FILTERING ASSOCIATION RULES WITH NEGATIONS ON THE
BASIS OF THEIR CONFIDENCE BOOST
Jos
´
e L Balc
´
azar, Cristina T
ˆ
ırn
˘
auc
˘
a and Marta E. Zorrilla
Departamento de Matem
´
aticas, Estad
´
ıstica y Computaci
´
on, Universidad de Cantabria, Santander, Spain
Keywords:
Association mining, Transactional dataset, Negated items, Confidence, Support, Confidence boost.
Abstract:
We consider a recent proposal to filter association rules on the basis of their novelty: the confidence boost. We
develop appropriate mathematical tools to understand it in the presence of negated attributes, and explore the
effect of applying it to association rules with negations.
We show that, in many cases, the notion of confidence boost allows us to obtain reasonably sized output
consisting of intuitively interesting association rules with negations.
1 INTRODUCTION
Among the many data mining techniques widely
available nowadays, association rules are a major
tool. Association rules are basically defined on trans-
actional data, where there is a global set of items,
and the dataset is structured in transactions, each of
which is an itemset, that is, a subset of the global set
of items. Many standard applications of association
mining (e.g. market basket data) obey this syntax, and
many association algorithms, both proprietary and
open source (such as the apriori implementation of
(Borgelt, 2003), for instance) work on it. An enor-
mous amount of literature is connected to this topic:
see http://michael.hahsler.net/research/
bib/association rules/ where almost a hundred
of the most cited references are enumerated.
In relational data, the dataset consists of tuples
where each transaction maps each attribute into one
of a number of values available for the attribute.
Relational data can be casted into transactional data
by considering each potential attribute-value pair as
an item. Often, associations on relational data are
computed in that way. Conversely, one can consider
transactional data as relational in several ways. The
one employed in several association miners, such as
the associators of Weka as of version 3.6, consists in
considering each item as a boolean-valued attribute.
But some of these transformations do not preserve
all semantics. For instance, the information that
different values for the same attribute in the same
tuple are incompatible is lost upon performing a
conversion into transactional. The associators of
Weka, applied to transactional data, give different
results than applying a standard transactional asso-
ciator: Weka will find associations not only among
items (attributes of the form “item = true”) but also
among their negations (as attributes of the form
“item = false”), and rules that mix them arbitrarily.
These rules can be found on a standard associator
as well by “composing” both transformations, that
is, preprocessing the transactional data to compute
the set of all items and adding to each transaction
the corresponding negations: this is the outcome of
transforming the transactional dataset into relational
and back. We will call this transformation the
neg-expansion of the dataset. In fact, there may
be datasets where considering negated attributes is
convenient (Boulicaut et al., 2000; Kryszkiewicz,
2005; Kryszkiewicz, 2009).
However, this “relational-like” expansion of a
transactional dataset, where each item is transformed
into a pair of items, namely, the positive and the
negative versions of the same original item, exhibits
an important drawback on many datasets. It is often
the case that the universe of items becomes much,
much larger than the average size of the transactions.
In that case, many transactions “have” the negative
versions of many attributes. In standard terminology,
the dataset becomes “dense”, with the additional
algorithmic and conceptual difficulties associated to
all dense datasets. Then, rules consisting of negative
information easily reach very high confidence and
support thresholds. The outcome is a large amount
263
Balcázar J., Tîrn
ˇ
auc
ˇ
a C. and Zorrilla M..
FILTERING ASSOCIATION RULES WITH NEGATIONS ON THE BASIS OF THEIR CONFIDENCE BOOST.
DOI: 10.5220/0003095802630268
In Proceedings of the International Conference on Knowledge Discovery and Information Retrieval (KDIR-2010), pages 263-268
ISBN: 978-989-8425-28-7
Copyright
c
 2010 SCITEPRESS (Science and Technology Publications, Lda.)

