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(IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 9, September 2011 Parallel Edge Projection and Pruning (PEPP) Based Sequence Graph Protrude Approach for Closed Itemset Mining kalli Srinivasa Nageswara Prasad Prof. S. Ramakrishna Research Scholar in Computer Science Department of Computer Science Sri Venkateswara University, Tirupati Sri Venkateswara University, Tirupati Andhra Pradesh , India. Andhra Pradesh , India. . . Abstract: Past observations have shown that a frequent item set there are less methods for mining closed sequential item sets. mining algorithm are supposed to mine the closed ones as the end This is because of intensity of the problem and CloSpan is the gives a compact and a complete progress set and better efficiency. only variety of algorithm [17], similar to the frequent closed Anyhow, the latest closed item set mining algorithms works with item set mining algorithms, it follows a candidate maintenance- candidate maintenance combined with test paradigm which is and-test paradigm, as it maintains a set of readily mined closed expensive in runtime as well as space usage when support threshold is less or the item sets gets long. Here, we show, PEPP, sequence candidates used to prune search space and verify which is a capable algorithm used for mining closed sequences whether a recently found frequent sequence is to be closed or without candidate. It implements a novel sequence closure not. Unluckily, a closed item set mining algorithm under this checking format that based on Sequence Graph protruding by an paradigm has bad scalability in the number of frequent closed approach labeled “Parallel Edge projection and pruning” in short item sets as many frequent closed item sets (or just candidates) can refer as PEPP. A complete observation having sparse and consume memory and leading to high search space for the dense real-life data sets proved that PEPP performs greater closure checking of recent item sets, which happens when the compared to older algorithms as it takes low memory and is more support threshold is less or the item sets gets long. faster than any algorithms those cited in literature frequently. Finding a way to mine frequent closed sequences without the Key words – Data Mining; Graph Based Mining; Frequent itemset; Closed itemset; Pattern Mining; candidate; Itemset Mining; help of candidate maintenance seems to be difficult. Here, we Sequential Itemset Mining. show a solution leading to an algorithm, PEPP, which can mine efficiently all the sets of frequent closed sequences through a I. INTRODUCTION sequence graph protruding approach. In PEPP, we need not eye Sequential item set mining, is an important task, having many down on any historical frequent closed sequence for a new applications with market, customer and web log analysis, item pattern’s closure checking, leading to the proposal of Sequence set discovery in protein sequences. Capable mining techniques graph edge pruning technique and other kinds of optimization are being observed extensively, including the general sequential techniques. item set mining [1, 2, 3, 4, 5, 6], constraint-based sequential The observations display the performance of the PEPP to find item set mining [7, 8, 9], frequent episode mining [10], cyclic closed frequent itemsets using Sequence Graph. The association rule mining [11], temporal relation mining [12], comparative study claims some interesting performance partial periodic pattern mining [13], and long sequential item set improvements over BIDE and other frequently cited algorithms. mining [14]. Recently it’s quite convincing that for mining frequent item sets, one should mine all the closed ones as the In section II, most frequently cited work and their limits end leads to compact and complete result set having high explained. In section III, the Dataset adoption and formulation efficiency [15, 16, 17, 18], unlike mining frequent item sets, explained. In section IV, introduction to PEPP and its utilization 74 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 9, September 2011 for Sequence Graph protruding explained. In section V, the another closed pattern mining algorithm and ranked high in algorithms used in PEPP described. In section V1, results performance when compared to other algorithms discussed. gained from a comparative study briefed and followed by Bide projects the sequences after projection it prunes the conclusion of the study. patterns that are subsets of current patterns if and only if subset and superset contains same support required. But this model is II. RELATED WORK opting to projection and pruning in sequential manner. This The sequential item set mining problem was initiated by sequential approach sometimes turns to expensive when Agrawal and Srikant , and the same developed a filtered sequence length is considerably high. In our earlier literature[27] algorithm, GSP [2], basing on the Apriori property [19]. Since we discussed some other interesting works published in recent then, lots of sequential item set mining