Placement-and-Profit-Aware Association Rules Mining
Runyu Ma
1,
, Hantian Li
1,
, Jin Cen
1
and Amrinder Arora
2
1
The George Washington University, Washington D.C., U.S.A.
2
BizMerlinHR, Reston, Virginia, U.S.A.
Keywords:
Association Rule Mining, Data Mining, Placement-and-Profit-Aware Association Rules Mining.
Abstract:
Previous approaches on association rule mining in recommendation have already achieved promising perfor-
mances. However, to the best of our knowledge, they seldom simultaneously take the profit and placement
factor into consideration. In E-commerce recommendation scenario, the order of the recommendation reflects
as placement. In this paper, we propose a novel placement-and-profit-aware association rule mining algorithm
to maximize profit as well as maintaining recommendation accuracy. We also propose two metrics: Expecta-
tion of Profit (EOP), which measures the overall profit, and Expectation of Click rate (EOC), which measures
the user experience. Experiments on SPMF dataset show that the proposed algorithm can improve the EOP
significantly with only slight decrease in EOC.
1 INTRODUCTION
In order to increase their net revenue and help
customers discover potentially desired items, e-
commerce service providers typically recommend ad-
ditional items to customers after they add items to
the shopping cart. For example, Figure 1 shows
an online-shopping recommendation after a customer
has added a hamper and a chair pad into the cart. In
this example, three rows of items are recommended at
the check-out page based on merchandise in the cart.
These recommended items serve two purposes: in-
crease the satisfaction of customers, and increase the
profit of the merchant. Previously, researchers have
proposed Collaborate Filtering (CF) (Schafer et al.,
2007), Association Rules Mining (ARM) (Agrawal
et al., 1993) and Weighted Association Rules Min-
ing (WARM) (Cai et al., 1998) to recommend these
additional items. Although CF and ARM have shown
decent performance, they do not generally take profit
into consideration. For instance, a patent about col-
laborative filtering proposes a method to place ad-
vertisements automatically (Robinson, 1999). This
patent takes the users’ interests into consideration,
but ignores the profit of items. So, the popular-but-
low-profit item tend to be recommended. As a re-
sult, the profit of E-commerce company is not guar-
anteed to be maximized. WARM is profit-aware,
*
These authors contributed equally to this study and
share first authorship.
but could possibly result in worse recommendation
accuracy, because it would recommend high profit
but unattractive items (Cai et al., 1998). Also,
in the practice, the click-through rates of items is
highly related to their placement (McMahan et al.,
2013). However, none of these methods take the
placement into account. We propose a more com-
prehensive model that considers profit maximization,
placement and recommendation accuracy. To expli-
cate this proposed model, Figure 2 shows the ab-
stract structure of the scenario in Figure 1. This
paper proposes a confidence-based solution which
takes Placement, Click-through Rate Model (Chuklin
et al., 2015) and Profit into account to recommend
items to maximize the profits and click-through rate
which reflects the correlation of items. We evaluate
the proposed method on the retail dataset of Sequen-
tial Pattern Mining Framework (SPMF) (Fournier-
Viger et al., 2016) (Brijs et al., 1999) dataset, which
was downloaded from http://www.philippe-fournier-
viger.com/spmf/. Retail dataset is an anonymous re-
tail market basket data from an anonymous Belgian
retail store. Our proposed method shows a good trade-
off between profit and click-through rate compared
with ARM and WARM.
Ma, R., Li, H., Cen, J. and Arora, A.
Placement-and-Profit-Aware Association Rules Mining.
DOI: 10.5220/0007380606390646
In Proceedings of the 11th International Conference on Agents and Artificial Intelligence (ICAART 2019), pages 639-646
ISBN: 978-989-758-350-6
Copyright
c
2019 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
639
Figure 1: An example of Recommendation Based on
Bought Items (Amazon.com, 2018).
1.1 Background on Association Rules
Mining
Suppose X and Y are two sets such that X Y =
/
0. An
association rule X Y represents an association be-
tween the presence of the item sets X and Y in trans-
actions (Nguyen et al., 2017). As far as this paper
concerned, X means the selected item set in the shop-
ping cart and Y means the item set that may be rec-
ommended.
