A Fast Association Rule Algorithm Based on Bitmap Computing with Multiple Minimum Supports using Maximum Constraints

Transcription

1 A Fat Aociation Rule Algorithm Baed on Bitmap Computing with Multiple Minimum Support uing Maximum Contraint Jyothi Patil, and Dr. V.D.Mytri Abtract Mining aociation rule from databae i a timeconuming proce. Finding the large item et fat i the crucial tep in the aociation rule algorithm. In thi paper we preent a algorithm baed on the Apriori approach to find the large-itemet and aociation rule under the contraint multiple minimum upport uing maximum contraint. Mot of the previou approache et a ingle minimum upport threhold for all the item or itemet. But in real application, different item may have different criteria to judge it importance. The upport requirement hould then vary with different item. Thi algorithm alo doen t follow the generationand-tet trategy of Apriori algorithm and adopt the divide-andconquer trategy, thu avoid the time-conuming table can to find and prune the itemet, all the operation of finding large itemet from the dataet are the fat bit operation baed on it correponding granular. The experimental reult of our algorithm with Apriori, AprioriTid and AprioirHybrid algorithm how thi algorithm i 2 to 3 order of magnitude fater. Our reearch indicate that multiple minimum upport uing maximum contraint and granular computing. can greatly improve the performance of aociation rule algorithm, and are very promiing for data mining application. Keyword Data mining, Multiple minimum upport, Aociation rule, Maximum contraint, Granular computing. C I. INTRODUCTION ONSIDER a upermarket with a large collection of item. Typical buine deciion that the management of the upermarket ha to make include what to put on ale, how to deign coupon, how to place merchandie on helve in order to maximize the profit, etc. Analyi of pat tranaction data i a commonly ued approach in order to improve the quality of uch deciion. Until recently, however, only global data about the cumulative ale during ome time period (a day, a week, a month, etc.) wa available on the computer. Progre in bar-code technology ha made it poible to tore the o called baket data that tore item purchaed on a per-tranaction, bai. Baket data type tranaction do not necearily conit of item bought together at the ame point Jyothi Patil i Reearch Scholar of CM Univerity, Karnataka, India. - jyothip_pda2003@yahoo.com. Dr V.D.Mytri i with the Electronic Engineering Department, Shetty Intitute of Technology, Karnataka, India mytri@gmail.com. of time. It may conit of item bought by a cutomer over a period of time. Example include monthly purchae by member of a book club or a muic club.several organization have collected maive amount of uch data. Thee data et are uually tored on tertiary torage and are very lowly migrating to databae ytem. One of the main reaon for the limited ucce of databae ytem in thi area i that current databae ytem do not provide neceary functionality for a uer intereted in taking advantage of thi information. In thi tudy we conidered Aociation Rule Mining for knowledge dicovery and generate the rule by applying our developed approach on real databae. Mining Aociation i one of the technique involved in Data mining. Dicovering aociation rule i at the heart of data mining. Mining for aociation rule between item in large databae of ale tranaction ha been recognized a an important area of databae reearch [1]. Thee rule can be effectively ued to uncover unknown relationhip, producing reult that can provide a bai for forecating and deciion making. The original problem addreed by aociation rule mining wa to find a correlation among ale of different product from the analyi of a large et of upermarket data. Today, reearch work on aociation rule i motivated by an extenive range of application area, uch a banking, manufacturing, health care, and telecommunication. It i alo ued for building tatitical theauru from the text databae [2], finding web acce pattern from web log file [3], and alo dicovering aociated image from huge ized image databae [4]. A number of aociation rule mining algorithm have been developed in the lat few year [5, 6, 7, 8, 9, 10], which can be claified into two categorie: (a) candidate generation/tet approach uch a Apriori [6] (b) pattern growth approach [9, 10]. A miletone in the firt category tudie i the development of an Apriori baed, level wie mining method for aociation, which ha parked the development of variou kind of Apriori like aociation mining algorithm. Among thee, the Apriori algorithm ha been very influential. Since it inception, many cholar have improved and optimized the Apriori algorithm and have preented new Apriori like algorithm [11, 12, 13, 14, 15]. The Apriori like algorithm adopt an iterative method to dicover frequent 210

