of Association Rules can 4. nonRedundant = falsereduce the quantity of discovered rules. Because we wish to 5. if c C such that c  c and c g Gc , we haveremove redundancy on top of the redundancy already being (c or c)g)  g)removed, our approach uses the closed itemsets and 6. then nonRedundant = truegenerators to discover the non-redundant rules. [14, 17, 18] 7. elsehave both proposed condensed/more concise bases to 8. nonRedundant = falserepresent non-redundant exact rules. Exact rules refer to rules 9. breakwhose confidence is 1. The proposed approach will be 10. end ifextended to other rules (i.e., so called approximate rules). 11. for all g GThe following definitions outline these two bases: 12. if g ′ ≠ g Definition 2: For the Min-MaxExact (MME) basis, C is the 13. if ( g′ is ancestor set of g ) and (c=c or g=g) and ( g′ isset of the discovered frequent closed itemsets. For each not ancestor set of (c or g) and (g′ is not descendant setclosed itemset c in C, Gc is the set of generators for c. From of (c or g′ )this the exact basis for min-max is: 14. then nonRedundant = true and there exists 15. breakno rules gc where cC, gGc, c  c, g  c and g is 16. end ifdescendant set of g, g has no ancestor or descendant of c or 17. end ifg 18. end for Definition 8: (Reliable Exact Basis without Hierarchy 19. if nonRedundant = trueRedundancy) Let C be the set of frequent closed itemsets. For 20. insert { (g c or g, g.supp} in ReliableExact 21. end ifeach frequent closed itemset c, let Gc be the set of minimal 22. end forgenerators of c. The Reliable exact basis is: 23. end for (c or c g), where 24. return ReliableExactcC, c c, gGc, and there exists no rules g c wherecc, gc and g is descendant set of g, g has no ancestor ordescendant of c or g. 47 All Rights Reserved © 2012 IJARCSEE
  5. 5. ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering Volume 1, Issue 5, July 2012 C. Deriving Exact Rules from the Exact Basis Rules The Min-MaxExact approach and ReliableExact approachhave proven that they can deduce all of the exact rules from V. EVALUATIONtheir basis set [17]. Comparing with the Min-MaxExact Experiments were conducted to test and evaluate theapproach and ReliableExact approach, our work results in a effectiveness of the proposed hierarchically non-redundantsmaller exact basis set by not only removing the redundant exact basis and to confirm that it is also a lossless basis set.rules that are removed by the Min-MaxExact approach and This section presents and details the experiments and theirReliableExact approach, but also removing the hierarchically results.redundant rules. If we can recover all of the hierarchicallyredundant rules, then we can derive all the exact rules by A. Datasetsusing the Min-MaxExact or ReliableExact recovery We used 6 datasets to test our approach to discover whether italgorithm. This will ensure that all the exact rules can still be reduced the size of the exact basis rule set and to test that thederived and by achieving this, our approach will be a lossless basis set was lossless, meaning all the rules could berepresentation of the exact Association Rules. The following recovered. These datasets were composed of 10, 20, 50, 200algorithm is designed to recover the hierarchically redundant and 500 transactions and are named A to F respectively. Therules from the exact basis. By adding it to the algorithms used key statistics for these built datasets are detailed in Table 5.by Min-MaxExact and ReliableExact to derive the exact rules Table 5 Obtained Frequent itemsets using Exact Basisit is then able for the existing ReliableExact recovery Dataset MME MMEHR RE REHRalgorithm to derive all of the exact rules. This is because our A 15 10 13 9algorithm will give them a basis set that includes thehierarchically redundant rules (which the ReliableExact B 106 68 80 58approach would not have removed in the first place). The C 174 134 113 89basic idea is that, for each exact basis rule, first from D 577 429 383 305generators to construct all possible exact basis rules whose E 450 405 315 287antecedent is a descendant of the exact basis rule (steps 4 to 7in Algorithm 3). These rules are potential exact basis rules F 725 602 91 80that might have been eliminated due to the Fig. 2. Multi Level association Rulesancestor-descendant relationship. Then check to make surethese potential rules are valid (steps 8 to 12), finally, from thepotential exact rules to find exact basis rules. These exactbasis rules have been eliminated due to theancestor-descendant relationship (steps 13 to 18).Algorithm 3: DeriveExactHR()Input: Set of exact basis rules denoted as Exact basis, set offrequent closed itemsets C and generators G.Output: Set of rules that covers the exact basis and thehierarchically redundant rules.1. Recovered := 2. r Exact basis3. CandidateBasis:= 4. for all generator g in G5. if any of the item x in the antecedent X of rule r: X Y isthe ancestor of g.6. then add all of the possible subsets of g into S7. end for VI. CONCLUSION8. for all s in S, check every , x X if x doesn’t have adescendant in s, add x to s to make s a descendant set of X Redundancy in Association Rules affects the quality of the9. if s has no ancestors in Y and s has no descendants in Y and information presented and this affects and reduces the use of the rule set. The goal of redundancy elimination is to improvefor all items i s there are no ancestor-descendant relations the quality, thus allowing them to better solve problems