algorithms are being literature. developed for efficiency. Some are, SPADE [4], PrefixSpan [5], Here, we bring Sequence Graph protruding that based on edge and SPAM [6]. SPADE is on principle of vertical id-list format projection and pruning, an asymmetric parallel algorithm for and it uses a lattice-theoretic method to decompose the search finding the set of frequent closed sequences. The giving of this space into many tiny spaces, on the other hand PrefixSpan paper is: (A) an improved sequence graph based idea is implements a horizontal format dataset representation and generated for mining closed sequences without candidate mines the sequential item sets with the pattern-growth paradigm: maintenance, termed as Parallel Edge Projection and pruning grow a prefix item set to attain longer sequential item sets on (PEPP) based Sequence Graph Protruding for closed itemset building and scanning its database. The SPADE and the mining. The Edge Projection is a forward approach grows till PrefixSPan highly perform GSP. SPAM is a recent algorithm edge with required support is possible during that time the edges used for mining lengthy sequential item sets and implements a will be pruned. During this pruning process vertices of the edge vertical bitmap representation. Its observations reveal, SPAM is that differs in support with next edge projected will be better efficient in mining long item sets compared to SPADE considered as closed itemset, also the sequence of vertices that and PrefixSpan but, it still takes more space than SPADE and connected by edges with similar support and no projection PrefixSpan. Since the frequent closed item set mining [15], possible also be considered as closed itemset (B) in the Edge many capable frequent closed item set mining algorithms are Projection and pruning based Sequence Graph Protruding for introduced, like A-Close [15], CLOSET [20], CHARM [16], closed itemset mining, we create a algorithms for Forward edge and CLOSET+ [18]. Many such algorithms are to maintain the projection and back edge pruning(C) the performance clearly ready mined frequent closed item sets to attain item set closure signifies that proposed model has a very high capacity: it can be checking. To decrease the memory usage and search space for faster than an order of magnitude of CloSpan but uses order(s) item set closure checking, two algorithms, TFP [21] and of magnitude less memory in several cases. It has a good CLOSET+2, implement a compact 2-level hash indexed result- scalability to the database size. When compared to BIDE the tree structure to keep the readily mined frequent closed item set model is proven as equivalent and efficient in an incremental candidates. Some pruning methods and item set closure way that proportional to increment in pattern length and data verifying methods, initiated the can be extended for optimizing density. the mining of closed sequential item sets also. CloSpan is a new algorithm used for mining frequent closed sequences [17]. It III. DATASET ADOPTION AND FORMULATION goes by the candidate maintenance-and-test method: initially create a set of closed sequence candidates stored in a hash Item Sets I: A set of diverse elements by which the sequences indexed result-tree structure and do post-pruning on it. It generate. requires some pruning techniques such as Common Prefix and n Backward Sub-Item set pruning to prune the search space as I = U ik CloSpan requires maintaining the set of closed sequence k =1 Note: ‘I’ is set of diverse elements candidates, it consumes much memory leading to heavy search space for item set closure checking when there are more Sequence set ‘S’: A set of sequences, where each sequence frequent closed sequences. Because of which, it does not scale contains elements each element ‘e’ belongs to ‘I’ and true for a well the number of frequent closed sequences. BIDE [26] is function p(e). Sequence set can formulate as 75 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 9, September 2011 m Qualified support ‘qs’: The resultant coefficient of total support s = U < ei | ( p (ei ), ei ∈ I ) > divides by size of sequence database adopt as qualified support i =1 ‘qs’. Qualified support can be found by using following formulation. Represents a sequence‘s’ of items those belongs to set of distinct items ‘I’. fts ( st ) f qs ( st ) = ‘m’: total ordered items. | DBS | P(ei): a transaction, where ei usage is true for that transaction. Sub-sequence and Super-sequence: A sequence is sub sequence t for its next projected sequence if both sequences having same S = U sj total support. j =1 Super-sequence: A sequence is a super sequence for a sequence from which that projected, if both having same total support. S: represents set of sequences Sub-sequence and super-sequence can be formulated as ‘t’: represents total number of sequences and its value is volatile sj: is a sequence that belongs to S If f ts ( st ) ≥ rs where ‘rs’ is required support threshold given by user Subsequence: a sequence s p of sequence set ‘S’ is considered as subsequence of another sequence sq And