2 itemet. The exiting mining algorithm have ome drawback: Firtly, the exiting mining algorithm are motly deigned in form of everal pae o that the whole databae need to be read from dik everal time for each uer query under the contraint that the whole databae i too large to be tored in memory. Thi i very inefficient in conidering the big overhead of reading the large databae even though only partial item are intereted in fact. A a reult, they cannot perform efficiently in term of reponding the uer query quickly. Secondly, in many cae, the algorithm generate an extremely large number of aociation rule, often in thouand or even million. Further, the aociation rule are ometime very large. It i nearly impoible for the end uer to comprehend or validate uch large number of complex aociation rule, thereby limiting the uefulne of the data mining reult. Thirdly, no guiding information i provided for uer to chooe uitable etting for the contraint uch a upport and confidence uch that an appropriate number of aociation rule are dicovered. Conequently, the uer have to ue a try and -error approach to get uitable number of rule. Thi i very time conuming and inefficient. Therefore, one of the main challenge in mining aociation rule i developing fat and efficient algorithm that can handle large volume of data. In thi paper we attack the aociation rule mining by an apriori baed approach to find the large-itemet and aociation rule under the contraint multiple minimum upport uing maximum contraint and ue bitmap computing to peed up the algorithm,pecifically deigned for the optimization in very large tranactional databae. The ret of the paper i organized a follow. We introduce the theoretical propertie and formal definition of aociation rule in ection 2. Section 3, preent ome related work.. In Section 4, the propoed method i decribed in detail. Section 5 preent comparion and experiment reult of our propoed approach with variou Apriori algorithm. Finally, a concluion and the future work are given in Section 6. II. ASSOCIATION RULES MINING Aociation rule of data mining involve picking out the unknown inter-dependence of the data and finding out the rule between thoe item.let I = I1; I2;...; Im be a et of binary attribute, called item. Let T be a databae of tranaction. Each tranaction t i repreented a a binary vector, with t[k] = 1 if t bought the item Ik, and t[k] = 0 otherwie. There i one tuple in the databae for each tranaction. Let X be a et of ome item in I. We ay that a tranaction t atifie X if for all item Ik in X, t[k] =1. A rule i defined a an implication of the form A=>B where X I, Y I, and A B Ǿ. The left-hand ide of the rule i called a antecedent. The right-hand ide of the rule i called a conequent. For example the rule { Onion, Potatoe}=>{beef} found in the ale data of a upermarket would indicate that if a cutomer buy Onion and potatoe together then the cutomer i likely to buy beef alo. Such information i ueful to make deciion about marketing activitie. Aociation rule are alo ued in many application including Web uage Mining, Intruion Detection and Bioinformatic. The election of aociation rule i baed on upport and confidence. The confidence factor indicate the trength of the implication rule, i.e. the confidence for an aociation rule i the ratio of the number of tranaction that contain X U Y to the number of tranaction that contain X; wherea the upport factor indicate the frequencie of the occurring pattern in the rule. i.e., the upport for an aociation rule i the percentage of tranaction in the databae that contain X U Y. Given the databae D, the problem of mining aociation rule involve the generation of all aociation rule among all item in the given databae D that have upport and confidence greater than or equal