of “noisy” rules that make it difficult to extract
knowledge.
Specifically, in previous, recent works a notion
of “confidence boost” for association rules has been
proposed (Balc
´
azar, 2010) that is able to select a
reasonably sized set of output rules, in many cases, in
the transactional setting. Confidence boost measures
a form of objective “novelty”, quantifying to what
extent the information in each association rule “looks
different” from that of the rest of the rules. Two
variants of this intuition can be deployed on closure
spaces and several notions of bases. Specifically,
we start indeed from the notion of confidence boost
for the B
∗
basis, and we lift both the basis and its
corresponding variant of boost into confidence-boost
bounded B
∗
rules with negated attributes. We define
the neg-expanded closure space, and state and prove
mathematically its exact connection with the original
closure space: the neg-expansion does not alter the
mathematical structure of the original closures, but
just extends it. Then we demonstrate that there are
interesting cases of association rules in neg-expanded
datasets that can be handled efficiently by this form
of closure-aware confidence boost.
2 PRELIMINARIES
A given set of available items U is assumed; subsets
of it are called itemsets. We will denote itemsets by
capital letters from the end of the alphabet, and use
juxtaposition to denote union, as in XY . For a given
dataset D, consisting of n transactions, each of which
is an itemset labeled with a unique transaction iden-
tifier, we can count the support s(X) of an itemset X,
which is the cardinality of the set of transactions that
contain X. An alternative rendering of support is its
normalized version s(X)/n. The confidence of a rule
X → Y is c(X → Y ) = s(XY )/s(X), and its support is
s(X → Y ) = s(XY ). We assume that no transaction of
D includes all items.
Definition 1. Given a dataset D over universe of
items U, the neg-expanded dataset D

over universe
U

is formed by adding to U a “negative copy” A

of each item A ∈ U to obtain U

, and adding to each
transaction t ∈ D all the negative items A

for all
A /∈ t, to obtain D

.
Definition 2. Given a set X ⊆ U, the closure of X
with respect to D, denoted by cl
D
(X), is the max-
imal set (with respect to the set inclusion) Y ⊆ U
such that X ⊆ Y and s(X) = s(Y ). Similarly, given
X ⊆ U

, the closure of X with respect to D

, de-
noted by cl
D

(X), is the maximal set Y ⊆ U

such
that X ⊆ Y and s(X) = s(Y ).
It is well-known that the closure of a set is well-
defined since there is a single such maximal; clo-
sure operators are characterized by the three prop-
erties of monotonicity X ⊆ cl
D
(X), idempotency
cl
D
(cl
D
(X)) = cl
D
(X), and extensivity, cl
D
(X) ⊆
cl
D
(Y ) if X ⊆ Y .
Definition 3. 1. Given a dataset (D,U), we say that
X ⊆ U is (D, U)-closed (or simply closed when the
dataset and the set of attributes is understood from the
context) if cl
D
(X) = X.
2. Given the neg-expanded dataset (D

,U

), we say
that X ⊆ U

is (D

,U

)-closed if cl
D

(X) = X.
Table 1: Dataset D with U = {a, b, c}.
a b c
1 0 1
1 0 1
1 0 0
0 1 0
0 1 1
Example 1. Imagine we have the dataset D repre-
sented in Table 1. The neg-expanded dataset D

is
represented in Table 2. It is easy to check that al-
though the set X = {a} is (D, U)-closed (s({a}) =
3,s({a, b}) = 0,s({a,c}) = 2), it is not (D

,U

)-
closed (s({a,b

}) = s({a}) = 3).
Table 2: Dataset D

with U

= {a, b, c,a

,b

,c

}.
a b c a

b

c

1 0 1 0 1 0
1 0 1 0 1 0
1 0 0 0 1 1
0 1 0 1 0 1
0 1 1 1 0 0
The following property trivially follows:
Proposition 1. A set X ⊆ U is (D, U)-closed if and
only if there is no X
0
⊆ U such that X ⊂ X
0
and
s(X
0
) = s(X). Likewise, a set X ⊆ U

is (D

,U

)-
closed if and only if there is no X
0
⊆ U

such that
X ⊂ X
0
and s(X
0
) = s(X).
Closure operators are also characterized by the
property that any intersection of closed sets is closed.
The empty set is closed ((D

,U

)-closed) if and
only if no item appears in each and every transaction
(and all items appear in at least one transaction, re-
spectively). Note that s(X) = 0 implies cl
D
(X) = U
for any X ⊆ U (since s(U) = 0 by our assumptions).
U is always closed. Again, cl
D

(X) = U

for any
X ⊆ U

with s(X ) = 0. Note also that a set X that
is (D,U)-closed is not necessarily (D

