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# GenMax PowerPoint PPT Presentation

GenMax. From: “ Efficiently Mining Frequent Itemsets ” By : Karam Gouda & Mohammed J. Zaki. The Problem. Given a large database of items transactions, find all frequent itemsets

GenMax

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## GenMax

From:

“Efficiently Mining Frequent Itemsets”

By :

Karam Gouda & Mohammed J. Zaki

Zeev Dvir – [email protected]

### The Problem

• Given a large database of items transactions, find all frequent itemsets

• A frequent itemset is a set of items that occurs in at-least a user-specified percentage of the data-base

• We call this percentage : min_sup (for minimum support).

Zeev Dvir – [email protected]

• A Maximal Frequent Itemset is a frequent itemset, that doesn’t have a frequent superset

• FI := frequent itemsets

MFI := maximal frequent itemsets

• Fact:

|MFI| << |FI|

GenMax is an algorithm to find the exact MFI

Zeev Dvir – [email protected]

### Example

Min_sup = 3

ABCD

ABC ABD ACD BCD

AB AC AD BC BD CD

A B C D

Zeev Dvir – [email protected]

### Some Useful Definitions

• The Combine-Set of an itemset I , is the set of items that can be added to I to create a frequent itemset.

• For example , in the previous example, The combine-set of the itemset {A} is {B, C}.

• The combine-set of the empty itemset is called F1 and is actually the set of frequent itemsets ofsize 1.

Zeev Dvir – [email protected]

Zeev Dvir – [email protected]

Zeev Dvir – [email protected]

### Improvement

• At each level, sort the combine-set (C) in increasing order of support

• An itemset with low support has a smaller chance of producing a large combine-set in the next level

• The sooner we prune the tree, the more work we save

• This heuristic was first used in MaxMiner

Zeev Dvir – [email protected]

### Bottlenecks

• Superset checking :

The best algorithms for superset checking give an amortized bound of per operation.

that’s bad if we have many itemsets in the MFI.

2. Frequency testing :

How can we make frequency testing faster ?

Zeev Dvir – [email protected]

### Optimizing Superset Checking

• A technique called “Progressive Focusing” is used to narrow down the group of potential supersets, as the recursive calls are made

• LMFI := Local MFI

• Before each recursive call, we construct the LMFI for the next call, based on the current LMFI and the new item added.

Zeev Dvir – [email protected]

### LMFI Example

FGHI FGHJ …

FGH FGI …

FG …

Zeev Dvir – [email protected]

Zeev Dvir – [email protected]

### Frequency Testing Optimization

• GenMax uses a “vertical database format”:

• For each item , we have a set of all the transactions containing this item.

• This set is called a tidset. (Transaction ID Set).

• This method makes support computations easier, because we don’t have to go over the entire database.

Zeev Dvir – [email protected]

### Vertical Database

A {1, 3, 4, 5}

B {1, 3, 4, 6}

C {1 ,2 ,3 ,4 ,7}

D {2, 4, 6}

t(A) = {1, 3, 4, 5}

t(AC) = {1, 3, 4}

supp(I) = |t(I)|

Zeev Dvir – [email protected]

ABC ABD ABE

AB …

= { C , E }

t(ABC) t(ABE)

Each item y in the combine-set , actually represents the itemset

, and stores the tidset associated with it.

Zeev Dvir – [email protected]

• Diffsets:don’t store the entire tidsets, only the differences between tidsets (described in “Fast Vertical Mining Using Diffsets”)

Zeev Dvir – [email protected]

### Experimental Results

• GenMax is compared with:

MaxMiner , MAFIA, MAFIA-PP

• MaxMiner & MAFIA-PP give the exact MFI, while MAFIA gives a superset of the MFI

• The Databases used in the experiments are grouped according to the MFI length distribution

Zeev Dvir – [email protected]

### Type I Datasets

Zeev Dvir – [email protected]

### Type II Datasets

Zeev Dvir – [email protected]

### Type III Datasets

Zeev Dvir – [email protected]

### Type IV Datasets

Zeev Dvir – [email protected]

The End

Zeev Dvir – [email protected]