Association rule mining has various measures to
evaluate how interesting the rules are. Two most pop-
ular measures are the support and confidence. The
support of an association rule X Y , denoted as
sup[X Y ], is the ratio between the number of trans-
actions containing X and the number of transactions
containing X Y .
Suppose T is a set of transactions, I is a set of
items. Then we define tid[X ] as a set of Transaction
IDs, which contain all items in set X. Then sup can
be defined as:
sup[X Y ] =
|tid[X Y ]|
|T |
(1)
con f can be defined as:
con f [X Y ] =
|tid[X Y ]|
|tid[X ]|
(2)
In past research, many methods of Association
Rules Mining have been developed, such as Apri-
ori algorithm (Agrawal and Srikant, 1994), FpGrowth
algorithm (Han et al., 2004) and ETARM (Nguyen
et al., 2017). Apriori and FpGrowth have exponential
time complexity which is not practical. ETARM pro-
poses a way to mine top-k association rules (Fournier-
Viger et al., 2012) effectively. It expands item set X
and item set Y while only reserving top-k valid associ-
ation rules with the highest support. As far as this pa-
per concerned, item set X is given and does not need
to be expanded. Item set Y contains only one item
for each placement. So this paper applies a simplified
version of ETARM to get top-k association rules.
1.2 Mining Association Rules with
Weighted Item
In 1998, Cai proposed Mining Association Rules with
Weighted Item (MARWI) (Cai et al., 1998), which
first come up with the idea of weighted support and
weighted confidence. As Cai’s definition, normal-
ized weighted support and normalized weighted con-
fidence are:
w_sup(A B) =
1
n
n
i=1
w
i
× sup(A B) (3)
w_con f (A B) =
1
n
n
i=1
w
i
× conf(A B) (4)
where there are n items in set A B; w
i
means
the weight of item i; w_conf and w_sup represents
weighted confidence and weighted support, respec-
tively.
MARWI is a solution for WARM problem. Let
w
i
be the profit of item i, maximizing the expec-
tation of profit can be achieved by maximizing the
weighted_con f idence. However, this could result
in low recommendation accuracy. To be specific, if
the profit of recommended items is quite high while
their confidence is very low, the weighted confidence
could still be very high. In this situation, profitable
but unattractive items are recommended to customers.
As a result, the shopping experience of customers is
greatly undermined. Our proposed method in Sec-
tion 3 offers an approach that increases expectation
of profit while having less recommendation accuracy
loss.
1.3 Click-through Rate
Click-through Rate (CTR) (Chuklin et al., 2015) is
the ratio of users who click on a specific link to the
number of total users who view a page (Association
et al., 2014). This paper utilizes CTR as the average
ICAART 2019 - 11th International Conference on Agents and Artificial Intelligence
640
Figure 2: An abstract structure of Recommendation Scenario with Click-through Rate Models 1.
prior placement click probability to predict the possi-
ble click probability of a recommended item. In the
experiment, three different CTR models are shown in
Table 1.
1.4 Structure of this Paper
This paper is structured as follows. Section 1 intro-
duces the background, the achievement and related
works. After that, section 2 introduces the definitions
and problem statement. Next, the proposed method
and algorithm is presented in Section 3. Section 4
presents experiments and empirical results. Section 5
discusses some of the challenges. Finally, the paper is
concluded in Section 6.
2 DEFINITIONS AND PROBLEM
STATEMENT
2.1 Definition
In this section, several key concepts and definitions
are introduced.
Transaction Database: Suppose there is a finite
set of items I = {i
1
, i
2
, ..., i
n
} which represents all
unique items or products. Transaction Database T =
{T
1
, T
2
, ..., T
m
} refers to a database which stores all
paid transactions. Each transaction, with a unique
number transaction ID, is a subset of I.
Profits of Items: Profits of Items p indicates the prof-
its realized when an item is sold. This data is gener-
ally highly confidential by its nature, and for the pur-
pose of model, we seed this data which can be down-
loaded from https://github.com/yourexpress/PPARM.