to the uer pecified minimum upport and minimum confidence. Typically large confidence value and a maller upport are ued. Rule that atify both minimum upport and minimum confidence are called trong rule. Since the databae i large and uer concern about only thoe frequently purchaed item, uually threhold of upport and confidence are predefined by uer to drop thoe rule that are not o intereting or ueful. The dicovery of aociation rule for a given dataet D i typically done in two tep [5, 16]: dicovery of frequent itemet and the generation of aociation rule. The firt tep i to find each et of item, called a itemet, uch that the cooccurrence rate of thee item i above the minimum upport, and thee itemet are called a large itemet or frequent itemet. In other word, find all et of item (or itemet) that have tranaction upport above minimum upport. Finding large itemet i generally very eay but very cotly. The naive approach would be to count all itemet that appear in any tranaction. Suppoe one of the large itemet i Lk, Lk = {I1, I2,, Ik}, aociation rule with thi itemet are generated in the following way: the firt rule i {I1, I2,, Ik1} {Ik}, by checking the confidence thi rule can be determined a intereting or not. Then other rule are generated by deleting the lat item in the antecedent and inerting it to the conequent, further the confidence of the new rule are checked to determine the interetingne of them. Thoe procee iterated until the antecedent become empty. The ize of an itemet repreent the number of item in that et. If the ize of an itemet i equal to k, then thi itemet i called a the k itemet. The econd tep i to find aociation rule from the frequent itemet that are generated in the firt tep. The econd tep i rather traightforward. Once all the large itemet are found generating aociation rule i traightforward. The firt tep dominate the proceing time and for that reaon, it ha been one of the mot popular reearch field in data mining. So, focu ha been made in thi paper on the firt tep. III. PREVIOUS WORK The problem of dicovering aociation rule wa firt 211

3 introduced in [5] and an algorithm called AIS wa propoed for mining aociation rule. For lat fifteen year many algorithm for rule mining have been propoed. Mot of them follow the repreentative approach by Agrawal et al. [16], namely Apriori algorithm. Variou reearche were done to improve the performance and calability of Apriori included uing parallel computing. There were alo tudie to improve the peed of finding large itemet with hah table, map, and tree data tructure. Here we review ome of the related work that form a bai for our algorithm. In AIS algorithm[5] candidate itemet are generated and counted on-the-fly a the databae i canned. After reading a tranaction, it i determined which of the itemet that were found to be large in the previou pa are contained in thi tranaction. New candidate itemet are generated by extending thee large itemet with other item in the tranaction. A large itemet l i extended with only thoe item that are large and occur later in the lexicographic ordering of item than any of the item in l. The candidate generated from a tranaction are added to the et of candidate itemet maintained for the pa, or the count of the correponding entrie are increaed if they were created by an earlier tranaction. The main drawback of the AIS algorithm i that it make multiple pae over the databae. Furthermore, it generate and count too many candidate itemet that turn out to be mall, which require more pace and wate much effort that turned out to be uele. In SETM algorithm [17] wa motivated by the deire to ue SQL to compute large itemet. Like AIS, the SETM algorithm alo generate candidate on-the-fly baed on tranaction read from the databae. It thu generate and count every candidate itemet that the AIS algorithm generate. However, to ue the tandard SQL join operation for candidate generation, SETM eparate candidate generation from counting.it ave a copy of the candidate itemet together with the TID of the generating tranaction in a equential tructure. At the end of the pa, the upport count of candidate itemet i determined by orting and aggregating thi equential tructure.setm remember the TID of the generating tranaction with the candidate itemet. To avoid needing a ubet operation, it