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Discovering Relational Patterns across Multiple Databases

This study explores the methodologies for discovering relational patterns across multiple databases. An introduction to three fundamental solutions—Sequential Pattern Verification (SPV), Parallel Pattern Mining (PPM), and Collaborative Pattern Mining (CPM)—is provided. The research includes query decomposition and hybrid frequent pattern tree (HFP-tree) techniques for effective pattern discovery. Through empirical experiments, results demonstrate the superiority of a proposed method, DRAMA, over SPV and CPM, particularly in runtime efficiency. Addressing key aspects of query formulation, data mining approaches, and the importance of frequent patterns in diverse datasets, the findings contribute to advancements in relational data analysis.

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Discovering Relational Patterns across Multiple Databases

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  1. Discovering Relational Patterns across Multiple Databases Xingquan Zhu1 Xindong Wu ICDE 07

  2. Outline. • Introduction • Preliminaries • Discovering relational patterns • Experiments • Conclusion

  3. Introduction • In a naïve sense, the problem of discovering relational patterns across multiple databases can be solved by three simple solutions: • (1) Sequential Pattern Verification (SPV) • (2) Parallel Pattern Mining (PPM) • (3) Collaborative Pattern Mining (CPM)

  4. Preliminaries • Query 1: Finding the patterns that are frequent with a support level of α in either of the cancer datasets: D2, D3, or D4, but are significantly infrequent in D1. i.e., {(D2 | D3 | D4) ≥α} & {(D1 <β)} • Query 2: Finding the patterns that are frequent with a support level of α in all cancer datasets, but with support in Leukemia tissues higher than other cancers tissues. i.e., {(D2 | D3) ≥ D4 ≥α}

  5. Preliminaries(cont) • Relationship factors: • X ≥ α (X > α) indicates that X is no less than α ( X is larger than α) • X ≤ α ( X < α) indicates that X is no larger than α ( X is less than α) • Operators: • X + Y indicates the operation of summing up the support values in both X and Y • X - Y indicates the operation of subtracting the support in Y from the support in X. • X & Y (X | Y) indicates the operation of X and Y ( X or Y) • |X| indicates the absolute support value in X • {ME > (NH | VT) >MA > (CT | RI) ≥α}

  6. Preliminaries(cont) • Hybrid Frequent Pattern Tree Construction

  7. Preliminaries(cont)

  8. Preliminaries(cont) • 3 • D1, D2, D3,…., DM • Denoting Rji the ranking order of item Ij in database Di • 3 • Si is the number of transactions in Di • S=S1+S2+..+SM

  9. Discovering relational patterns • User Query Decomposition • All decomposed sub queries are placed into a Down Closure (DC) subset. • For example, the query {A ≥ B ≥ C ≥α} can be decomposed into three sub queries (A ≥α ), (B ≥α ), and (C ≥α ), and placed into the DC set. • A sub query like {(A+B+C) ≥α} complies with the down closure property, and can be directly put into the DC set.

  10. Discovering relational patterns(cont) • Relational Pattern Discovery Using HFP-tree • Start from each of ai’s locations and track upwards towards the root. • Start from g, tracking from g upwards towards • the Root will produce a set {ecba}.

  11. Discovering relational patterns(cont) • Replace the support of each item in the set by the current support and it will produce a path called hybrid prefix path (HPP). • {e | 1:0, c | 1:0, b | 1:0, a | 1:0}、{d | 1:1, b | 1:1, a | 1:1}、…….

  12. Discovering relational patterns(cont) • Sum up all HPP’s frequencies. • Freqg={a | 4:2, b | 2:1, c | 2:2, d | 3:2, e | 1:0, f | 1:2}. • Dividing all the frequency values by the total number of transactions in each database. • D1=8 and D2=7, • Supg=={a | 0.5:0.29, b | 0.25:0.14, c | 0.25:0.29, d | 0.38:0.29, e | 0.13:0, f | 0.13:0.29}

  13. Discovering relational patterns(cont) • User Query Decomposition • Q={D1 ≥ D2 ≥ 0.25} • DC={(D1 ≥ 0.25) AND (D2 ≥ 0.25)} • Comparing all items’ support values in Supi with the DC set will explicitly indicate that any of the following items • {b | 0.25:0.14}, {e | 0.13:0}, and {f | 0.13:0.29}

  14. Discovering relational patterns(cont) • Prune out those unqualified items directly with filtered HPPs and build a Meta HFP-tree. • {c | 1:0, a | 1:0}, {d | 1:1, a | 1:1}, {d | 0:1, c | 0:1, a | 0:1}, {d | 1:0, c | 1:0, a | 1:0}, {d | 1:0, a | 1:0}, and {c | 0:1}

  15. Discovering relational patterns(cont) • The mining process recursively calls the HFP-growth procedure, until the meta HFP-tree eventually contains one path only.

  16. Discovering relational patterns(cont) • The recursive HFP-growth process will eventually lead to a meta HFP-tree containing one or zero path. At this stage, there is no need to grow patterns any further. • means the support value of the kth item in P and K is the number of items in P. • P={g | 4:3, d |3:2, a |3:2} then choose 3:2 • PSup={0.38:0.28}, which satisfy Q={D1 ≥ D2 ≥ 0.25},

  17. Experiments

  18. Conclusion • SPV, PPM and CPM are all Apriori-based. DRAMA is FP-tree based. • We can see that DRAMA consistently outperforms both SPV and CPM with a significant runtime improvement. • Use it in streams ?

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