Researchers typically have access to data of the spe-
cific e-commerce providers that they are working
with, and can run the proposed method on their own
data set simply by replacing the profit data file.
Set A: Set A is a set of the items in the shopping cart.
The union of set A and recommended items could be
treated as a potential transaction. That is to say, for an
item i, the higher con f (A {i}) is, the more possi-
bility item i will be of interest to the customer.
Placement and corresponding Click-through Rate:
Placement means a location where recommended
items are displayed on the website. For example,
there are 12 placements with different items in Fig-
ure 1. Each placement s has a corresponding Click-
through Rate CT R(s) which reflects the average prob-
ability for that placement over all items.
Expectation of Profit and Expectation of Click
Rate: The expectation of profit, denoted as EOP, is
the expectation of profit in the recommendation for a
single transaction. It is a measurement of how well
the recommendation algorithm is in terms of profit.
The expectation of click rate, denoted as EOC, is the
expectation of click probability of all recommended
items in the recommendation for a single transaction.
Thus, EOC is the measurement of the recommenda-
tion accuracy as measured in terms of click probabil-
ity.
Recommendation Result: Recommendation result,
denoted as R, is the an arrangement of k items outputs
by the proposed method, where R = {I
i1
, I
i2
, ..., I
ik
}.
I
i j
means we put item i to placement j. So R is an
ordered result of k items.
Performance Score: Performance score, denoted
simply as score, is a linear weighted function of EOP
and EOC used to evaluate the recommendation result
R:
score = EOP(R) + α EOC(R) (5)
2.2 Problem Statement
Given a transaction database T , an item profit list P,
and a placement click-through rate list CT R of size k.
The problem is to maximize score by recommending
an arrangement of k items and assigning them to the
corresponding k slots in the placement.
3 PROPOSED ALGORITHM
3.1 Modeling the Problem
The problem is to find an arrangement R =
{I
i1
, I
i2
, ..., I
ik
} of k items from items set I which can
balance EOP and EOC.
Placement-and-Profit-Aware Association Rules Mining
641
Assumption 1: To calculate EOP and EOC, suppose
any two of recommended items are independent. That
is, the selection of item a is irrelevant to the selection
of item b and vice versa. For a given R we can derive:
EOC(R) =
1
k
k
s=1
[CT R(I
is
, s|A)] (6)
EOP(R) =
1
k
k
s=1
[p(i)CT R(I
is
, s|A)] (7)
where:
CT R(I
is
, s|A) = CT R(I
is
|s, A)CT R(s|A) (8)
CT R(I
is
|s, A) represents the click-through rate of item
I
is
for a specific placement s given set A; CT R(s|A)
represents the click-through rate of s given set A.
Assumption 2: The click-through rate of item i are
equal given any different placement s and the same
set A.
CT R(I
is
|A, s) = CT R(I
is
0
|A, s
0
), s, s
0
[1, k] (9)
Thus:
CT R(I
is
|A, s) =
1
k
CT R(I
is
|A). (10)
Since CT R(I
is
|A) is directly proportional to
con f (A {I
is
}), CT R(I
is
|A, s) is also directly pro-
portional to con f (A {i}):
CT R(I
is
|A, s) con f (A {i}) (11)
Assumption 3: The CTR of placement s given set A
is directly proportional to the CTR of placement s:
CT R(s|A) CT R(s) (12)
Based on aforementioned assumptions, we can
simplify the EOP and EOC:
EOP(R)
k
s=1
con f (A {I
is
})CT R(s)p(I
is
) (13)
EOC(R)
k
s=1
con f (A {I
is
})CT R(s) (14)
3.2 Balancing EOP and EOC
It would be best if we can maximize EOP and EOC
simultaneously. Unfortunately, it is not always fea-
sible. To clarify this problem, we can analyze EOP
maximization problem and EOC maximization prob-
lem separately:
To maximize EOC, simply multiply top k ele-
ments in con f (A {I
is
}) and CT R(s) (both sorted)
correspondingly. Thus, the problem becomes to find
top k items with the largest confidence given set A:
R
0
= arg max
i1,i2,...,ik
k
s=1
con f (A {I
is
})CT R(s) (15)
This is exactly what ARM method does.
