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International Journal on Advanced Computer Theory and Engineering (IJACTE)length n can be calculated by using two n-1 lengthpatterns belonging to the same class[5]. Example:Consider three atoms corresponding to three web pagesP1, P2 and P3. Sample lattice up to some length-3patterns and all length-2 patterns shown in fig.8.GSP AlgorithmFig.7. Flowchart for GSP algorithmInput: S(sessions), F1(Frequent 1-sequences),min_sup(the minimal access count that satisfies thesupport threshold).Output: the set of all the access patterns: FTable: 3 Mining result for GSP algorithm1-Frequentaccesspatterngenerated2-Frequentaccesspatterngenerated3-Frequentaccesspatterngenerated4-Frequentaccesspatterngenerated{A}:4 {AB}:3 {ABC}:2 {ABCD}:2{B}:5 {BC}:3 {ABE}:2{C}:6 {BE}:2 {BCD}:2{D}:3{E}:3{G}:2{I}:4{CD}:3C. Depth First Search(DFS)In this algorithm, the patterns are categorizedaccording to the length executed on lattice model.Patterns will form a lattice based on the pattern-lengthand pattern-frequency. And using this lattice, frequentpatterns are searched depth first.Lattice Construction: The basic element of the latticeis an atom i.e. single page. Each atom or page stands forlength-1 prefix equivalence class. Beginning frombottom elements the frequency of upper elements withFig.8. Pattern Lattice[5]Session id-timestamp list: After data preprocessing, aseries of web pages visited in each session is obtained.Session id timestamp list is a list which keeps session idand timestamp information for any patterns in allsessions. The timestamp information keeps thetimestamp value of last atom for patterns with length >1. Example: 4 pages and 3 sessions given below.S1 = Page1 →Page2 → Page4 → Page1 → Page3S2 = Page4 → Page3 → Page1 → Page2S3 = Page3 → Page4 → Page1Table 4. Session id-timestamp listTable 5. Session id-timestamp list for Page3Page1The count for pattern Page3Page1 is 2/3 since itoccurs twice in three sessions. They are then prunedbased on the minimum support. Fig.9. shows theflowchart depicting the working of DFS algorithm.48ISSN (Print) : 2319 – 2526, Volume-2, Issue-3, 2013
International Journal on Advanced Computer Theory and Engineering (IJACTE)Fig.10. Comparison of performance of GSP and DFS[5]Fig.9. Flowchart for DFS algorithmII. PERFORMANCE COMPARISONFAP mining algorithm mines the complete set offrequent itemsets without generating the candidate set.FAP-growth works in a divide-and-conquer way. Thefirst pass of the database derives a list of frequent itemsarranged in the descending order of frequency togenerate a frequent-access-pattern tree, or FAP-tree. Thealgorithm searches for shorter ones recursively and thenconcatenates the suffix finding the long frequentpatterns. Performance studies demonstrate that themethod substantially reduces search time.[6]GSP can suffer from two-nontrivial costs: (1)generating a huge number of candidate sets, and (2)repeatedly scanning the database and checking thecandidates by pattern matching.DFS gives a good performance since it eliminatesinfrequent patterns at each level and in the memory itkeeps fewer patterns at each step.Murat Ali Bayir et al. have performed experimentalresults on the web logs of the departmental web serveron GSP and DFS algorithm. The log files of the webserver at Computer department are used.(www.ceng.metu.edu.tr).In the experiments GSP has given the worst resultsbecause it does not use pattern lattice structure and ateach step it has to perform a session scan. DFS is betterbecause it eliminates infrequent patterns at each leveland in the memory it keeps fewer patterns at each step.Session-id timestamp list structure prevents unnecessarydatabase scans for evaluating frequency of length 1 andlength 2 patterns. Hence DFS gives a betterperformance. Fig.10. compares discovery time of allfrequent patterns of different lengths for DFS and GSPalgorithms.Comprehensive Study Comparison of FAP-growth, DFSand GSP Algorithms:GSP algorithm is based on apriori property: if anitemset α is not frequent, then any of its superset cannotnot be frequent either. GSP uses a bottom-up searchimplying that in order to produce a frequent sequence oflength n, all 2 n subsequences have to be generated.Therefore this exponential complexity limits it todiscover only short patterns, since it prunes anycandidate sequence in which there is a subsequencewhich is infrequent. Table 4. gives a comparisonbetween the three algorithms based on various factors.Table 4. Performance comparison of FAP, GSP and DFSAlgorithmFAP-growth GSP DFS. Constructs FP tree.finds long frequentpatterns bysearching shorterones andconcatenating suffixCandidateGenerationCountPrune.ConstructPattern Lattice.Search Patternsby creatingsession Id-Timestamp List.PruneCandidate No Yes NoGenerationBased on FP tree Candidate Pattern LatticeGenerationScan entiredatasetMemoryWhen largedataset/ lowsupportScalableExecutiontimeOnly twice toconstruct FP treeand later works onFP treeHolds FP-tree inmemoryBushy FP tree maynot fit in the mainmemoryNot when support isvery low else yesScan repeatedlyfor patternmatchingAll candidatesgenerated aswell as datasetsExponentialnumber ofcandidatesOnly whensupport is fairlyhighScans to createSession Id-Timestamp ListVery fewpatterns aspatterns arepruned at eachlevelPattern latticebecomes hugeNot whensupport is verylow else yesLower Fairly high Lower49ISSN (Print) : 2319 – 2526, Volume-2, Issue-3, 2013
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