ue thi information to determine the large itemet contained in the tranaction read. (L_k ) (C_k ) and i obtained by deleting thoe candidate that do not have minimum upport.auming that the databae i orted in TID order, SETM can eaily find the large itemet contained in a tranaction in the next pa by orting (L_k ) on TID. n fact, it need to viit every member of (L_k ) only once in the TID order, and the candidate generation can be performed uing the relational merge-join operation[17]. The diadvantage of thi approach i mainly due to the ize of candidate et (C_k ). For each candidate itemet, the candidate et now ha a many entrie a the number of tranaction in which the candidate itemet i preent. Moreover, when we are ready to count the upport for candidate itemet at the end of the pa, (C_k ) i in the wrong order and need to be orted on itemet. After counting and pruning out mall candidate itemet that do not have minimum upport, the reulting et (L_k ) need another ort on TID before it can be ued for generating candidate in the next pa. The Apriori [16] and AprioriTid algorithm generate the candidate itemet to be counted in a pa by uing only the itemet found large in the previou pa without conidering the tranaction in the databae. The baic intuition i that any ubet of a large itemet mut be large. Therefore, the candidate itemet having k item can be generated by joining large itemet having k-1 item, and deleting thoe that contain any ubet that i not large. Thi procedure reult in generation of a much maller number of candidate itemet. The AprioriTid algorithm ha the additional property that the databae i not ued at all for counting the upport of candidate itemet after the firt pa. Rather, an encoding of the candidate itemet ued in the previou pa i employed for thi purpoe. In later pae, the ize of thi encoding can become much maller than the databae, thu aving much reading effort. Another algorithm, called Apriori Hybrid, i introduced in [16]. The baic idea of the Apriori Hybird algorithm i to run the Apriori algorithm initially, and then witch to the AprioriTid algorithm when the generated databae, i.e. large k itemet in the tranaction with identifier TID, would fit in the memory. The DHP (Direct Hahing and Pruning) algorithm [12] i an effective hah baed algorithm for the candidate et generation. It reduced the ize of candidate et by filtering any k itemet out of the hah table if the hah entry doe not have minimum upport. The hah table tructure contain the information regarding the upport of each itemet. The DHP algorithm conit of three tep. The firt tep i to get a et of large 1-itemet and contruct a hah table for 2itemet. The econd tep generate the et of candidate itemet Ck baed on the hah table generated in previou pa, determine the et of large k-itemet Lk, reduce the ize of databae for the next large itemet and make a hah table for candidate large (k+1)-itemet. The third tep i the ame a the econd tep except it doe not ue the hah table in determining whether to include a particular itemet into the candidate itemet. Thi tep i ued for later iteration when the number of hah bucket with a upport count greater than or equal to the minimum tranaction upport required i le than a predefined threhold. The partition algorithm[18] execute in two phae. In the firt phae, the Partition algorithm logically divide the databae into a number of non-overlapping partition. The partition are conidered one at a time and all large itemet for that partition are generated. At the end of phae I, thee large itemet are merged to generate a et of all potential large itemet. In phae II, the actual upport for thee itemet are generated and the large itemet are identified. The partition ize are choen uch that each partition can be accommodated in the main memory o that the partition are read only once in each phae. Thi approach will work only if 212

