Dynamic Itemset Counting

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Presentation transcript:

Dynamic Itemset Counting Presented by : Atefeh Rahimi Bahareh Hajihashemi Adviser : Dr. Vahidipour December 2017

The Problem The “market-basket” Problem Given a set of items and a large collection of transactions which are subsets (baskets) of these items. What is the relationships between the presence of various items within those baskets? TID Items 1 Milk, Bread 2 Milk, Bread, Eggs 3 Milk, Beer 4 Milk, Eggs, Beer

Mining association rules Frequent itemset generation Apriori Dynamic Itemset Counting(DIC) Implication rules generation by a “threshold” Confidence Conviction

DIC Algorithm Why do we have to wait till the end of the pass? DIC  allows us to start counting an itemset as soon as we suspect it may be necessary to count it.

The Apriori Algorithm — Example Database D L1 C1 Scan D C2 C2 L2 Scan D C3 L3 Scan D

DIC Algorithm

DIC Algorithm Itemsets are marked in different ways Solid box : confirmed large itemsets Solid circle: confirmed small itemsets Dashed box: suspected large itemsets Dashed circle: suspected small itemsets

DIC Algorithm Mark the empty itemset with a solid square. Mark all the 1-itemsets with dashed circles Leave all other itemsets unmarked.

DIC Algorithm while any dashed items set remain: 1.read M transactions for each transaction increment the respective counters for the itemsets that appear in the transaction and are marked with dashes.

DIC Algorithm 2-if a dashed circles count exceeds minsupp, turn it into a dashed Square if any immediate superset of it has all of its subsets as solid or dashed squares add a new counter for it and make it a dashed circle.

DIC Algorithm 3-If a dashed itemset has been counted through all the transactions make it solid and stop counting it. a =3+2=5 , b=3+3=6 , c=3+2=5 ,d=5+4=9 , e=4+2=6, ab=1 , ac=1, ad=1, ae=1, bc=1, bd=2, be=1, cd=1, ce=0 ,de=2

DIC Algorithm 4-if we are at the end of the transaction file, rewind to the beginning. 5-if any that item sets remain go to step one. ab=3 , ac=2, ad=4, ae=4, bc=3, bd=5, be=4, cd=4, ce=2 ,de=6, adc=0,adb=0, abe=0,…,cde=0

DIC Algorithm abc=1, abd=0, ade=1, acd=0, ace=0, ade=0, bcd=0, bce=0, bde=1, cde=0

DIC Algorithm abc=1, abd=0, ade=0, acd=0, ace=0, ade=4, bcd=0, bce=0, bde=3, cde=0, adbe=0

DIC Algorithm adbe=0

DIC Algorithm adbe=0

Homogeneous data Solution : Randomness. Randomize order of how to read transactions. every pass must be the same order. it may be expensive to do

Extension to DIC Parallelism incremental updates

Parallelism Divide the database among the nodes and to have each node count all the itemsets for its own data segment DIC can dynamically in incorporate new itemsets to be added, it is not necessary to wait. Nodes can proceed to count the itemsets they suspect are candidates and make adjustments as they get more results from other nodes.

Incremental update Handling incremental updates involves two things: detecting when a large itemset becomes small and detecting when a small itemsets becomes large. if a small itemset becomes large. we must count over the entire day data, not just the update. Therefore, when we determine that a new itemset that must be counted. we must go back and count it over the prefix of the data that we missed.