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FPtree/FPGrowth

FPtree/FPGrowth. FP-Tree/FP-Growth Algorithm. Use a compressed representation of the database using an FP-tree Then use a recursive divide-and-conquer approach to mine the frequent itemsets. Building the FP-Tree. Scan data to determine the support count of each item.

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FPtree/FPGrowth

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  1. FPtree/FPGrowth

  2. FP-Tree/FP-Growth Algorithm • Use a compressed representation of the database using an FP-tree • Then use a recursive divide-and-conquer approach to mine the frequent itemsets.

  3. Building the FP-Tree • Scan data to determine the support count of each item. Infrequent items are discarded, while the frequent items are sorted in decreasing support counts. • Make a second pass over the data to construct the FP­tree. As the transactions are read, before being processed, their items are sorted according to the above frequency order.

  4. First scan – determine frequent 1-itemsets, then build header

  5. null B:1 A:1 null B:2 C:1 A:1 D:1 FP-tree construction After reading TID=1: After reading TID=2:

  6. null B:8 A:2 A:5 C:3 C:1 D:1 C:3 D:1 D:1 E:1 D:1 E:1 D:1 E:1 FP-Tree Construction Transaction Database Header table Chain pointers help in quickly finding all the paths of the tree containing some given item.

  7. FP-Tree size • Size of FP­tree is typically smaller than the size of the uncompressed data. • Because many transactions often share a few items in common. • Best­case scenario: • All transactions have the same set of items, and the FP­tree contains only a single branch of nodes. • Worst­case scenario: • Every transaction has a unique set of items. • As none of the transactions have any items in common, the size of the FP­tree is effectively the same as the size of the original data. • Size of FP­tree also depends on how the items are ordered. • If the ordering scheme in the preceding example is reversed, i.e., from lowest to highest support item, the resulting FP­tree is denser.

  8. FP-Growth • FP­growth generates frequent itemsets by exploring the FP-tree in a bottom­up fashion. • It starts with the less frequent item, in this example, E. • Then, the algorithm looks for frequent itemsetsending in E first, followed by D, C, A, and finally, B. • We can derive the frequent itemsets ending with E, by examining only the paths containing node E. • These paths can be accessed rapidly using the pointers associated with node E.

  9. null null B:1 B:8 A:2 A:2 A:5 C:1 C:3 C:1 C:1 D:1 D:1 C:3 D:1 D:1 E:1 E:1 D:1 D:1 E:1 E:1 D:1 E:1 E:1 Paths containing node E

  10. Conditional FP-Tree for E • FP-Growth builds a conditional FP-Tree forE, which is the tree of itemsets ending in E. • It is not the tree obtained in the previous slide as result of deleting nodes from the original tree. Why? • Because the order of the items can change. • Now, C has a higher count than B.

  11. null B:1 A:2 C:1 C:1 D:1 E:1 D:1 E:1 E:1 Suffix E (New) Header table Conditional FP-Tree for suffix E null B doesn’t survive because its support is 1, which is lower than minsupport of 2. A:2 C:1 C:1 D:1 The set of paths ending in E. Insert each path (after truncating E) into a new tree. D:1 We continue recursively. Base of recursion: When the tree has a single path only. FI: E

  12. Steps of Building Conditional FP-Trees • Find the paths containing on focus item. • Read the tree to determine the new counts of the items along those paths. Build a new header. • Read again the tree. Insert the paths in the conditional FP-Tree according to the new order.

  13. Suffix DE (New) Header table null The conditional FP-Tree for suffix DE A:2 C:1 D:1 null D:1 A:2 The set of paths, from the E-conditional FP-Tree, ending in D. Insert each path (after truncating D) into a new tree. We have reached the base of recursion. FI: DE, ADE

  14. Base of Recursion • We continue recursively on the conditional FP-Tree. • Base case of recursion:when the tree is just a single path. • Then, we just produce all the subsets of the items on this path merged with the corresponding suffix.

  15. Suffix CE (New) Header table null The conditional FP-Tree for suffix CE A:1 C:1 C:1 null The set of paths, from the E-conditional FP-Tree, ending in C. Insert each path (after truncating C) into a new tree. We have reached the base of recursion. FI: CE

  16. Suffix AE (New) Header table The conditional FP-Tree for suffix AE null null A:2 The set of paths, from the E-conditional FP-Tree, ending in A. Insert each path (after truncating A) into a new tree. We have reached the base of recursion. FI: AE

  17. null B:3 A:2 A:2 C:1 C:1 D:1 C:1 D:1 D:1 D:1 D:1 Suffix D (New) Header table Conditional FP-Tree for suffix D null A:4 B:1 B:2 C:1 C:1 C:1 The set of paths ending in D. Insert each path (after truncating D) into a new tree. We continue recursively. Base of recursion: When the tree has a single path only. FI: D

  18. Suffix CD (New) Header table null Conditional FP-Tree for suffix CD A:4 B:1 B:2 C:1 null C:1 C:1 A:2 B:1 B:1 The set of paths, from the D-conditional FP-Tree, ending in C. Insert each path (after truncating C) into a new tree. We continue recursively. Base of recursion: When the tree has a single path only. FI: CD

  19. Suffix BCD (New) Header table Conditional FP-Tree for suffix CDB null A:2 B:1 null B:1 The set of paths from the CD-conditional FP-Tree, ending in B. Insert each path (after truncating B) into a new tree. We have reached the base of recursion. FI: BCD

  20. Suffix ACD (New) Header table Conditional FP-Tree for suffix ACD null null The set of paths from the CD-conditional FP-Tree, ending in A. Insert each path (after truncating B) into a new tree. We have reached the base of recursion. FI: ACD

  21. Suffix C null (New) Header table Conditional FP-Tree for suffix C B:6 A:1 A:3 C:3 C:1 null C:3 B:6 A:1 A:3 The set of paths ending in C. Insert each path (after truncating C) into a new tree. We continue recursively. Base of recursion: When the tree has a single path only. FI: C

  22. Suffix AC (New) Header table null Conditional FP-Tree for suffix AC B:6 A:1 null A:3 B:3 The set of paths from the C-conditional FP-Tree, ending in A. Insert each path (after truncating A) into a new tree. We have reached the base of recursion. FI: AC, BAC

  23. Suffix BC (New) Header table null Conditional FP-Tree for suffix BC B:6 null The set of paths from the C-conditional FP-Tree, ending in B. Insert each path (after truncating B) into a new tree. We have reached the base of recursion. FI: BC

  24. Suffix A null (New) Header table Conditional FP-Tree for suffix A B:5 A:2 A:5 null B:5 The set of paths ending in A. Insert each path (after truncating A) into a new tree. We have reached the base of recursion. FI: A, BA

  25. Suffix B (New) Header table Conditional FP-Tree for suffix B null null B:8 The set of paths ending in B. Insert each path (after truncating B) into a new tree. We have reached the base of recursion. FI: B

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