4 the given et contain all actual large itemet. The frequent pattern growth[19] algorithm ue compact data tructure, called frequent-pattern tree, or FP-tree in hort, which i an extended prefix-tree tructure toring crucial, quantitative information about frequent pattern. Every tranaction databae i mapped onto one path in the FP tree, and the frequent itemet information i completely tored in the tree.since there are often a lot of haring of frequent item among tranaction the ize of the tree i much maller than it original databae. Subequent frequent-pattern mining will only need to work on the FP-tree intead of the whole data et. Sampling large databae[20] for aociation rule ue a- A Fat Aociation Rule Algorithm Baed On Bitmap Computing with Multiple Minimum Support Uing Maximum Contraint random ample, to determine all aociation rule that probably hold in the whole databae, and then to verify the reult with the ret of the databae. The algorithm thu produce exact, aociation rule in one full pa over the databae. In thoe rare cae where ampling method doe not produce all aociation rule, the miing rule can be found in a econd pa. Mining aociation rule with multiple minimum [14] propoed an approach for mining aociation rule with nonuniform minimum upport value. Their approach allowed uer to pecify different minimum upport to different item. The minimum upport value of an itemet i defined a the lowet minimum upport among the item in the itemet. Wang et al. [22] then generalized the above idea and allowed the minimum upport value of an itemet to be any function of the minimum upport value of item contained in the itemet. Although their approach i flexible in aigning the minimum upport to itemet, the mining algorithm i a little complex due to it generality. IV. PROPOSED APPROACH In the propoed algorithm, item may have different minimum upport and the maximum contraint i adopted in finding large itemet. That i, the minimum upport for an itemet i et a the maximum of the minimum upport of the item contained in the itemet. Under the contraint, the characteritic of level-by-level proceing i kept, uch that the original Apriori algorithm can be eaily extended to find the large itemet. The propoed algorithm firt find all the large 1-itemet L1 for the given tranaction by comparing the upport of each item with it predefined minimum upport. After that, candidate 2-itemet C2 can be formed from L1. Note that the upport of all the large 1-itemet compriing each candidate 2-itemet mut be larger than or equal to the maximum of the minimum upport of them. Thi feature provide a good pruning effect before the databaei canned for finding large 2-itemet.The propoed algorithm then find all the large 2-itemet L2 for the given tranaction by comparing the upport of each candidate 2-itemet with the maximum of the minimum upport of the item contained in it. The ame procedure i repeated until all large itemet have been found. The detail of the propoed mining algorithm under the maximum contraint are decribed below. An Example: In thi ection, an example i given to demontrate the propoed data-mining algorithm. Thi i a imple example to how how the propoed algorithm can be ued to generate aociation rule from a et of tranaction with different minimum upport value defined on different item. Aume the ten tranaction hown in Table I are ued for mining. TABLE I THE SET OF TEN TRANSACTION DATA TABLE II THE PREDEFINED MINIMUM SUPPORT VALUES FOR ITEMS. Item A B C D E F G Min- Sup TID Item 1 ABDG 2 BDE 3 ABCEF 4 BDEG 5 ABCEF 6 BEG 7 ACDE 8 BE 9 ABEF 10 ACDF TABLE III THE SUPPORT VALUES OF ALL THE ITEMS FOR THE GIVEN TEN TRANSACTIONS. Item A B C D E F G Support Each tranaction conit of two feature, tranaction identification (TID) and item purchaed. Alo aume that the predefined minimum upport value for item are defined in Table 2.Moreover, the confidence value λ i et at 0.85 to be a threhold for the intereting aociation rule.in order to find the aociation rule from the data in Table I with the multiple predefined minimum upport value, the propoed mining algorithm proceed a follow: STEP 1: The count and upport of each item occurring in the ten tranaction in Table I are to be found. Take item A a an example. The count of item A i 6, and it upport value i calculated a 6/10 (=0.6). The upport value of all the item for the ten tranaction are hown in Table III. STEP 2: The upport value of each item i compared with it predefined minimum upport value. Since the upport value of item A, B, C,E and F are repectively larger than or equal to their predefined minimum upport, thee five item are then put in the large 1-itemet L1. TABLE IV THE SUPPORT VALUES OF ALL THE CANDIDATE 2-ITEMSETS. 2- A,C A,E B,E C,F Itemet Support