To maximize EOP, perform the same method as
above, except confidence is replaced by weighted
confidence, i.e., con f (A {I
is
})p(I
is
):
R
1
= arg max
i1,i2,...,ik
k
s=1
con f (A {I
is
})p(I
is
)CT R(s)
(16)
This is exactly what WARM method does.
However, R
0
is not always equal to R
1
. A common
case is when EOP reaches maximum, EOC is very
low and vice versa.
We introduce the performance score, denoted as
score, described in Equation 5 to evaluate the recom-
mendation result according to both EOP and EOC.
In this paper, we propose a target function to find a
recommendation result R that gets a better score com-
pared with WARM and ARM:
R
γ
= arg max
i
1
,i
2
,...,i
k
k
s=1
[con f (A {I
is
})
CT R(s)p(I
is
)
γ
], γ [0, 1] (17)
By varying γ, we can change the proportion of
how much we prefer the profit over the confidence.
Thus, WARM method becomes a special case of
our new rule where γ = 1. The ARM method becomes
another special case where γ = 0.
Our experiment shows that Equation 17 improves
the EOP significantly while reduces the EOC slightly.
3.3 Overview of Proposed Algorithm
This section explains the proposed Placement-and-
Profit-Aware Association Rules Mining (PPAARM)
algorithm to solve the problem stated in 2.2. A di-
agram of input-and-output flow of the PPAARM is
illustrated in Figure 3.
In Figure 3, Item Database, Transaction History,
Profits of items, γ and the Set A of items in cart are
the Input 1. These parameters can generated candi-
dates by Profit-weighted Association Rules Mining
Algorithm as the Output 1. These candidates are
well balanced between profit and correlation with set
A. Next, these candidates, Placements and CTR of
Placements play a role of Input 2 to generate the fi-
nal results which are a group of arrangement of items
{I
i1
, I
i2
, ..., I
ik
}. Each I
is
indicates item i is recom-
mended to display at the location where s represents.
The notations that/ appear in Figure 3 are introduced
in section 2.1. Algorithm 1 is the pseudo-code for the
algorithm flow.
ICAART 2019 - 11th International Conference on Agents and Artificial Intelligence
642
Figure 3: Input and Output Flow Diagram of PPAARM.
Algorithm 1 : Placement-and-Profit-Aware Association
Rules Mining(PPAARM).
function RECOMMEND(T, I, A, p, k, γ)
Calculate con f [A i] i I A
for all i I A do
w_con f [A i] con f [A i] p[i]
γ
end for
// We can get largest k elements in linear time
complexity using quick-select based algorithm
topk_w_con f largest_k_elements(w_con f )
sort(topk_w_con f )
return The items which each element in
topk_w_con f refers to.
end function
4 EMPIRICAL RESULTS
4.1 Basic Settings
Scenario: At the check-out page, based on the cart
and transaction history, the E-commerce website rec-
ommends 12 items to customers in 3 rows. Each row
displays 4 items.
Input data:
Transaction History Database: The “Re-
tail” dataset in SPMF (Fournier-Viger et al.,
2016) (Brijs et al., 1999). This dataset includes
88162 transactions and 16470 unique items. Each
transaction is a sequence of items, each item is
marked with an Item ID which is an integer from
1 to 16470.
Profit Data: A dataset of profit for each item. The
values of profits are normalized by the maximum
profit.
Items in Cart: This data includes 100 items sets.
Each items set is a set A that is generated from
Transaction History Database. Then mark these
items sets from m = 1 to m = 100.
Click-through Rate Models: Three click-through
rate models are presented in Table 1. Take Fig-
ure 2 as an example, the placements are marked
from s = 1 to s = 12 and customers click place-
ments are shown in CT R(s).
