The document discusses the Apriori algorithm and modifications using hashing and graph-based approaches for mining association rules from transactional datasets. The Apriori algorithm uses multiple passes over the data to count support for candidate itemsets and prune unpromising candidates. Hashing maps itemsets to integers for efficient counting of support. The graph-based approach builds a tree structure linking frequent itemsets. Both modifications aim to improve efficiency over the original Apriori algorithm. The document also notes challenges in designing perfect hash functions for this application.

1. Apriori Algorithm Hash Based and Graph Based Modifications

2. Agenda Data Mining Association Rule Ariori Algorithm Hash Based Method Graph Based Approach Conclusion and Future Work

3. Data Mining Data mining is the process of extracting patterns (knowledge) from data . The aim of data mining is to automate the process of finding interesting patterns and trends from a given data. It is seen as an increasingly important tool by modern business to transform data into business intelligence giving an informational advantage. It is currently used in a wide range of profiling practices , scientific discovery, and decision making.

4. Association Rules Association rule learning is a popular and well researched method for discovering interesting relations between variables in large database. For example, the rule found in the sales data of a supermarket would indicate that if a customer buys onions and potatoes together, he or she is likely to also buy burger. Such information can be used as the basis for decisions about marketing activities.

5. Problem Description I = {A, B, C} Possible Item sets:

6. Support and Confidence Support (A -> B) = No. of transactions containing A & B ________________________________ No. of total transactions Confidence (A -> B) = No. of transactions containing A & B _________________________________ No. of transactions containing A

7. Original Apriori Algorithm

8. L1 = {large 1-itemsetsg} for ( k = 2; Lk !=0, k++ ) do begin Ck = apriori-gen(Lk-1 ); // New candidates for all transactions t Є D do begin Ct = subset (Ck , t); // Candidates contained in t for all candidates c Є Ct do c.count++; end Lk = {c Є Ck | c.count >= minsup} end

10. Hash based method Repeat //for each transaction of the database { D = { set of all possible k-itemsets in the ith transaction} For each element of D { Find a unique integer uniq_int using thehash function for k-itemset Increment freq[uniq_int] } Increment trans_pos //Moves pointer to next transaction until end_of_file For (freq_ind=0; freq_ind<length_of_the_array(two_three_freq[]); freq_ind++) { if (freq[freq_ind] >= required support) mark the corresponding k-itemset } }

11. Graph based approach Procedure FrequentItemGraph (Tree, F) { scan the DB once to collect the frequent 2-itemsets and their support ascending; add all items in the DB as the header nodes for each 2-itemset entry (top down order) in freq2list do if (first item = item in header node) then create a link to the corresponding header node i=3 for each i-itemsets entry in the tree do call buildsubtree (F) end } Procedure buildsubtree (F) If (first i-1 itemset = itemsets in their respective header nodes) then create a link to the corresponding header node i=i+1 repeat buildsubtree (F) end }

12. Example: a c g T4 b c e f g T3 a b c e f g T2 b e T1 Items Transaction

13. Conclusion and Future Work In order to be able to continue with the hashing method, we need a perfect hash function h(e1, e2,…, ek), this hash function can be obtained by one of the following methods: h(e1,e2,…,ek) = prm(1)^e1 + prm(2)^e2 + … + prm(k)^ek Where prm is the set of prime numbers, prm = {2, 3, 5, 7…} Although this hash function guarantee a unique key for every itemset, but it requires an irrational memory space, for example, consider an original item set X with only 10 items, and the following T hashed item set, T = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, consider a 4-itemset (1, 2, 3, 10), this item set will be hashed to the value “282475385”, this will result in reserving large memory space without being used effectively. Other perfect hash functions, used in hashing strings, are not applicable here, because the input variables are limited to 26, which is the number of alphabets, while the number of items in a certain database can be very larger than this.

14. Use hashing techniques to find the efficient frequent 2-itemsets in order to reduce the time and memory requirements to build a graphical structure