st <: s p for any p value where f ts ( st ) ≅ f ts ( s p ) of Sequence Set ‘S’ if all items in sequence Sp is belongs to sq as an ordered list. This can be formulated as IV. PARALLEL EDGE PROJECTION AND PRUNING n BASED SEQUENCE GRAPH PROTRUDE If (U s pi ∈ sq ) ⇒ ( s p ⊆ sq ) Preprocess: i =1 <:U s As a first stage of the proposal we perform dataset s p ∈ S and sq ∈ S n m Then U s pi i =1 j =1 qj preprocessing and itemsets Database initialization. We find where itemsets with single element, in parallel prunes itemsets with single element those contains total support less than required Total Support ‘ts’ : occurrence count of a sequence as an support. ordered list in all sequences in sequence set ‘S’ can adopt as total support ‘ts’ of that sequence. Total support ‘ts’ of a Forward Edge Projection: sequence can determine by following formulation. In this phase, we select all itemsets from given itemset database f ts ( st ) =| st <: s p ( for each p = 1.. | DBS |) | as input in parallel. Then we start projecting edges from each selected itemset to all possible elements. The first iteration includes the pruning process in parallel, from second iteration DBS Is set of sequences onwards this pruning is not required, which we claimed as an efficient process compared to other similar techniques like fts ( st ) : Represents the total support ‘ts’ of sequence st is the BIDE. In first iteration, we project an itemset s p that spawned number of super sequences of st from selected itemset si from DBS and an element ei considered from ‘I’. If the f ts ( s p ) is greater or equal to rs , 76 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 9, September 2011 then an edge will be defined between si and ei . If Figure 1: Generate initial DBS with single element itemsets f ts ( si ) ≅ f ts ( s p ) then we prune si from DBS . This pruning process required and limited to first iteration only. From second iteration onwards project the itemset S p that spawned from S p ' to each element ei of ‘I’. An edge can be defined between S p ' and ei if f ts ( s p ) is greater or equal to rs . In this description S p ' is a projected itemset in previous iteration and eligible as a sequence. Then apply the fallowing validation to find closed sequence. If any of f ts ( s p ' ) ≅ f ts ( s p ) that edge will be pruned and all disjoint graphs except s p will be considered as closed sequence and moves it into DBS and remove all disjoint graphs from memory. Algorithm 1: Generate initial DBS with single element itemsets If f ts ( s p ' ) ≅ f ts ( s p ) and there after no projection spawned Input: Set of Elements ‘I’. then s p will be considered as closed sequence and moves it Begin: into DBS and remove s p ' and s p from memory. L1: For each element ei of ‘I’ The above process continues till the elements available in memory those are connected through direct or transitive edges Begin: and projecting itemsets i.e., till graph become empty. Find f ts (ei ) If f ts (ei ) ≥ rs then V. ALGORITHMS USED IN PEPP Move ei as sequence with single element to DBS This section describes algorithms for initializing sequence End: L1. database with single elements sequences, spawning itemset projections and pruning edges from Sequence Graph SG. End. 77 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 9, September 2011 Figure2: spawning projected Itemsets and protruding sequence Algorithm 2: spawning projected Itemsets and protruding graph sequence graph DBS and ‘I’; Input: si in DBS L1: For each sequence Begin: ei of ‘I’ L2: For each element Begin: C1: if edgeWeight( si , ei ) ≥ rs Begin: ( si , ei ) Create projected itemset s p from si from DBS If f ts ( si ) ≅ f ts ( s p ) then prune End: C1. End: L2. End: L1. L3: For each projected Itemset s p in memory Begin: (a) First iteration sp' = sp ei of ‘I’ L4: For each Begin: Project s p from ( s p ' , ei ) C2: If f ts ( s p ) ≥ rs Begin Spawn SG by adding edge between s p ' and ei End: C2 End: L4 C3: If s p ' not spawned and no new projections added for s p ' Begin: Remove all duplicate edges for each edge weight from s p ' and keep edges unique by not deleting most recent edges for each edge weight. Select elements from each disjoint graph as closed sequence and add it to DB S and remove disjoint graphs from SG. End C3 End: L3 (b) Rest of all Iterations If SG ≠ φ go to L3. 78 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 9, September 2011 VI. Comparative Study This segment focuses mainly on providing evidence on asserting the claimed assumptions that 1) The PEPP is similar to BIDE which is actually a sealed series mining algorithm that is competent enough to momentously surpass results when evaluated against other algorithms such as CloSpan and spade. 