ABSTRACTAmong difficulties encountered by modern shopping recommenders is the long tail shape of sold items also related to cold-start issues. Various approaches including content-based recommendations attempt to overcome this problem that has serious impact on the accuracy of recommendations especially when new products are continuously added to the catalogue. This paper investigates the use of an algorithm to search for highly correlated pairs between abstractions of items. The advantage of this approach is evaluated on the basis of real data showing better results compared to an approach onlybased on the concrete pairs of items. Using rigorous protocols such as Given-n, experimental results show significant improvement in both the recommendation accuracy and the recommendation of products in the long tail.Keywords. Knowledge Discovery, Mining Correlated Pairs, Recommender Systems

Jean, Daniel Zucker

Thu Minh, Tran Nguyen

English

Vietnam Academy of Science and Technology: Journals Online

 133
Journal of Science and Technology Volume 48, Issue 4, 2010 pp. 133-140 
DOMAIN ABSTRACTION OF HIGHLY CORRELATED PAIRS                
TO RECOMMEND IN THE LONG TAIL 
MINH THU TRAN NGUYEN, JEAN DANIEL ZUCKER 
ABSTRACT 
Among difficulties encountered by modern shopping recommenders is the long tail shape 
of sold items also related to cold-start issues. Various  approaches  including  content-based  
recommendations attempt to overcome this problem that has serious impact on the accuracy of 
recommendations especially when new products are continuously added to the catalogue. This 
paper investigates the use of an algorithm to search for highly correlated pairs between 
abstractions of items. The advantage of this approach is evaluated on the basis of real data 
showing better results compared to an approach only based on the concrete pairs of items. Using 
rigorous protocols such as Given-n, experimental results show significant improvement in both 
the recommendation accuracy and the recommendation of products in the long tail.  
Keywords. Knowledge Discovery, Mining Correlated Pairs, Recommender Systems. 
1. INTRODUCTION 
In recent years, recommendation systems have been extensively explored in scientific 
literature, in merchant and community sites [11,13]. On e-commerce sites [12, 11], the problem 
can be reformulated as a problem of predicting the k target items with the greatest chance of 
being selected by the user U based on p items  . . .  already selected by her/him. In practice, 
p is small and k is often three [2]. In other words, for any item we seek the probability 
 [2]. There are many statistical models used to discover this probability from 
historical data:  association rules [5], highly correlated pairs [15,10], collaborative filtering [1], 
etc. One of the simplest models is based on the support of the association → by the formula: 
 .       (1) 
 
 
Figure 1.  Empirical distribution of the popularity of items in shopping carts showing a             
“long tail”  (left) and its characteristic curve in a log-log scale (right). In these curves, the 
ordinate represents the number of transactions (or caddies) containing a given item and the 
abscissa represents the rank of items per decreasing number of transactions 
 134
Although widely used, strong association rules (or correlated pairs) based on these 
measures may prove unsatisfactory in practice because supporting data is often missing and are 
biased (only partially representative of the real distribution).  Indeed, the distributions of items in 
transactions have a “long tail” following a law also known as the Pareto law  [9].  This is true in 
the case of the e-commerce data we have used, shown in figure 1.  Recommender systems often 
recommend products in the head, and on the other hand when products from the tail are selected 
(including never sold or new products) no personalized recommendation can be made. 
In this paper, both the problem of increasing recommendation in the long tail and the 
problem of accuracy are addressed.  The approaches proposed rely on an existing item taxonomy 
[6], which is very detailed or very basic. Frequently, in ecommerce there are categorical 
attributes that segment items into groups of items  [2].  For instance, a merchant site offering 
some  “Clothes”  items, will have categories such as Outwear, Pants, Shirts  (See figure  2).  At 
the level of categories (“abstract items”) the long tail effect is weaker. This article proposes an 
approach based on the research of highly correlated pairs between abstract items and a 
framework to use in estimating the probability . 
 