beingwith item i s and for all item i Y there are no faced. Our work aims to remove hierarchical redundancy inancestor-descendant relation with item i Y multi-level datasets, thus reducing the size of the rule set to10. then insert s Y in CandidateBasis improve the quality and usefulness, without causing the loss11. end if of any information. We have proposed an approach which12. end for removes hierarchical redundancy through the use of frequent13. for all B D  CandidateBasis closed itemsets and generators. This allows it to be added to14. if BUD= itemset i C and B = gGi other approaches which also remove redundant rules, thereby15. insert {B D , g.supp} in Recovered allowing a user to remove as much redundancy as possible.16. end if The next step in our work is to apply this approach to the17. end for approximate basis rule set to remove redundancy there. We18. end for will also review our work to see if there are other hierarchical19. return Exactbasis U Recovered 48 All Rights Reserved © 2012 IJARCSEE
  6. 6. ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering Volume 1, Issue 5, July 2012redundancies in the basis rule sets that should be removed Lal Nehru University, Delhi and Ph.D from JNT University in 2003. He is very eminent person in the field of teaching he guided 4 Ph.D scholars.and will investigate what should and can be done to furtherimprove the quality of multi-level Association Rules. Prof. SSVN. Sarma is an eminent professor in Mathematics, He Worked in Department of Mathematics and Department of Informatics, Kakatiya University over period of 30 years. He is well known person in the field of Mathematics and Computer Science. He guided many Ph.D Scholars REFERENCES[1] Bayardo, R.J., Agrawal, R. & Gunopulos, D.(2000). Constraint-based rule mining in large,dense databases. Data Mining and Knowledge Discovery, 4: 217-240[2] Berry, M.J.A. & Linoff, G.S. (1997). Data Mining Techniques for Marketing Sales and Customer Support. John Wiley and Sons[3] [3] Brin, S., Motwani, R., Ullman, J.D. & Tsur, S. (1997). Dynamic itemset counting and implication rules for market basket data. In: Proceedings of the 1997 ACM SIGMOD Conference, 255-264[4] [4] Ganter, B. & Wille, R. (1999). Formal Concept Analysis: Mathematical Foundations. Springer-Verlag[5] [5] Han, J. & Fu, Y. (1995). Discovery of multiple-level Association Rules from large databases. In: Proceedings of the 21st International Conference on Very Large Databases, 420-431[6] [6] Han, J. & Fu, Y. (1999). Mining multiple-level Association Rules in large databases. IEEE Transactions on Knowledge and Data Engineering, 11 (5): 798-805[7] [7] Han, J. & Fu, Y. (2000). Mining multiple-level Association Rules in large databases. IEEE Transactions on Knowledge and Data Engineering, 11: 798-804[8] [8] Hong, T.P., Lin, K.Y. & Chien, B.C. (2003). Mining fuzzy multiple-level Association Rules from quantitative data. Applied Intelligence, 18 (1): 79-90[9] [9] Kaya, M. & Alhajj, R. (2004). Mining multi-cross-level fuzzy weighted Association Rules. In: the 2nd International IEEE Conference on Intelligent Systems, 225-230[10] [10] Kryszkiewicz, M., Rybinski, H. & Gajek, M. (2004). Dataless transitions between concise representations of frequent patterns. Journal of Intelligent Information Systems, 22 (1): 41-70[11] [11] Ng, R.T., Lakshmanan, V., Han, J. & Pang, A. (1998). Exploratory mining and pruning otimizations of constrained Association Rules. In: Proceedings of the SIGMOD conference, 13-24[12] [12] Pasquier, N., Bastide, Y., Taouil, R. & Lakhal, L. (1999). Efficient mining of association rultes using closed itemset lattices. Information Systems, 24 (1): 25-46[13] [13] Pasquier, N., Taouil, R., Bastide, Y., Stumme, G. & Lakhal, L. (2005). Generating a condensed representation for Association Rules. Journal of Intelligent Information Systems, 24 (1): 29-60[14] [14] Srikant, R., Vu, Q. & Agrawal, R. (1997). Mining Association Rules with item constraints. In: Proceedings of the KDD Conference, 67-73[15] [15] Thakur, R.S., Jain, R.C. & Pardasani, K.P. (2006). Mining level-crossing Association Rules from large databases. Journal of Computer Science, 76-81[16] [16] Wille, R. (1982). Restructuring lattices theory: An approach based on hierarchies of concepts. In: Rival, I. (ed.), Ordered Sets. Dordrecht-Boston[17] [17] Xu, Y. & Li, Y. (2007). Generating concise Association Rules. In: Proceedings of the 16th ACM Conference on Conference on Information and Knowledge Management (CIKM07), 781-790[18] [18] Zaki, M.J. (2000). Generating nonredundent Association Rules. In: Proceedings of the KDD Conference, 34-43[19] [19] Zaki, M.J. (2004). Mining non-redundant Association Rules. Data Mining and Knowledge Discovery, 9: 223-248[20] [20] Ziegler, C.N., McNee, S.M., Konstan, J.A & Lausen, G. (2005). Improving recommendation lists through topic diversification. In: Proceed. of the 14th Inter. World Wide Web Conference, 22-32 R. Vijaya Prakash is presently working as AssociateProfessor in Department of Computer science &Engineering, SR Engineering College., Pursuing Ph.Dfrom Kakatiya University, Warangal. He completed hisMCA from Kakatiya University and M.Tech (IT) form Punjabi University,Patiala. Dr. A. Govardhan is working as professor inDepartment of Computer Science & Engineering, JNTUniversity, Hyderabad. He Received his B.Tech in 1992from Osmain University, M.Tech in 1994 from Jawahar 49 All Rights Reserved © 2012 IJARCSEE

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