2) Utilization of memory and momentum is rapid when compared to the CloSpan algorithm which is again analogous to BIDE. 3) There is the involvement of an enhanced occurrence and a probability reduction in the memory exploitation rate with the aid of the trait equivalent prognosis and also rim snipping of the PEPP. This is on the basis of the surveillance done which concludes that PEPP’s implementation is far more noteworthy Figure 3: A comparison report for Runtime and important in contrast with the likes of BIDE, to be precise. JAVA 1.6_ 20th build was employed for accomplishment of the PEPP and BIDE algorithms. A workstation equipped with core2duo processor, 2GB RAM and Windows XP installation was made use of for investigation of the algorithms. The parallel replica was deployed to attain the thread concept in JAVA. Dataset Characteristics: Pi is supposedly found to be a very opaque dataset, which assists in excavating enormous quantity of recurring clogged series with a profitably high threshold somewhere close to 90%. It also has a distinct element of being enclosed with 190 protein Figure4: A comparison report for memory usage series and 21 divergent objects. Reviewing of serviceable legacy’s consistency has been made use of by this dataset. Fig. 5 portrays an image depicting dataset series extent status. In assessment with all the other regularly quoted forms like spade, prefixspan and CloSpan, BIDE has made its mark as a most preferable, superior and sealed example of mining copy, taking in view the detailed study of the factors mainly, memory consumption and runtime, judging with PEPP. Figure 5: Sequence length and number of sequences at different thresholds in Pi dataset 79 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 9, September 2011 In contrast to PEPP and BIDE, a very intense dataset Pi is used research studies that limitations are crucial for a number of which has petite recurrent closed series whose end to end chronological outlined mining algorithms. Future studies distance is less than 10, even in the instance of high support include proposing of claiming a deduction advance on perking amounting to around 90%. The diagrammatic representation up the rule coherency on predictable itemsets. displayed in Fig.3 explains that the above mentioned two algorithms execute in a similar fashion in case of support being REFERENCES 90% and above. But in situations when the support case is 88% [1]F. Masseglia, F. Cathala, and P. 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Hsiao, CHARM: An efficient algorithm for closed itemset AUTHORS PROFILE: mining. In SDM’02, Arlington, VA, April 2002. Kalli Srinivasa Nageswara Prasad has completed [17]X. Yan, J. Han, and R. Afshar, CloSpan: Mining Closed Sequential Patterns M.Sc(Tech)., M.Sc., M.S (Software Systems)., in Large Databases. In SDM’03, San Francisco, CA, May 2003. P.G.D.C.S. He is currently pursuing Ph.D degree in the field of Data Mining at Sri Venkateswara [18]J. Wang, J. Han, and J. Pei, CLOSET+: Searching for the Best Strategies for University, Tirupathi, Andhra Pradesh State, India. Mining Frequent Closed Itemsets. In KDD’03, Washington, DC, Aug. 2003. He has published Five Research papers in International journals. [19]R. Agrawal and R. Srikant. Fast algorithms for mining association rules. In VLDB’94, Santiago, Chile, Sept. 1994. S.Ramakrishna is currently working as a professor in the [20]J. Pei, J. Han, and R. Mao, CLOSET: An efficient algorithm for mining Department of Computer Science, College of Commerce, frequent closed itemsets . In DMKD’01 workshop, Dallas, TX, May 2001. Management & Computer Sciences in Sri Venkateswara university, Tirupathi, Andhra Pradesh State, India. He has [21]J. Han, J. Wang, Y. Lu, and P. Tzvetkov, Mining Top- K Frequent Closed completed M.Sc, M.Phil., Ph.D., M.Tech(IT). He is Patterns without Minimum Support. In ICDM’02, Maebashi, Japan, Dec. 2002. specialized in Fluid Dynamics and Theoretical Computer Science. His area of research includes Artificial [22]P. Aloy, E. Querol, F.X. Aviles and M.J.E. Sternberg, Automated Structure- Intelligence, Data Mining and Computer Networks. He based Prediction of Functional Sites in Proteins: Applications to Assessing the has an experience of 25 years in Teaching Field. He has Validity of Inheriting Protein Function From Homology in Genome Annotation published 36 Research Papers in National & and to Protein Docking. Journal of Molecular Biology, 311, 2002. International Journals. He has also attended 13 National Conferences and 11 International Conferences. He has [23]R. Agrawal, and R. Srikant, Mining sequential patterns. In ICDE’95, Taipei, guided 15 Ph.D. Scholars and 17 M.Phil Scholars. Taiwan, Mar. 1995. [24]I. Jonassen, J.F. Collins, and D.G. Higgins, Finding flexible patterns in unaligned protein sequences. Protein Science, 4(8), 1995. [25]R. Kohavi, C. Brodley, B. Frasca, L.Mason, and Z. Zheng, KDD-cup 2000 organizers’ report: Peeling the Onion. SIGKDD Explorations, 2, 2000. [26]Jianyong Wang, Jiawei Han: BIDE: Efficient Mining of Frequent Closed Sequences. ICDE 2004: 79-90 [27]Kalli Srinivasa Nageswara Prasad and Prof. S Ramakrishna. Article: Frequent Pattern Mining and Current State of the Art. International Journal of Computer Applications 26(7):33-39, July 2011. Published by Foundation of Computer Science, New York. 81 http://sites.google.com/site/ijcsis/ ISSN 1947-5500

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