Figure 2.  An example of a product taxonomy (From[6]) 
2. STATE OF THE ART 
2.1. Item-based Recommendation Systems 
The problem of estimating the co-occurrence of two items is the heart of recommendation 
systems.  Among the choices for calculating the strength of association,  [7] proposes to modify 
the calculation of the formula  1  by another one taking into account the number of items per 
transaction. The conditional probability is the ratio of the number of transactions 
containing the co-occurrences of , |  and the total number of transaction 
containing . This estimate means to increase the strength of associations for items that 
appear in transactions having few items.  The results show that when applying real data, we can 
improve the quality of the estimator. This work highlights the importance of the estimator of the 
co-occurrence without addressing rare items issues. 
2.2. Recommendation system supplying long tail problem 
The long tail problem is related to the “rare item issue”, i.e. the lack of ratings or purchases 
is able to make valuable recommendation. To provide a good method to leverage the long tail, 
Y. Park [9] suggests splitting the whole itemset into two parts: the head and the tail parts. Then 
recommendations are built on each part separately. Another method to address the long tail 
problem is implemented in HyPAM  (Hybrid Poisson Aspect Model)  [4].  This model is able to 
solve the issues of data skew and sparsity. 
2.3. Association rules for recommendation systems 
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In the field of recommendation systems, several approaches have focused on the problems 
of mining rare data [14]. The original approach consists of searching association  rules  without  
using  a  single  minimum  support,  but  rather  using multiple  ones  depending  of  the  data  
considered  [5, 3, 14].   This  approach  has been proved useful for discovering rare associations 
that are not embedded in rules which are more important, but have less support.  The use of 
abstraction items has been already investigated by Han and Fu [3]. They have extended the 
scope of the study of mining association rules from single level to multiple concept levels 
(different granularity) and studied methods for mining multiple-level association rules from 
large transaction databases. However, association rules are inefficient for collaborative  
recommendation when  they mine  many rules that are not relevant to a given user. Rules mined 
for specific target user reduce the time required for the mining process with the minimum 
support for each user corresponding [8]. 
2.4. The Search for Highly Correlated Pairs 
The search for correlated pairs permits the estimation of the probability  based on 
the correlation of  with . The difficulty often comes from the large number of pairs: due to 
the lack of memory space, all of them cannot be stored in memory [16].  It is therefore necessary 
to devise heuristics that both ensure that most correlated pairs are identified, and that a limited 
number of pairs only is tested. Several approaches support the use of an upper bound of Pearson 
correlation to prune the pairs that cannot be highly correlated [16].  In fact in the presented 
AbREC algorithm we rely on another algorithm that “TOP-COP” [15] to search efficiently for 
highly correlated pairs of concrete items. 
3. DEFINITION AND ALGORITHM 
A general view of the proposed approach is shown in Figure 3 below. Based on this 
abstracted transactions, a mining algorithm may be used to find abstract correlated pairs or 
associations rules. These pairs or rules are then in turn transformed in concrete association rules 
or concrete correlated pairs by instantiating the abstract items by one of its elements. 
 