Number of recommended items k: k = 12;
γ = {0, 0.1, 0.2, 0.25, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0}
4.2 Set A Generator
In order to generate a group of Set A, the Set A Gen-
erator scans all items in Transaction History Database
and select unique items with top 100 highest confi-
dence as the Item Pool, then select random amount of
items arbitrarily from the Item Pool as a Set A. Fi-
nally, repeat this process 100 times to get a group of
set A. The same group of set A would be used to cal-
culate all experiment results.
4.3 Evaluation Metrics
In this experiment, the total EOP is the sum of
EOP
m
(R
γ
) among all groups of set A. The total EOC
is the sum of EOP
m
(R
γ
) among all groups of set A. In
order to evaluate the experiment, total EOC and total
EOP should be normalized. Define the N as the num-
ber of A, Normalized EOP(NEOP) and Normalized
EOC(NEOC) are defined respectively as
NEOP(R
γ
) =
N
m=1
EOP
m
(R
γ
)
N
(18)
NEOC(R
γ
) =
N
m=1
EOC
m
(R
γ
)
N
(19)
Placement-and-Profit-Aware Association Rules Mining
643
Table 1: Click-through Rate Matrix.
Click-through Rate
CTR Model 1 CTR Model 2 CTR Model 3
Placement 1 0.1 0.1 0.1
Placement 2 0.1 0.1 0.09
Placement 3 0.1 0.1 0.08
Placement 4 0.1 0.1 0.07
Placement 5 0.05 0.01 0.01
Placement 6 0.05 0.01 0.009
Placement 7 0.05 0.01 0.008
Placement 8 0.05 0.01 0.007
Placement 9 0.01 0.001 0.001
Placement 10 0.01 0.001 0.0009
Placement 11 0.01 0.001 0.0008
Placement 12 0.01 0.001 0.0007
To evaluate the performance of the proposed al-
gorithm 1, this paper utilizes Equation 5, denoted as
score, as a metric of combined performance of EOP
and EOC. In this experiment, the score is normal-
ized. Normalized Score is the linear combination of
NEOC(R
γ
) and NEOP(R
γ
) as Equation 20. Further-
more, modifying α can change the preference to profit
or recommendation accuracy. In this paper, α is equal
to 1, which means the performance score treats the
recommendation accuracy and the profit expectation
as equally important.
NS(γ) = NEOP(R
γ
) + αNEOC(R
γ
) (20)
4.4 Results
4.4.1 NEOP & NEOC
In the experiment, we execute algorithm PPAARM 1
with click-through model 1. According to the re-
sults in Table 3 and Figure 4, the scatter spots of
NEOP(R
γ
) and NEOC(R
γ
) form a upper convex
curve. Thus the optimal point where NEOC(R
γ
) starts
decreasing faster than NEOP(R
γ
) exists on the curve.
To be specific, the recommended items can trade-off
profit and recommendation accuracy best in this chart.
So, the proposed algorithm PPAARM can find a better
trade-off solution between profit and recommendation
accuracy.
4.4.2 Optimal Point Locating and Evaluation
According to Figure 5 and Table 3, NS(R
γ
) achieves
the largest value when γ = 0.25. So, this point where
γ = 0.25 is the optimal point in this chart. We also set
two points where γ = 0 and γ = 1 as reference point.
Based on Equation 5, the PPAARM is equivalent
to ARM method while γ is 0; The PPAARM is equiv-
alent to MARWI method while γ is 1. By compar-
ing the evaluation metrics values of the optimal point
and reference points, we present the performance dif-
ference of PPAARM method, ETARM method and
MARWI method in Table 2.
According to Table 2, PPAARM earns much more
profits than ETARM with little recommendation ac-
curacy loss, meanwhile, PPAARM achieves much
higher recommendation accuracy than MARWI with
insignificant profit loss. Additionally, NS(R
γ
) of
PPAARM is larger than ETARM and MARWI. As
NS(R
γ
) considers both profit and recommendation ac-
curacy, we can conclude that PPAARM achieves a
good balance between EOP and EOC and performs
better than ETARM method and MARWI method.
Figure 4: Trend of NEOP and NEOC when γ varies from 0
to 1 with CTR model 1.