5 STEP 3: r i et at 1, where r i ued to keep the current number of item in an itemet. STEP 4: The candidate et C2 i generated from L1, and the upport of the two item in each itemet in C2 mut be larger than or equal to the maximum of their predefined minimum upport value. Take the poible candidate 2-itemet {A,C} a an example. The upport of item A and C are 0.6 and 0.4 from STEP 1, and the maximum of their minimum upport value i 0.4. Since both of the upport of thee two item are larger than 0.4, the itemet {A,C} i put in the et of candidate 2-itemet. On the contrary for another poible candidate 2-itemet {A, B}, ince that the upport (0.6) of item A i maller than the maximum (0.7) of their minimum upport value, the itemet {A, B} i not a member of C2. All the candidate 2-itemet generated in thi way are found a:c2 = {{A,C}, {A,E}, {B,E}, {C, F}}. STEP 5: The count and upport of each candidate itemet in C2 are found from the given tranaction. Reult are hown in Table IV. STEP 6: The upport value of each candidate 2-itemet i then compared with the maximum of the minimum upport value of the item contained in the itemet. Since the upport value of all the candidate 2-itemet {A,C} and {B,E} atify the above condition, thee four itemet are then put in the et of large 2-itemet L2. STEP 7: Since L2 i not null, r i et at 2 and STEPS 4 to 7 are repeated. No candidate 3-itemet, C3, i generated and L3 i thu null. The next tep i then executed. STEP 8: The aociation rule for each large q-itemet, q 2, are contructed by the following ubtep: (a) All poible aociation rule are formed a follow: (1) If A i bought, then C i bought ; (2) If C i bought, then A i bought ; (3) If B i bought, then E i bought ; (4) If E i bought, then B i bought ; (b) The confidence factor of the above aociation rule are calculated. Take the firt poible aociation rule If A i bought,then C i bought a an example. The confidence factor for thi rule i then: = =0.67 Reult for all the four aociation rule are hown a follow: (1) If A i bought, then C i bought with a confidence factor of 0.67; (2) If C i bought, then A i bought with a confidence factor of 1.0; (3) If B i bought, then E i bought with a confidence factor (4) If E i bought, then B i bought with a confidence factor STEP 9: The confidence factor of the above aociation rule are compared with the predefined confidence threhold λ. Aume the confidence λ i et at 0.85 in thi example. The following four rule are thu output: (1) If C i bought, then A i bought with a confidence factor of 1.0; (2) If B i bought, then E i bought with a confidence factor (3) If E i bought, then B i bought with a confidence factor In thi example, three large q-itemet, q 2, and three aociation rule are generated. Note that if the tranaction are mined uing the minimum contraint propoed in [21], eighteen large q-itemet, q 2, are found. The propoed mining algorithm uing the maximum contraint thu find le large itemet and aociation rule than that uing the minimum contraint. The propoed algorithm can, however, find the large itemet level by level without backtracking. It i thu more time-efficient than that with the minimum contraint. Lin [23] approach can eaily be ued in our algorithm for mining from a tranaction databae. An item or an itemet i regarded a an equivalence cla (a granule). If a tranaction contain a certain item, the tranaction then belong to the equivalence cla of the item and the correponding bit in it granular repreentation i et at 1. The granular repreentation for the data in Table 1 i hown in Table V. TABLE V THE GRANULAR REPRESENTATION Item Equivalence Cla Granular Repreentation Count A {TID1, TID3, TID5, TID7, TID9, TID10} { } 6 B C D E {TID1, TID2, TID3, TID4, TID5, TID6, TID8, TID9} {TID3, TID5, TID7, TID10} {TID1, TID2, TID4, TID7, TID10} {TID2, TID3, TID4, TID5, TID6, TID7, TID8, TID9, TID10} { } 8 { } 4 { } 5 { } 9 F { TID3, TID5, TID9} { } 3 G {TID1, TID4, TID6} { } 3 In thi example, A, B, C, E and F are large 1-itemet. According to our algorithm, the candidate 2-itemet are found a: C2 = {{A,C}, {A,E}, {B,E},{C, F}}. The boolean AND operation can then be ued to form the bit pattern of the 2-itemet. The reult are hown in Table VI.Since the two 2- itemet, {A,C} and {B,E}, have their upport larger than the upport contraint, they are then put in the large 2-itemet. Itemet with more item can be formed in the imilar way. TABLE VI USING THE BOOLEAN AND OPERATION TO FIND THE GRANULES FOR C2 2-Item Granular operation Granular Count Repreentation A AND C { } \ { } A AND E { } \ { }