Figure 3.  A general view of the abstraction process used to discover highly correlated 
concrete pairs of items.  The Transactions table is abstracted in an abstract Transaction 
table where each item is replaced by its abstraction.  Transaction T1={a,d,ek} is abstacted 
in {A1,A3} as A1 abstracts a and d,e,k are all abstracted by A3 
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3.1. Highly correlated abstract pairs 
In recommendation systems, items and transactions are represented by:  
1. A set of  items data set  which contains their identifier and characteristics.  
2. A set  of transactions in the form . Each transaction is defined 
as a subset of .   denotes the subset of  of all transactions that contains the item .  
We consider the notion of abstract items to describe particular categories or group of items.  
An “abstract item” is dually represented by its description and its extension . 
This notion of abstract item corresponds to a domain abstraction that is widely used in the field 
of Abstraction [17]. Using this definition, we may define the support of an “abstract item”  as 
the ratio of the number of transactions which contain the abstract item  , and the total 
number of transactions in the database . The value of  is the number of transactions in 
which at least one of the concrete items that belongs to  appears. 
 .     (2) 
3.2. Highly Correlated Abstract Pairs to improve recommendation. 
Finding some highly correlated abstract item pairs is not sufficient (cf.  Figure 3).  So, we 
propose to define an algorithm that lists the TOP-K items (in practice K = 3 [13]) combining the 
information from correlated pairs of concrete items and those correlated pairs of abstract items at 
the same time. The approach we propose is, therefore, to compute a new estimate of the 
confidence of the association rule called Conf  that combines the confidence 
of the concrete confidence Conf  and an abstract confidence of ; which  (resp. 
) is the domain abstraction of  (resp ). It reads: 
       (3) 
      (4) 
for α = 0, we have a system purely concrete that does not use abstraction, and for α = 1, the 
system is purely based on the abstract highly correlated pairs. 
3.3. The AbsTopKα algorithm 
The algorithm AbsTopKα that we propose is a form of discretisation of the heuristics 
presented above. We consider the Top-K(1 − α) items outcome from the recommendation 
concrete (by pairs  ) and the Top-Kα pairs outcome from the abstract pairs of items. In 
practice, K is often chosen to be 3[13]) and for  this amounts to 2 items from the 
concrete pairs et 1 item from the abstract pairs. The principle of the algorithm is as follows: 
Algorithm 1 The AbsTopKα algorithm 
1. Input : a set of transactions on items  
2. Output: the top  items to be recommended. 
 (a) For each  , build its associated abstract item  
 (b) For each , build the list of the top  most correlated abstract 
 137
pairs items 
 
 (c)  For each item  
 i.  Find the top  most correlated concrete pairs of items 
; 
 
 ii.   
 iii. Return the list  of  items associated with  
 
4. RESULTS AND EVALUATION 
4.1. Dataset 
To test the AbsTopKα and AbsExtract algorithms, like most authors, we used a database of 
real world data that cannot be made public for confidentiality reasons. Indeed, unlike the 
artificially generated data, this data corresponds to a volume of transactions that is found only 
very rare in data available in the public domain.  There  are  several  publicly  available  database  
to test recommender systems but most of them correspond to products (such as movies) 
associated to user ratings.   
Algorithm 2 The AbsExtract algorithm 
1. Input :  a concrete item , a set of  abstract items associated to the 
abstract item of ,  
2. Output: the top  items  to recommend based on abstract 
rules. 
3. Algorithm 
 (a)  Find all concrete items  whose abstract items belong to  
 (b)  For each  compute the correlation (resp. support) of pair 
)   
(c)  Return the top  items  such that associated pair ) has      
       maximum correlation (resp. support) 
The data we are interested in are  0-1 Data  (products that have been bought or not by 
users). We used real data from a merchant site that consists of transactions of books, cds, clothes 
and gifts sales.  The dataset includes shopping date, customer id, product id and the number of 
purchase in each shopping record.  And table 1 is the summary of the main characteristics of the 
database we have used. 
 