,U

)-closed,
as shown in Example 1.
KDIR 2010 - International Conference on Knowledge Discovery and Information Retrieval
264

2.1 Confidence Boost
Motivated by a number of previous works, in
(Balc
´
azar, 2010) we proposed to filter rules according
to confidence boost, which measures to what extent
the rule at hand has higher confidence than rules re-
lated to it.
Some notions of redundancy allow for character-
izing irredundant bases of absolutely minimum size.
A basis for a dataset at a given confidence is a set of
rules that hold in the dataset at least at that confidence,
and such that every rule that holds in the dataset at
the same confidence or higher is made redundant by
some rule in the basis; we wish the basis also to be as
small as possible. Specifically, the variant of redun-
dancy that takes into account the closure space de-
fined by the dataset leads to the B
∗
basis (Balc
´
azar,
2010). This basis offers several computational advan-
tages over its main competitor (called representative
rules) at a little price: occasionally it is slightly larger
but can be computed much faster. In fact, in the tests
we made on educational data, the B
∗
rules did coin-
cide exactly with the representative rules.
One can push the intuition of redundancy further
in order to gain a perspective of novelty of association
rules. Intuitively, an irredundant rule is so because
the actual value of its confidence is higher than the
value that the rest of the rules would suggest; then,
one can ask: “how much higher?”. If other rules sug-
gest, say, a confidence of 0.8 for a rule, and the rule
has actually a confidence of 0.81, the rule is indeed
irredundant and brings in additional information, but
its novelty, with respect to the rest of the rules, is not
high; whereas, in case its confidence is 0.95, quite
higher than the 0.8 expected, the fact can be consid-
ered novel, in that it states something really different
from the rest of the information mined. For instance,
in the shopping dataset discussed below, one could
consider a rule indicating that market baskets with
canned vegetables and frozen meals tend to include
beer, with a confidence of 0.84; it turns out that the
rule that says that such baskets not only tend to con-
tain beer but they are also bought by a male person
has confidence 0.81. We may not want to reduce the
right hand side, removing the sex attribute from it, if
it is to gain just about a 0.03 percent of improvement
of the confidence: more likely, we wish to keep the
larger rule and postpone (or altogether remove from
consideration) the slightly more confident but less in-
formative rule having only beer as consequent.
For an association rule X → Y , denote C (X → Y )
the set of all rules X
0
→ Y
0
for which the follow-
ing three conditions are true: (cl
D
(X
0
) 6= cl
D
(X) ∨
cl
D
(XY ) 6= cl
D
(X
0
Y
0
)), X
0
⊆ cl
D
(X), Y ⊆ cl
D
(X
0
Y
0
).
The first condition corresponds to both rules not be-
ing equivalent to each other. This is very close to
a nontrivial mathematical characterization of a spe-
cific form of closure-based redundancy, as discussed
in (Balc
´
azar, 2010).
Definition 4. The confidence boost of an association
rule X → Y (always with X ∩Y =
/
0) is β(X → Y ) =
=
c(X → Y )
max{c(X
0
→ Y
0
)


X
0
→ Y
0
∈ C (X → Y )}
From the definition of the confidence boost, it fol-
lows immediately that X ∩Y =
/
0 implies β(X → Y) =
c(X→Y )
max{A
(X,Y )
,B
(X,Y )
}
where A
(X,Y )
= max
a/∈XY
s(XY {a})
s(X)
and
B
(X,Y )
= max
X
0
⊂X
s(X
0
Y )
s(X
0
)
. Intuitively, this means the
following: there may be two reasons to assign a low
confidence boost to a rule, one of them due to low
relative confidence improvement over some alterna-
tive rule having larger right-hand side (corresponding
to the added item a); and the other due to low rel-
ative confidence improvement over some alternative
rule having a smaller left-hand side X
0
.
The fact that a low confidence boost corresponds
to a low novelty is argued in (Balc
´
azar, 2010). Also, it
is proved there that all rules that would be pruned off
due to low lift will be pruned as well due to low con-
fidence boost; actually, for rules of the form a → b for
single items a and b, low confidence boost may be due
to a possibility of extending the right hand side, but,
if this is not so, then the confidence boost is exactly
equal to the lift, which is, therefore, also low.
3 MATHEMATICAL TOOLS
We can apply the facts explained after the definition
of confidence boost as follows:
Proposition 2. Let XY and X
0
Y
0
be two closed sets
such that XY ⊂ X
0
Y
0
and X ∩Y = X
0
∩Y
0
=
/
0. Then
β(X → Y ) ≤
s(XY )
s(X
0
Y
0
)
.
Proof. Let us first notice that from β(X → Y ) =
c(X→Y )
max{A
(X,Y )
,B
(X,Y )
}
we can deduce β(X → Y ) ≤
c(X→Y )
A
(X,Y )
.
On the other hand,
max
a/∈XY
s(XY {a}) ≥ s(XY Z)
for any non-empty Z such that Z ∩ XY =
/
0, as it suf-
fices to pick any a ∈ Z; hence,
max
a/∈XY
s(XY {a}) ≥ s(X
0
Y
0
).
Therefore, β(X → Y ) ≤
c(X→Y )
s(X
0
Y
0
)/s(X)
=
s(XY )
s(X
0
Y
0
)
.
This property is heavily employed in our algorith-
mics. Given a dataset D over universe U, let
FILTERING ASSOCIATION RULES WITH NEGATIONS ON THE BASIS OF THEIR CONFIDENCE BOOST
265

