Classification based on Positive and Negative Association Rules

B.Ramasubbareddy, A.Govardhan & A.Ramamohanreddy
International Journal of Data Engineering, (IJDE), Volume (2): Issue (2) : 2011 84
Classification Based on Positive and Negative Association Rules
B.Ramasubbareddy rsreddyphd@gmail.com
Associate Professor,Dept.of CSE,
Jyothishmathi Institute of Technology& Science,
Karimnagar505001, India
A.Govardhan govardhan_cse@yahoo.co.in
Professor of CSE,
JNTUH College of Engineering,
Nachupally,Karimnagar,505001,India
A.Ramamohanreddy ramamohansvu@yahoo.com
Professor of CSE, S.V.University,
Tirupati 517502, India.
Abstract
Association analysis, classification and clustering are three different techniques in data mining.
Associative classification is a classification of a new tuple using association rules. It is a
combination of association rule mining and classification. In this, we can search for strong
associations between frequent patterns and class labels. The main aim of this paper is to improve
accuracy of a classifier. The accuracy can be achieved by producing all types of negative class
association rules.
Keywords: data Mining, Association Analysis, Classification, Positive and Negative Association
Rules.
1. INTRODUCTION
Data mining algorithms aim at discovering knowledge from massive data sets. Association
analysis, classification and clustering are three different data mining techniques. The aim of any
classification algorithm is to build a classification model given some examples of the classes we
are trying to model. The model we obtain can then be used to classify new examples or simply to
achieve a better understanding of the available data. Classification generally involves two
phases, training and test. In the training phase the rule set is generated from the training data
where each rule associates a pattern to a class. In the test phase the generated rule set is used
to decide the class that a test data record belongs to. Different approaches have been proposed
to build accurate classifiers, for example, naive Bayes classification, Decision trees, and SVMs.
Data mining community proposed Association Rule Mining based Classification. This approach is
called Associative Classification produces transparent classifier consisting of rules that are
straight forward and simple to understand. Associative classification based on association rule
mining searches globally for all rules that satisfy minimum support and confidence thresholds. In
associative classification the classifier model is composed of a particular set of association rules,
in which consequent of each rule is restricted to classification class attribute. Many improvements
have been done in associative classification approach in recent studies and experiments thereof
show that this approach achieves higher accuracy than traditional approaches.
The traditional associative classification algorithms basically have 3 phases: Rule Generation,
Building Classifier and Classification as shown in Fig.1. Rule Generation employ the association
rule mining technique to search for the frequent patterns containing classification rules. Building
Classifier phase tries to remove the redundant rules, organize the useful ones in a reasonable
order to form the classifier and the unlabeled data will be classified in the third step. Some
experiments done over associative classification algorithms such as CBA [26], CMAR [23] and

MCAR [28] state that the associative classification methods share the features of being more
accurate and providing more classification rules.
FIGURE 1: Associative Classifier
This paper is structured as follows: section II recalls preliminaries about Association Rules, In
Section III, existing methods for associative classification are reviewed. The proposed algorithm
is presented in Section IV and V. Section VI contains conclusions and future work.
2. BASIC CONCEPTS AND TERMINOLOGY
This section introduces association rules terminology and some related work on negative
association rules and associative classification systems.
2.1 Association Rules
Let I = {i1, i2 ...in} be a set of items. Let D be a set of transactions, where each transaction T is a
set of items such that T ⊆ I. Each transaction is associated with a unique identifier TID. A
transaction T is said to contain X, a set of items in I, if X ⊆ T. An association rule is an implication
of the form “X ⇒ Y”, where X ⊆ I, Y ⊆ I, and X ∩ Y = ∅. The rule X ⇒ Y has a support s in the
transaction set D if s% of the transactions in D contains X ∪ Y. In other words, the support of the
rule is the probability that X and Y hold together among all the possible presented cases. It is said
that the rule X ⇒ Y holds in the transaction set D with confidence c if c% of transactions in D that
contain X also contain Y . In other words, the confidence of the rule is the conditional probability
that the consequent Y is true under the condition of the antecedent X. The problem of discovering
all association rules from a set of transactions D consists of generating the rules that have a
support and confidence greater than given thresholds. These rules are called strong rules.
2.2 Negative Association Rules
A negative association rule is an implication of the form X ┐Y (or ┐ X Y or ┐ X ┐ Y),
where X ⊆ I, Y ⊆ I and X ∩ Y = Φ (Note that although rule in the form of ┐ X ┐ Y
contains negative elements, it is equivalent to a positive association rule in the form of Y X.
Therefore it is not considered as a negative association rule. In contrast to positive rules, a
negative rule encapsulates relationship between the occurrences of one set of items with the
absence of the other set of items. The rule X ┐ Y has support s% in the data set s, if s % of
transactions in T contain itemset X while do not contain itemset Y. The support of a negative
association rule, supp(X ┐Y), is the frequency of occurrence of transactions with item set X in
the absence of item set Y. Let U be the set of transactions that contain all items in X. The rule
X ┐ Y holds in the given data set (database) with confidence c, if c% of transactions in U do
not contain item set Y. Confidence of negative association rule, conf ( X ┐ Y), can be
calculated with P( X ┐ Y )/P(X), where P(.) is the probability function. The support and confidence
of itemsets are calculated during iterations. However, it is difficult to count the support and
confidence of non-existing items in transactions. To avoid counting them directly, we can
compute the measures through those of positive rules.
3. RELATED WORK IN ASSOCIATIVE CLASSIFICATION
The problem of AC is to discover a subset of rules with significant supports and high confidences.
This subset is then used to build an automated classifier that could be used to predict the classes
of previously unseen data. It should be noted that MinSupp and MinConf terms in ARM
Training Data
Set of class
association rules
Classifier

