Mining Multiple-level Association Rules in Large Databases

Mining Multiple-level Association Rules in Large

DatabasesAuthors :

JIAWEI HAN, Simon Fraser University, British Columbia.

YONGJIAN FU, University of Missouri-Rolla, Missouri.

Presenter : Zhenyu Lu

(based on Mohammed’s previous slides, with some changes)

IEEE Transactions on Knowledge and Data Engineering, 1999

Outline Introduction

Algorithm

Performance studies

Cross-level association

Filtering of uninteresting association rules

Conclusions

Introduction:Why Multiple-Level Association Rules?

TID items

T1 {m1, b2}

T2 {m2, b1}

T3 {b2}

Frequent itemset: {b2}

A.A rules: none

Is this database useless?


TID items

T1 {milk, bread}

T2 {milk, bread}

T3 {bread}

minisup = 50% miniconf = 50%

Frequent itemset: {milk, bread} A.A rules: milk <=> bread

food

milk bread

m1 m2 b1 b2

What if we have this abstraction tree?


• Sometimes, at primitive data level, data does not show any significant pattern. But there are useful information hiding behind.

• The goal of Multiple-Level Association Analysis is to find the hidden information in or between levels of abstraction

Introduction:Requirements in Multiple-Level Association Analysis Two general requirements to do multiple-level association

rule mining:

1) Provide data at multiple levels of abstraction. (a common practice now)

2) Find efficient methods for multiple-level rule mining. (our

focus)


Algorithm

Performance studies



Conclusions

Algorithm : observation

TID items

T1 {m1, b2}

T2 {m2, b1}

T3 {b2}

T4 {m2, b1}

T5 {m2}

minisup = 50% miniconf = 50%

food

milk bread

m1 m2 b1 b2

Level 1

Level 2

Frequent itemset: {milk, bread}A.A rule: milk <=> breadTID items

T1 {milk, bread}

T2 {milk, bread}

T3 {bread}

T4 {milk, bread}

T5 {milk}

Frequent itemset: {m2}A.A rule: none

One minisup forall levels?

What about {m2, b1}?

Algorithm : observation

miniconf = 50%

food

milk bread

m1 m2 b1 b2

Level 1: minisup = 50%

Level 2: minisup = 40%

Frequent itemset: {milk, bread}A.A rule: milk <=> bread

Frequent itemset: { m2, b1, b2}A.A rule: m2 <=> b1

makes more sense now

Algorithm : observationDrawbacks to use only one minisup:

• If the minisup is too high, we are losing information from lower levels

• If the minisup is too low, we are gaining too many rules from higher levels, many of them are useless

Approach: ascending minisup on each level

food

milk bread

m1 m2 b1 b2

minisup

Algorithm: An Example

An entry of sales_transaction Table

A sales_item Description Relation

Transaction_id Bar_code_set

351428 {17325,92108,55349,88157,…}

Bar_code

category Brand Content

Size Storage_pd

price

17325 Milk Foremost 2% 1ga. 14(days) $3.89


GID bar_code category content brand

112 17325 Milk 2% Foremost

food

milk

Dairyland Foremost

2% chocolate

bread

white wheat

First 1: implies milk

2: implies Foremost brand

Second 1: implies 2% content

Encode the database with layer information

Encoded Transaction Table:T[1]

TID Items

T1 {111,121,211,221}

T2 {111,211,222,323}

T3 {112,122,221,411}

T4 {111,121}

T5 {111,122,211,221,413}

T6 {211,323,524}

T7 {323,411,524,713}


T[2]Level-1 minsup = 4L[1,1]

L[1,2]

TID Items

T1 {111,121,211,221}

T2 {111,211,222}

T3 {112,122,221}

T4 {111,121}

T5 {111,122,211,221}

T6 {211}

Itemset Support

{1**} 5

{2**} 5

Itemset Support

{1**,2**} 4

Algorithm: An ExampleThe frequent 1-itemset on level 1

Use Apriori on each level

only keep itemsin L[1,1] from T[1]

Level-2 minsup = 3

L[2,1]

Itemset Support

{11*} 5

{12*} 4

{21*} 4

{22*} 4

L[2,2]

Itemset Support

{11*,12*}

4

{11*,21*}

3

{11*,22*}

4

{12*,22*}

3

{21*,22*}

3

L[2,3]

Itemset Support

{11*,12*,22*}

3

{11*,21*,22*}

3


Frequent Item Sets at Level 3Level-3 minsup = 3

L[3,1]

Itemset

Support

{111} 4

{211} 4

{221} 3

L[3,2]

Itemset Support

{111,211} 3

E.g.Level-1: 80% of customers that purchase milk also purchase bread. milk bread with Confidence= 80%

Level-2:75% of people who buy 2% milk also buy wheat bread. 2% milk wheat bread with Confidence= 75%

Only generate T[1] & T[2], all frequent itemsets after level 2 is generated from T[2]

Algorithm ML_T2L1

Purpose: To find multiple-level frequent item sets for mining strong association rules in a transaction database

Input T[1]: a hierarchy-information encoded transaction

table of form <TID,Item-set> minisup threshold for each level L in the form:

(minsup[L])

Output: Multiple-level frequent item sets

Algorithm variations Algorithm ML_T1LA

Use only the first encoded transaction table T[1]. Support for the candidate sets at all levels computed at the same time. pros: Only one table and maximum k-scans cons: May consist of infrequent items and requires large space.