(D

,U

) be the neg-expansion as defined previ-
ously. In order to ease the readability of this section
we will denote cl
D
(X) by
¯
X and cl
D

(X) by
˜
X.
Lemma 1. Let X
1
,X
2
⊆ U be such that
¯
X
1
=
¯
X
2
. Then
˜
X
1
=
˜
X
2
.
Proof. Note that it is enough to show that if Y =
¯
X for
some X ,Y ⊆ U then
˜
X =
˜
Y . From Y =
¯
X we deduce
s(Y ) = s(X) and X ⊆ Y . On the other hand, s(Y ) =
s(
˜
Y ), so s(X) = s(
˜
Y ). Moreover X ⊆ Y ⊆
˜
Y . Hence,
it must be that
˜
X ⊇
˜
Y . And since
˜
Y is a closed set, we
get the desired equality.
Lemma 2. For any X ⊆ U,
¯
X ⊆
˜
X and
¯
X =
˜
X ∩U.
Proof. The inclusion
¯
X ⊆
˜
X is obvious given the way
the two closures were defined. Let us now show that
the closure of X in (D, U) can be obtained by taking
all and only the positive elements from the closure
of X in (D

,U

). Clearly,
¯
X ⊆
˜
X ∩ U, so we only
need to show that
¯
X ⊇
˜
X ∩ U. On one hand, we have
˜
X ∩ U ⊆
˜
X, so s(
˜
X ∩ U) ≥ s(
˜
X) = s(X). On the other
hand, X ⊆
˜
X ∩ U, so s(X) ≥ s(
˜
X ∩ U). Therefore,
s(
˜
X ∩ U) = s(X ). We have obtained a set
˜
X ∩ U in
U that includes X and has the same support as X . It
follows immediately that
˜
X ∩U ⊆
¯
X.
Let us define ϕ : cl
D
(P (U)) → cl
D

(P (U

)) by
ϕ(
¯
X) =
˜
X. We prove that this function is an injective
homomorphism from the lattice of original closures
into the lattice of neg-expanded closures.
Proposition 3. ϕ is well-defined, injective and it pre-
serves the inclusion relation (i.e., if
¯
X
1
⊆
¯
X
2
then
ϕ(
¯
X
1
) ⊆ ϕ(
¯
X
2
)).
Proof. Obviously, for any closed set Y ∈ P (U) there
might be several X with
¯
X = Y , so for ϕ to be well-
defined we need to show that given X
1
,X
2
with
¯
X
1
=
¯
X
2
, we have
˜
X
1
=
˜
X
2
. But this is clear from Lemma 1.
To see that ϕ is injective, let us take
¯
X
1
,
¯
X
2
in
cl
D
(P (U)) such that ϕ(
¯
X
1
) = ϕ(
¯
X
2
). From
˜
X
1
=
˜
X
2
we get
¯
X
1
=
˜
X
1
∩ U =
˜
X
2
∩ U =
¯
X
2
(by Lemma 2).
Let X
1
,X
2
⊆ U be such that
¯
X
1
⊆
¯
X
2
. We have
X
1
⊆
¯
X
1
⊆
¯
X
2
⊆
˜
X
2
. But X
1
⊆
˜
X
2
implies
˜
X
1
⊆
˜
X
2
.
This proposition explains how a “copy” of the
original closure structure appears inside the neg-
expanded closures, but does not give any informa-
tion about “the rest”, that is, what is added to the lat-
tice by the neg-expansion process. Now, define ψ :
cl
D