(Association Rule Mining) are different than those defined in AC since classes are not considered
in ARM, only itemsets occurrences are used for the computation of support and confidence.
The CBA algorithm[26] was one of the first AC(Associative Classification) algorithms that
employed an Apriori candidate generation step to find the rules. Classification Based on
Associations (CBA) was presented by (Liu et al., 1998) and it uses Apriori candidate generation
method (Agrawal and Srikant, 1994) for the rule discovery step. CBA operates in three steps,
where in step 1, it discretises continuous attributes before mining starts. In step 2, all frequent
ruleitems which pass the MinSupp threshold are found, finally a subset of these that have high
confidence are chosen to form the classifier in step3. Due to a problem of generating many rules
for the dominant classes or few and sometime no rules for the minority classes, CBA (2) has
introduced by (Liu et al. 1999), which uses multiple support thresholds for each class based on
class frequency in the training data set. Experiment results have shown that CBA (2) outperforms
CBA and C4.5 in terms of accuracy.
Classification based on Multiple Association Rules (CMAR)[23] adopts the FP-growth ARM
algorithm (Han et al., 2000) for discovering the rules and constructs an FP-tree to mine large
databases efficiently (Li et al., 2001). It consists of two phases, rule generation and classification.
It adopts a FP- growth algorithm to scan the training data to find the complete set of rules that
meet certain support and confidence thresholds. The frequent attributes found in the first scan are
sorted in a descending order, i.e. F-list. Then it scans the training data set again to construct an
FP-tree. For each tuple in the training data set, attribute values appearing in the F-list are
extracted and sorted according to their ordering in the F-list. Experimental results have shown
that CMAR is faster than CBA and more accurate than CBA and C4.5. The main drawback
documented in CMAR is the need of large memory resources for its training phase.
Classification based on Predictive Association Rules (CPAR)[29] is a greedy method proposed
by (Yin and Han, 2003). The algorithm inherits the basic idea of FOIL in rule generation
(Cohen,1995) and integrates it with the features of AC.
Multi-class Classification based on Association Rule (MCAR)[28] is the first AC algorithm that
used a vertical mining layout approach (Zaki et al.,1997) for finding rules. As it uses vertical
layout, the rule discovery method is achieved through simple intersections of the itemsets Tid-
lists, where a Tid-list contains the item’s transaction identification numbers rather than their actual
values. The MCAR algorithm consists of two main phases: rules generation and a classifier
builder. In the first phase, the training data set is scanned once to discover the potential rules of
size one, and then MCAR intersects the potential rules Tid-lists of size one to find potential rules
of size two and so forth. In the second phase, the rules created are used to build a classifier by
considering their effectiveness on the training data set. Potential rules that cover a certain
number of training objects will be kept in the final classifier. Experimental results have shown that
MCAR achieves 2-4% higher accuracy than C4.5, and CBA.
Multi-class, Multi-label Associative Classification (MMAC) [27] algorithm consists of three steps:
rules generation, recursive learning and classification. It passes over the training data set in the
first step to discover and generate a complete set of rules. Training instances that are associated
with the produced rules are discarded. In the second step, MMAC proceeds to discover more
rules that pass MinSupp and MinConf from the remaining unclassified instances, until no further
potential rules can be found. Finally, rule sets derived during each iteration are merged to form a
multi-label classifier that is then evaluated against test data. The distinguishing feature of MMAC
is its ability to generate rules with multiple classes from data sets where each data objects is
associated with just a single class. This provides decision makers with useful knowledge
discarded by other current AC algorithms.