 
Table  1.  Characteristics  of  the  database   
 138
(training  data  set: 2007;  test  data  set: January and February of 2008) 
Properties 2007 Jan and Feb of 2008 
# of items (concrete) 9332 3943 
# of items Abstracts by expert 451 365 
# of Transactions 30009 5097 
# average of items per transaction 2,53 2,65 
4.2. Experimental analysis 
The issue of evaluating of recommendation systems is one of the most difficult issues.   
However,  some  studies  suggest  several  evaluation  protocols  that  can gauge the performance 
of estimators  [13, 2, 4] and are of the statistic learning cross-validation test type. We use Given-
P method [4] for evaluating the system, the principle of the test method is to consider all of the 
transactions that have at least  items. The first  items of the transaction are used to predict 
the presence of an item  presented or not in the remaining items of the transaction.  
In table 2, we summarize the results of the evaluation of the AbsTopKα algorithm for  
and the value of α is varied from  0  to  1. We have used the data of the year 2007 to find the 
correlated pairs and that of the first two months of 2008 to check their effectiveness. The first 
remark is that the number returned by Given-1 is very small. This is also the case in the results 
of Hsu et al.[4]. This small number does not reflect the quality of recommendations but the 
result obtained by a particular stringent test which is implemented by Given-1. The second 
remark from table 4.2 is that the recommendations derived from the AbsTopK algorithm are 
better for alpha greater than 0 (the pure abstract system or combination between concrete and 
abstract). And the best result is obtained by alpha = 2/3 where we have used two abstracts and 
one concrete. There are 1051 (26,65%) new items in two months and we have about 10% good 
recommendation items for the new by our method. 
Table  2.  With  and differents value alpha.  For , the result of “maximum of 
theory” is 1030 good recommended items (14,56% new items) 
α 
#successful by Given-1 
(Maximum of theory) 
# successful by Given-1 
(AbsExtrait algorithm) 
 All items New items All items New items 
0 541 0 541 0 
1/2 846 10,53% 656 7,62% 
2/3 1030 14,56% 669 11,66% 
1 984 18,19% 477 18,45% 
 139
The third remark will be illustrated in table 3 providing some insight on the type of items 
that are recommended when α is increasing. The number of items recommended from the long 
tail is increasing in total and percentage. 
Table  3.  The accuracy of the algorithm in the Head and Long Tail.  The parameter 
alpha allows to control the proportion of abstract rules that are used.  Using abstract 
pairs does increase the number of good recommendation in the long tail up to 44% 
α 
# items from 
concrete pairs 
# items from 
abstract pairs 
# good reco. in 
the head 
# good reco. 
in the long tail 
Gain in the long tail 
with abstract pairs 
0 3 0 279 262 1 
1/2 2 1 468 378 1.44 
2/3 1 2 715 315 1.20 
1 0 3 657 327 1.25 
5. CONCLUSION 
This paper has attempted to address the issue of improving recommendation in the long tail. 
We have proposed an algorithm that relies on the search of abstract pairs of items. To evaluate 
the interest of our approach we evaluated the gain compared to a direct approach only based on 
the pairs of concrete items. We used a  “Given-N”  methodology to evaluate and quantify the 
gain. This reached  44% in our particular dataset of real transactions. The gain is made by 
recommending products that were in the long tail part, supporting the fact that using abstraction 
improves recommending in the long tail. However, this result also needs to be contrasted with 
studies of other databases, we are currently analysing if this framework could be implemented 
on the Netflix and could be used in the public data provided by Hsu and al. [4].  The present 
approach to search for abstract association rules means to improve the accuracy of 
recommendations on concrete items. However, if the domain abstraction is not relevant, the 
performance can be worse. Our claim is not that combining abstract and concrete pairs will 
always improve the results but rather that based on appropriate product hierarchy, performance 
may be improved significantly. 
Acknowledgments. The authors wish to thank Edith Nuss for her help in collecting the data used 
to test the AbsTopK algorithm. The authors also thank the authors of the TOP-COP algorithm 
[15] (Xiong et al.) who have sent us their code. 
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Address: Received June 16, 2010 
Minh Thu Tran Nguyen1, 2, 4 , Jean Daniel Zucker2, 3, 
1LimBio, University Paris 13, F93017 - Bobingy, France. 
 
2UMI 209 - UMMISCO, Centre IRD France Nord, F93143 - Bondy, France. 
3MI 209 - UPMC University Paris 6, Paris – France. 
4SI, Institut de la Francophonie pour l’Informatique (IFI), Hanoi, Vietnam. 
 


DOMAIN ABSTRACTION OF HIGHLY CORRELATED PAIRS  TO RECOMMEND IN THE LONG TAIL

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