(P (U

)) → P (U) by ψ(
˜
Y ) =
˜
Y ∩ U. We prove
that this function “explains” that each neg-expanded
closure is a variation of an original closure.
Proposition 4. The following properties hold:
- ψ(cl
D

(P (U

))) = cl
D
(P (U)) ∪ {
/
0}
- If X 6=
/
0 is (D,U)-closed then ψ(ϕ(X )) = X
- If Y ∩ U 6=
/
0 is (D

,U

)-closed then ϕ(ψ(Y )) ⊆ Y
Proof. Note that ψ is well-defined because even if
there might be various Y
0
⊆ U

such that
˜
Y =
˜
Y
0
, the
intersection of their closure with the set of positive
attributes will always coincide. So, let us start by de-
termining the image of the function ψ. Let Y ⊆ U

be
an arbitrary (D

,U

)-closed set. If Y ∩ U =
/
0, then
ψ(Y ) equals by definition the empty set, and we are
done. Assume now that Y ∩U 6=
/
0, and take Y = Y
1
Y
2
such that
/
0 6= Y
1
⊆ U and Y
2
⊆ U

\U (where “\”
denotes set-theoretic difference). We need to show
that Y
1
is (D,U)-closed. Suppose by contrary that
it is not. This means that there exists Z such that
Z ⊃ Y
1
and s(Z) = s(Y
1
). It follows immediately that
s(ZY
2
) = s(Y
1
Y
2
) = s(Y ), and we found a set ZY
2
that
strictly includes Y and has the same support, a contra-
diction.
Let X 6=
/
0 be a (D, U)-closed set. We have,
ψ(ϕ(X)) = ψ(
˜
X) =
˜
X ∩U =
¯
X = X.
As for the inequality ϕ(ψ(Y )) ⊆ Y , let us take Y a
(D

,U

)-closed set such that Y ∩U 6=
/
0. We have to
show that ϕ(Y ∩ U) ⊆ Y . That is, if we take Y = Y
1
Y
2
such that
/
0 6= Y
1
⊆ U and Y
2
⊆ U

\U we need to
prove that
˜
Y
1
⊆ Y . But this follows immediately from
Y =
˜
Y and Y
1
⊆ Y .
4 EMPIRICAL VALIDATION
We analyzed the role played by the B
∗
basis and the
closure-based confidence boost on several datasets,
comparing association rules mined from the original
dataset with the one obtained from its neg-expansion.
An important observation is that even if the size of B
∗
is exponentially bigger for the neg-expanded dataset,
filtering it on the basis of the confidence boost reduces
the number of output rules to a very reasonable size.
We describe here two such cases. As we shall see,
even strict confidence bounds, which lose interesting
rules of lower confidence, fail to reduce the output
into an usable and sufficiently irredundant outcome.
As indicated above, lift is not competitive either: all
rules pruned off by lift are also pruned off by confi-
dence boost, but many intuitive redundancies are un-
detected by lift.
The first example dataset that we analyze in this
paper is a typical market basket dataset, taken from
the Clementine data mining workbench (Clementine,
2005). The goal is to discover groups of customers
who buy similar products and can be characterized de-
mographically, such as by gender or home ownership.
The dataset has 1000 transactions over 13 attributes,
11 of them truly boolean (fruitveg, freshmeat, dairy,
cannedveg, cannedmeat, frozenmeal, beer, wine, soft-
drink, fish, confectionery), representing the existing
KDIR 2010 - International Conference on Knowledge Discovery and Information Retrieval
266