4. FINDING CLASS ASSOCIATION RULES
Apriori-based implementations are efficient but cannot generate all valid positive and negative
ARs. In this section, we try to solve that problem without paying too high a price in terms of
computational costs. Generating negative class association rules of the form ┐( = XY)=>C For
simplicity, we also limit ourselves to support and confidence to determine the validity of ARs.
Algorithm:
1. Generating negative class association rules of the form ┐I(= XY)=>C
2. Generate negative class association rules of the form ┐X C
3. Generate negative class association rules of the form ┐X ┐Y C
4. Generate negative class association rules of the form ┐XY C
4.1. Finding Positive class Association Rules XY=>C
1. AR φ;
2.S  φ;
3.Find L (P1)1 i.e. Frequent 1-itemsets
4. L(P1)  L(P1)
5. For k=2; L (P1)k-1≠Ø; k++
6.{
7.// Generating Ck
8.for each l1,l2 ε L(P1)k-1
9.If(l1[1]=l2[1]^………………l1[k-2]=l2[k-2]^l1[k-1]<l2[k-1])
10. Ck=Ck ∪ {{l1 [1]…….l1 [k-2],l1[k-1],l2[k-1]}
11. end if
12. end for
13. // Pruning using Apriori property
14. for each (k-1)- subsets s of I ε C
15. If s ∉ L (P1)k-1
16. Ck=Ck – {I}
17. end if
18. end for
19. //Pruning using Support Count
20. Scan the database and find supp(I) for all I ε Ck
21. S=S ∪ {I with support count}
22. For each I in Ck
23. If supp (I) ≥ ms
24. L (P1) k=L (P1) k
∪ {I}
25. end if
26. end for
27. L (P1) =L(P1) ∪ L(P1)k
28. }
29. end for
30. // Generating Positive Classification Rules of the form I(=XY) => c
31. for each I(=XY) ε L(P1)
32. for each c ε C
33. If conf (l c) ≥ mc
34. AR=AR ∪ {l c}
35. end if
36. end for
37. end for
4.2. Generating negative class association rules of the form ┐I(= XY)=>C
1. for each I ε L(P1)
2. if 1-supp(I) ≥ ms

International Journal of Data Engineering (IJDE), Volume (2) : Issue (2) : 2011 88
3. L(P2)=L(P2) U I
4. end for
5. // Generating Negative Association Rules of the from ┐(XY) => c
7. for each c ε C
8. If conf(┐I c)≥ mc
9. AR=AR ∪ {┐l c}
10. end for
11. end for
4.3. Generating negative class association Rules of the form I(=┐X┐Y) => C
1. C(P3 )2 = {¬{i1 }¬{i2 }|i1 , i2 ε L(P1 )1 , i1 ≠ i2 }
2. for {k = 2; C(P3 )k ≠ Ø; k + +} do
3. for all I = ¬X¬Y ε C(P3 )k do
4. if supp(I) ≥ ms then
5. insert I into L(P3 )k
6. else
7. for all i ∉ XY do
8. // Generating Candidates
9. Cand ={┐ (XU{i})┐Y, ┐X(┐Y U{i})}
10. // Pruning Cand
11. for each item in Cand
12. If (X{i} is not in L(P1) or ┐X
1
┐Y
1
is in L(P3) where X
1 ⊆X{i} and Y
1 ⊆Y)
13. Cand= Cand – {XY {i}}
14. C(P3)k+1= C(P3)k+1 U Cand
15. if Cand ≠ ∅∅∅∅, XY {i} ∉ S and
16. (!∃ I
1
⊆
XY {i}) (supp(I
1
) = 0) then
17. insert XY {i} into S(P3 )k+1
18. end if
19. end for
20. end if
21. end for
22. compute support of itemsets in S(P3 )k+1
23. S = S ∪ S(P3 )k+1
24. end for
25. // Generating Negative class association Rules of the from I(= ┐X┐Y) => C
27. for each c ε C
28. If conf(I c)≥ mc
29. AR=AR ∪ {I c}
30. If conf (I ┐c) ≥ mc
31. AR=AR ∪ {I ┐c}
32. end for
33. end for
4.4. Generating negative class Association Rules of the form ┐XY=>C
1. C(P4 )1,1 = {¬{i1 }{i2 }|i1 , i2 ε L(P1 )1 , i1 ≠ i2 }
2. for {k = 1; C(P4 )k,1 = Ø; k + +} do
3. for {p = 1; C(P4 )k,p ≠ Ø; p + +} do
4. for all I ε C(P4 )k,p do
5. if supp(I) ≥ ms then
6. insert I into L(P4 )k,p
7. end if