Algorithm ML_TML1 Generate multiple encoded transaction tables T[1],…,T[max_l+1] Pros: May save substantial amount of processing Cons: Can be inefficient if only a few items are filtered out at each level

processed.

Algorithm ML_T2LA Uses 2 encoded transaction tables as in ML_T2L1 algorithm. Support for the candidate sets at all levels computed at the same time. Pros: Potentially efficient if T[2] consists of much fewer items than T[1]. Cons: ?


Algorithm

Performance studies



Conclusions

Performance Study Assumptions:

The maximal level in concept hierarchy is 3

Use two data sets DB1 (Average frequent item length = 4 and Average transaction size =10) and DB2 (Average frequent item length = 6 and Average transaction size =20)

Conclusions: Relative performance of the four algorithms is highly relevant

to the threshold setting (i.e., the power of a filter at each level).

Parallel derivation of L(l,k) is useful and deriving a transaction table T(2) is usually beneficial.

ML_T1LA is found to be the BEST or the second best algorithm.

Average frequent item length = 4Average transaction size =10


Performance Study

minisup[2] = 2% minisup[3] = 0.75% minisup[2] = 3% minisup[3] = 1%



minisup[1] = 60% minisup[3] = 0.75% minisup[1] = 55% minisup[3] = 1%

Performance Study

minisup[1] = 60% minisup[2] = 2% minisup[1] = 55% minisup[2] = 3%

Performance Study

Performance Study

Two interesting performance features:

• The performance of algorithm is highly relative to

minisup, especially minisup[1] & minisup[2].

• T[2] is beneficial


Algorithm

Performance studies



Conclusions


food

milk bread

m1 m2 b1 b2

food

milk bread

m1 m2 b1 b2

expand

mine rules like milk => b1mine rules like milk => breadand m2 => b1


Two adjustments:

• A single minisup is used at all levels

• When the frequent k-itemsets are generated, items at all levels are considered, itemsets which contain an item and its ancestor are excluded


Algorithm

Performance studies



Conclusions

Filtering of uninteresting association rules Removal of redundant rules:

• To remove redundant rules, when a rule R passes the minimum confidence test, it is checked against every strong rule R' , of which R is a descendant. If the confidence of R, (R), falls in the range of the expected confidence with the variation of , it is removed.

• Example: • milk bread(12% sup, 85% con)• Chocolate milk bread(1% sup, 84% con)• Not interesting if 8% of milk is chocolate milk

• Can reduce rules by 30% to 60%

Filtering of uninteresting association rules (continued)

Removal of unnecessary rules:• To filter out unnecessary association rules, for each strong rule R’ :

A => B, we test every such rule R : A ‑ C => B, where C belongs to A. If the confidence of R, (R), is not significantly different from that of R' ,(R' ), R is removed.

• Example: • 80% customer buy milk => bread• 80% customer buy milk + butter => bread

• Reduces rules by 50% to 80%

Conclusions

Extended the association rules from single-level to multiple-level.

A top-down progressive deepening technique is developed for mining multiple-level association rules.

Filtering of uninteresting association rules.

Exams Questions

Q1: Give an example of multilevel association rules? A: Besides finding the 80% of customers that purchase

milk may also purchase bread, it is interesting to allow users to drill-down and show that 75% of people buy wheat bread if they buy 2 percent milk.

Exams Questions Q2: What are the problems in using normal Apiori methods?? A: One may apply the Apriori algorithm to examine data items at multiple levels of

abstraction under the same minimum support and minimum confidence thresholds. This direction is simple, but it may lead to some undesirable results.

First, large support is more likely to exist at high levels of abstraction. If one wants to find strong associations at relatively low levels of abstraction, the minimum support threshold must be reduced substantially; this may lead to the generation of many uninteresting associations at high or intermediate levels.

Second, since it is unlikely to find many strong association rules at a primitive concept level, mining strong associations should be performed at a rather high concept level, which is actually the case in many studies. However, mining association rules at high concept levels may often lead to the rules corresponding to prior knowledge and expectations, such as “milk => bread”, (which could be common sense), or lead to some uninteresting attribute combinations if the minimum support is allowed to be rather small, such as “toy => milk”, (which may just happen together by chance).

Exams Questions

Q3: What are the 2 general steps to do multiple-level association rule mining?

A: To explore multiple-level association rule mining, one needs to provide:

1) Data at multiple levels of abstraction, and 2) Efficient methods for multiple-level rule mining.

Mining Multiple-level Association Rules in Large Databases

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