types of products, and two other binary attributes,
gender and homeown. Due to the non transactional
nature of these last two attributes, we decided to in-
clude both of their values in the mining process of
the original database. The report in (Clementine,
2005) identifies three customer profiles: those who
buy beer, frozen meals, and canned vegetables (the
“beer, beans, and pizza” group), those who buy fish,
fruits and vegetables (the “healthy eaters”), and those
who buy wine and confectionery.
Table 3: Basket Dataset: Number of Rules.
S C
B
∗
β = 1.05 β = 1.20
pos | neg pos | neg pos | neg
0.7 12 | 31708 10 | 208 7 | 14
0.10 0.8 5 | 20517 5 | 43 5 | 4
0.9 4 | 72 4 | 5 0 | 0
0.7 6 | 13350 6 | 68 6 | 14
0.15 0.8 2 | 8529 2 | 20 2 | 5
0.9 0 | 1 0 | 0 0 | 0
0.7 0 | 1686 0 | 28 0 | 8
0.30 0.8 0 | 1015 0 | 16 0 | 3
0.9 0 | 0 0 | 0 0 | 0
The results obtained with different values for con-
fidence and support parameters are shown in Table 3,
which reports the number of rules passing the thresh-
olds for each case. The five B
∗
rules obtained with
support 0.10 and confidence 0.80 when mining the
original dataset reveal that those who buy beer, frozen
meals, and canned vegetables are mostly men, those
who buy sweets and wine are usually women, and
healthy eaters (fish, fruits and vegetables) do not own
a house.
[c: 0.89 s: 0.12] fish fruitveg ⇒ nohomeowner
[c: 0.82 s: 0.14] beer frozenmeal ⇒ male cannedveg
[c: 0.84 s: 0.14] beer cannedveg ⇒ male frozenmeal
[c: 0.81 s: 0.14] cannedveg frozenmeal ⇒ male beer
[c: 0.86 s: 0.12] confectionery wine ⇒ female
On the other hand, allowing “negative” instances,
the size of the basis, that is, after redundancy re-
moval, increases dramatically to 20517 rules, a num-
ber that would discourage any human trying to fig-
ure out some correlations in the dataset. It is only
due to the confidence boost that this number is de-
creased to reasonable values. However, it is important
to allow “negated” items, and applying the confidence
boost bound actually allows us to do so and remain
within reasonable figures: using negations, one may
discover other interesting facts that are hidden in the
data. For example, the 43 rules obtained with sup-
port 0.10, confidence 0.80 and confidence boost 1.05
reveal, besides some of the facts we knew from the
“positive” case, the following tendencies: - Those that
own a house do not buy fish:
[c: 0.81 s: 0.40] homeowner ⇒ nofish
- There are products very seldom bought, like
fresh meat, dairy and soft drinks:
[c: 0.81 s: 0.81] ⇒ nofreshmeat
[c: 0.82 s: 0.82] ⇒ nodairy
[c: 0.81 s: 0.81] ⇒ nosoftdrink
- Women do not buy beer or frozen meals:
[c: 0.81 s: 0.41] female ⇒ nobeer
[c: 0.81 s: 0.41] female ⇒ nofrozenmeal
[c: 0.85 s: 0.12] confectionery wine ⇒ nofrozenmeal
[c: 0.82 s: 0.11] confectionery wine ⇒ nobeer
- Men do not buy sweets:
[c: 0.80 s: 0.39] male ⇒ noconfectionery
The second dataset we analyze deals with real data
from a virtual course entitled “Introduction to mul-
timedia methods”. It is a subject of 6 ECTS which
was taught in the first semester of 2009 at the largest
virtual campus in Spain, called G9. It is a practical
course having as final objective teaching the students
how to use a particular multimedia tool. The goal is
to discover the resources which are commonly used
together in each session, thus allowing the instructors
to find out which collaborative tools are used more
frequently (wiki, chat, forum, etc.) by their students,
which ones are rather ignored, and which is the pro-
file of the learning process followed by the students.
This information is very valuable in order to propose
tasks according to the learner’s learning style.
Table 4: E-learning Dataset: Number of Rules
S C
B
∗
β = 1.05 β = 1.20
pos | neg pos | neg pos |neg
0.7 4 | 7152 3 | 34 1 | 9
0.3 0.8 3 | 6269 3 | 16 1 | 2
0.9 1 | 6943 1 | 1 0 | 0
0.7 2 | 4155 1 | 6 1 | 0
0.4 0.8 1 | 3605 1 | 4 1 | 0
0.9 0 | 3969 0 | 0 0 | 0
0.7 1 | 2131 1 | 14 1 | 0
0.5 0.8 1 | 2103 1 | 6 1 | 0
0.9 0 | 2275 0 | 0 0 | 0
This dataset contains 6206 transactions over 14
attributes, each of them having value 1 or 0, indi-
cating whether the respective course resource was
visited or not in that session. The attributes are:
content-page, mail, forum, chat, web-link, orga-
nizer, learning-objectives, assignment, calendar, file-
manager, who-is-online, announcement, my-grades
and student-bookmark.
The results obtained with different values for con-
fidence and support parameters are shown in Table 4.
FILTERING ASSOCIATION RULES WITH NEGATIONS ON THE BASIS OF THEIR CONFIDENCE BOOST
267