6 B AND E { } \ { } C AND F { } \ { } V. EXPERIMENTAL RESULTS Three different data are ued to compare the run time on the algorithm to find aociation rule. The data varie in the number of tuple, the attribute per relation and the minimal upport. The tet were conducted uing an IBM PC with 3.4GHz CPU,1 GB RAM under WindowXP. The program i coded in C++ for Apriori, AprioriTid and AprioriHybrid Data Set Row Column # Of Item Table Size Bitmap Size Mini mal Supp ort DS1 400k MB 10MB 20k DS2 800k MB 24.5MB 40k DS3 1MB MB 90MB 50k Lengt h DS1 # Cand # Item et Propoe d algorith m TABLE VII DATA SETS Apriori_ Hybrid Apriori_Tid Apriori Total Time DS S S S S S S S S 0.01S Total Time DS Total Time Here are ome obervation and explanation on the reult (1) The total time of our comparion include the time to write the aociation rule to a file; propoed algorithm i 2 to 3 order of magnitude fater than the variou Apriori algorithm ( time fater). The big the tet data et, the big the time difference between the propoed algorithm and the variou Apriori algorithm. (2) Propoed algorithm take the ame or litter longer time than the variou Apriori algorithm in contructing the 1- itemet becaue of the extra cot of building the bitmap for the 1-itemet. But after the 1-itemtet i done, propoed algorithm i ignificant fater than the Apriori algorithm in contructing large frequent itemet becaue it only ue the fat bit operation (AND,COUNT and SHIFT)and doen t need to tet the ubet of the newly candidate (3) Propoed algorithm only tore the bitmap of the frequent item, and the bitmap torage (uncompreed) i le than the original data et (1/2 to 1/4 of the original data ize). The main reaon that propoed algorithm i ignificant fater than Apriori and it variation are (1) Propoed algorithm adopt the divide-and-conquer trategy,the tranaction i decompoe into vertical bitmap format and lead to focued earch of maller domain.there i no repeated can of entire databae in propoed algorithm. (2) Propoed algorithm doen t follow the traditional candidate-generate-and tet approach, thu ave ignificant amount of time to tet the candidate (3) In propoed algorithm, the baic operation are bit Count and bit And operation, which are extremely fater than the pattern earch and matching operation ued in Apriori and it variation VI. CONCLUSIONS We preent a fat aociation rule algorithm in which the minimum upport for an itemet i et a the maximum of the minimum upport of the item contained in the itemet. The propoed mining algorithm uing the maximum contraint thu find le large itemet and aociation rule than that uing the minimum contraint. To peed up the algorithm granular technique i ued. Propoed algorithm avoid the time-conuming table can to find and prune the itemet, all the operation of finding large itemet from the dataet are the fat bit operation. The experimental reult of our propoed algorithm with Apriori, AprioriTid and AprioirHybrid algorithm how propoed algorithm i 2 to 3 order of magnitude fater. Thi reearch indicate that bitmap and granular computing technique can greatly enhance the performance for finding aociation rule, and bitmap technique are very promiing for the deciion upport query optimization and data mining application. Paralleling the bitmap-baed algorithm i another crucial apect of DSS and data mining performance. REFERENCES [1] Han and M. Kamber, Data Mining: Concept and Technique, Morgan Kaufmann Publiher, [2] J. D. Holt and S. M. Chung, Efficient Mining of Aociation Rule in Text Databae CIKM'99, Kana City, USA, pp , Nov [3] B. Mobaher, N. Jain, E.H. Han, and J. Srivatava, Web Mining: Pattern Dicovery from World Wide Web Tranaction, Department of Compute Science, Univerity of Minneota, Technical Report TR96-050, (March, 1996). [4] C. Ordonez, and E. Omiecinki, Dicovering Aociation Rule Baed on Image Content, IEEE Advance in Digital Librarie (ADL'99), [5] R.Agrawal, T. Imielinki, and A. Swami, Mining aociation rule between et of item in large databae, In Proceeding of the ACM 215

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