ICAART 2019 - 11th International Conference on Agents and Artificial Intelligence
644
Table 2: Compare PPAARM with ETARM and MARWI. ±x%” indicates the value of PPAARM is x% larger or less than
the value of ETARM or MARWI.
ETARM(γ = 0) MARWI(γ = 1)
PPAARM(γ = 0.25)
NS(R
γ
) NEOP(R
γ
) NEOC(R
γ
) NS(R
γ
) NEOP(R
γ
) NEOC(R
γ
)
+1.5% +7.5% -0.6% +12.6% -13.6% +27.2%
Table 3: Experimental Results.
γ NEOP(R
γ
) NEOC(R
γ
) NS(R
γ
) γ NEOP(R
γ
) NEOC(R
γ
) NS(R
γ
)
0.0 0.0652 0.1876 0.2528 0.5 0.0744 0.1797 0.2541
0.1 0.0677 0.1876 0.2554 0.6 0.0761 0.1732 0.2493
0.2 0.0688 0.1874 0.2562 0.7 0.0784 0.1663 0.2446
0.25 0.0701 0.1865 0.2565 0.8 0.0804 0.1549 0.2345
0.3 0.0702 0.1860 0.2562 0.9 0.0808 0.1502 0.2311
0.4 0.0721 0.1829 0.2550 1.0 0.0811 0.1466 0.2278
Figure 5: The trend of NS when γ varies from 0 to 1 with
CTR model 1.
4.4.3 Robustness
In actual situations, CTR models are uncertain. So,
we choose three different CTR models to verify the
robustness of our proposed method. After executing
PPAARM with three different click-through models
in Table 1, we get a line chart Figure 6. Also, Figure 7
can be obtained according to Equation 20.
According to Figure 6, when γ varies from 0 to 1.
Even though these three lines are relatively far apart
on the coordinate axis, their shapes are alike. Simi-
larly, we can observe the same pattern in Figure 7.
Although Table 1 indicates the CTR models are
totally different, the conclusion in 4.4.1 and 4.4.2
remains the same. In conclusion, PPAARM is robust
wit different CTR models.
Figure 6: The trend of NEOP and NEOC when γ varies from
0 to 1 with three CTR models.
5 DISCUSSION
5.1 Data Set Limitations
In this paper, the proposed method utilizes generated
placement click-through rate and profit on experiment
due to the insufficient of open-source datasets that
contain placement aware data and profit information
is usually very sensitive. As a result, this paper as-
sumes these two factors have little correlation and
proposes Assumption 2 and Assumption 3 in Sec-
tion 3.1. If the actual data of placement click-through
rate and profit has been provided, we can use a better
model such as logistic regression (Cox, 1 01) to model
CT R(I
is
, s|A), thus the estimation of the click-through
rate will be more accurate.
Placement-and-Profit-Aware Association Rules Mining
645
Figure 7: The trend of NS when γ varies from 0 to 1 with
three CTR models.
5.2 Adjusting γ
The parameter γ represents how much the website
prefer EOP rather than EOC. Higher EOP brings the
website more instant income while higher EOC in-
creases the recommendation accuracy, which leads to
better user experience. The larger γ is, the higher EOP
will be and the lower EOC will be.
In practical, NS(R
γ
) is a good way to determine
the specific value of γ, since it takes both EOP and
EOC into consideration. When NS(R
γ
) reaches a
maximum point, further increasing EOP will lead the
EOC decreasing drastically, which results in a worse
overall performance and vice versa. As a result, the
suggested value of γ should be the value that maxi-
mizes NS(R
γ
).
6 CONCLUSIONS
According to the results in section 4, we can conclude
that the novel method PPAARM can find a better so-
lution for placement-and-profit-aware recommenda-
tion problem than traditional methods. This method
gets much higher EOP (Expectation of Profit, a met-
ric of profit) than traditional ARM method with only
little EOC (Expectation of Click Rate, a metric of re-
ommendation accuracy) losses. It can also get much
higher EOC than the traditional WARM method with
only slight decrease in EOP. Further, experiment re-
sults show that PPAARM is robust with different CTR
models.
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