Observing it, one can see that the number of rules ob-
tained with support 0.30 and confidence 0.70 for the
original dataset (without negated attributes) is 4:
[c: 0.74 s: 0.45] forum ⇒ organizer
[c: 0.97 s: 0.34] content-page ⇒ organizer
[c: 0.89 s: 0.32] assignment ⇒ organizer
[c: 0.81 s: 0.81] ⇒ organizer
The rules obtained are not very informative, basi-
cally saying that whatever they do, students also visit
the organizer page. But this does not come as a sur-
prise, given the fact that “organizer” is the main front
page of the course.
Clearly, these rules cannot offer information about
which are the resources less used, like the ones ob-
tained by using the neg-expanded dataset. Here are
some of the 34 rules mined at support 0.3, confidence
0.7 and confidence boost 1.05 with negated attributes:
[c: 0.70 s: 0.70] ⇒ announcement=0 file-manager=0
calendar=0 learning-objectives=0 student-bookmark=0
web-link=0 who-is-online=0 chat=0
[c: 0.86 s: 0.30] content-page=1 ⇒ announcement=0
chat=0 organizer=1 student-bookmark=0
[c: 0.84 s: 0.30] content-page=1 ⇒ chat=0 student-
bookmark=0 mail=0
[c: 0.86 s: 0.30] content-page=1 ⇒ my-grades=0 orga-
nizer=1 student-bookmark=0
[c: 0.88 s: 0.31] content-page=1 ⇒ who-is-online=0
organizer=1 student-bookmark=0
[c: 0.86 s: 0.30] content-page=1 ⇒ organizer=1 web-
link=0 student-bookmark=0
[c: 0.85 s: 0.30] content-page=1 ⇒ calendar=0 chat=0
organizer=1 student-bookmark=0
[c: 0.85 s: 0.30] content-page=1 ⇒ chat=0 organizer=1
student-bookmark=0 file-manager=0
[c: 0.85 s: 0.30] content-page=1 ⇒ chat=0 organizer=1
who-is-online=0
In the first rule, one can see that there are many
resources that are scarcely used, like the chat or the
announcement page; therefore, if the instructor has
something important to communicate to the students,
the best option would be to put it in the forum (a re-
source known to be accessed more often from the pos-
itive rules). Furthermore, one may note that when the
students connect to the platform in order to study (i.e.,
when they visit content-page resources), they do not
visit the chat, their bookmark or email.
A further, similar analysis of this dataset, also by
comparison with a different one with similar origin
and quite different characteristics, in terms of associ-
ation rules with negations and high confidence boost,
and including an additional pruning heuristic, is de-
scribed in (Balc
´
azar et al., 2010).
5 CONCLUSIONS AND FUTURE
WORK
In many practical applications, the output of a data
mining process could greatly benefit from adding to
the dataset the “negated” versions of the attributes.
One of the problems that arises though is that the
resulting set of rules mined is huge, making human
interpretation unfeasible. In this paper we propose
to use a recently introduced notion called confidence
boost that is able to filter out those rules that are not
“novel”, by quantifying to what extent the informa-
tion in each association rule “looks different” from
that of the rest of the rules. Our implementation em-
ploys the open-source closure miner from (Borgelt,
2003), and is available at slatt.googlecode.com.
As future work, we would like to look into (mathe-
matical and practical) ways of pushing the confidence
boost constraint at an earlier stage of the algorithm,
thus avoiding the vast amount of time dedicated to
compute closed sets that will not be used, or to gener-
ate thousands of rules that will be later on discarded
based on their low confidence boost.
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