8. end for
9. //Generating Candidates
10. // I1 and I2 are joinable if I11
≠ I2 , I1 .negative = I2 .negative, I1 .positive and
//I2.positive share the same k − 1 items, and I1 .positive U I2 .positive ε L(P1 )p+1
11. for all joinable I1 , I2 ε L(P4 )k,p do
12. X = I1 .negative, Y = I1 .positive U I2 .positive
13. I = ¬XY
14. if (!∃X1 ⊂ X)(supp(¬X1
Y ) ≥ ms) and (!∃Y1 ⊂Y )(supp(¬XY1
) < ms) then
insert I into C(P4 )k,p+1
15. if XY∉ S and !∃I1 ⊂ XY, supp(I1
) = 0 then
16. insert XY into S(P4 )k,p+1
17. end if
18. end if
19. end for
20. compute support of itemsets in S(P4 )k,p+1
21. S = S ∪ S(P4 )k,p+1
22. end for
23. for all X ε L(P1 )k+1 , i ε L(P1 )1 do
24. if ( !∃X
1 ⊂ X)(¬X
1
{i} ε L(P4 ) then C(P4 )k+1,1 = C(P4 )k+1,1
∪ ¬X{i
25. end if
26. end for
27. end for
28. // Generating Negative Association Rules of the from ┐XY=> C
30. for each c ε C
31. If conf(I c)≥ mc
32. AR=AR ∪ {I c}
33. If conf(I ┐c)≥ mc
34. AR=AR ∪ {I->┐c}
35. end for
36. end for
5. ASSOCIATIVE CLASSIFIER
The set of rules that were generated as discussed in the previous section represent the actual
classifier. This categorizer is used to predict to which classes new objects are attached. Given a
new object, the classification process searches in this set of rules for those classes that are
relevant to the object presented for classification. The set of positive and negative rules
discovered as explained in the previous section are ordered by confidence and support. This
sorted set of rules represents the associative classifier. This subsection discusses the approach
for labeling new objects based on the set of association rules that forms the classifier
Algorithm: CPNAR ( Classification based on Positive and Negative Association Rules)
Input: A new object to be classified o;
The associative classifier (AC);
The confidence margin Ƭ;
Output: Category attached to the new object
Method:
1. Sφ /* set of rules that match o*/
2. for each r in AC /* the sorted set of rules */
3. If ( r⊂o) {count++}
4. SS U r
5. If(count==1)
6. fr.confr.conf /* keep the first rule confidence*/

7. SS U r
8. else if( r.conf>fr.conf- τ)
9. SS U r
10. else break
11. Divide S in subsets by category:S1,S2, . . . . Sn
12. for each subset S1,S2, . . . . Sn
13. Sum/substract the confidences of rules and divide by the number of rules in Sk
14. Scorei = Σr.conf/#rules
15. Put the new object in the class that has the highest confidence score
16. o ci, with scorei=max{ score1, .......scoren}
In the above algorithm (Classification of a new object), a set of applicable rules is selected in the
lines 1-8. The set of applicable rules is selected within a confidence margin. The interval of
selected rules is between the confidence of the first rule and this confidence minus the
confidence margin as checked in line 7. The prediction process is starting at line 10. The
applicable set of rules is divided according to the classes in line 10. In lines 11-12 the groups are
ordered according to the average confidence per class. In line 13 the classification is made by
assigning to the new object the class that has the highest score.
6. EXPERIMENTAL RESULTS
The implementation of our algorithm is a java program. The experiments have been performed
using datasets downloaded from UCI machine learning repository. To run the experiments, we
have used ten-fold cross validation test to compute the accuracy of the classifier. To discretize
the continuous attributes, we have adopted the technique used in CBA. All the experiments are
performed on a 600 MHz Pentium PC with 128MB main memory running Microsoft XP. From the
table 2, CPNAR algorithm has performed well for Heart, Iris and Zoo datasets when compared to
C4.5,CBA,CMAR and CPAR.
DATASET #ATTS #CLS #REC #Rules
Generated
BREST 10 2 699 478
HEART 13 2 270 209
HEPATITIS 19 2 155 87
IRIS 4 3 150 123
ZOO 16 7 101 68
TABLE 1: No. of CARs generated by our algorithm on various UCI ML datasets
DATASET C4.5 CBA CMAR CPAR CPNAR
BREST 95.0 96.3 96.4 96.0 96.6
HEART 80.8 81.9 82.2 82.6 83.0
HEPATITIS 80.6 81.8 80.5 82.6 82.3
IRIS 95.3 94.7 94 94.7 95.6
ZOO 92.2 96.8 97.1 95.1 97.5
TABLE 2: Accuracies of Various Classifiers on UCI ML datasets
7. CONCLUSION AND FUTURE WORK
We proposed an algorithm that integrates classification and association rule generation. It mines
both positive and negative class association rules. Our method generates positive and negative
class association rules with existing support-confidence framework. We conducted experiments
on UCI datasets. In future we wish to improve accuracy of our algorithm and then we conduct
experiments on some more datasets and compare the performance with other related algorithms.

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