Two-step recommendations: contrast analysis and matrix factorization techniques
In this paper we present a two-step recommendation model based on Contrast Analysis and Matrix Factorization techniques which mutually complement each other. We also provide a brief overview of different Matrix Factorization approaches. У даній статті представлена двокрокова модель рекомендаційної с...
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| Cite this: | Two-step recommendations: contrast analysis and matrix factorization techniques / M. Aleksandrova, A. Brun, A. Boyer, O. Chertov // Математичні машини і системи. — 2014. — № 1. — С. 122-128. — Бібліогр.: 20 назв. — англ. |
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| citation_txt | Two-step recommendations: contrast analysis and matrix factorization techniques / M. Aleksandrova, A. Brun, A. Boyer, O. Chertov // Математичні машини і системи. — 2014. — № 1. — С. 122-128. — Бібліогр.: 20 назв. — англ. |
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| description | In this paper we present a two-step recommendation model based on Contrast Analysis and Matrix Factorization techniques which mutually complement each other. We also provide a brief overview of different Matrix Factorization approaches.
У даній статті представлена двокрокова модель рекомендаційної системи, що використовує взаємодоповнюючим чином техніки контрастного аналізу та матричної факторизації. Також наданий короткий огляд варіацій методу матричної факторизації.
В данной статье представлена двушаговая модель рекомендационной системы, которая использует взаимодополняющим образом техники контрастного анализа и матричной факторизации. Также приведен краткий обзор вариаций метода матричной факторизации.
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122 © Aleksandrova M., Brun A., Boyer A., Chertov O., 2014
ISSN 1028-9763. Математичні машини і системи, 2014, № 1
UDC 004.942
M. ALEKSANDROVA*,**, A. BRUN*, A. BOYER*, O. CHERTOV**
TWO-STEP RECOMMENDATIONS: CONTRAST ANALYSIS AND MATRIX
FACTORIZATION TECHNIQUES
*University of Lorraine, France
**National Technical University of Ukraine “Kyiv Polytechnic Institute”, Kyiv, Ukraine
Анотація. У даній статті представлена двокрокова модель рекомендаційної системи, що викори-
стовує взаємодоповнюючим чином техніки контрастного аналізу та матричної факторизації.
Також наданий короткий огляд варіацій методу матричної факторизації.
Ключові слова: системи рекомендацій, матрична факторизація, контрастний аналіз.
Аннотация. В данной статье представлена двушаговая модель рекомендационной системы, ко-
торая использует взаимодополняющим образом техники контрастного анализа и матричной
факторизации. Также приведен краткий обзор вариаций метода матричной факторизации.
Ключевые слова: системы рекомендаций, матричная факторизация, контрастный анализ.
Abstract. In this paper, we present a two-step recommendation model based on Contrast Analysis and
Matrix Factorization techniques which mutually complement each other. We also provide a brief overview
of different Matrix Factorization approaches.
Keywords: recommender systems, matrix factorization, contrast analysis.
1. Introduction
In modern numerical world, automatic recommendations are used in a wide area of applications
starting from traditional recommendation of movies and music to considering search engines as a
special type of recommender systems. The task of recommender engine is to predict how much a
specific user will like a certain item and recommend the one, which has the highest predicted
rating. It can be viewed as a task of filling in the unknown values of the rating matrix R , the rows
of which usually represent users and columns – items (Fig. 1).As a rule, rating matrix is very
sparse. For example, GroupLens provided three datasets, which are widely used for testing differ-
ent recommendation algorithms and contain 5,9%, 4,2% and 1,4% of known ratings respectively
[1].
There exist many approaches for recommending, but they are usually classified into three
categories [2]:
1. Content-based recommendations.
2. Collaborative recommendations.
3. Hybrid recommendations.
Content-based recommender sys-
tems propose to user items with similar
characteristics as those products, which
were highly rated by a target user pre-
viously. Collaborative filtering approach
will recommend those items, which were
highly appreciated by users with similar
interests. Collaborative filtering is more
dynamic, as its recommendations can fol-
low such events as, for example, fashion
or change of interests in a certain user
group. It also allows recommending items
…
4 ? … 4 ?
? ? … ? 3
… … … … … …
? ? … ? 2
? 5 … ? ?
Fig. 1. Rating matrix
Items
U
se
rs
ISSN 1028-9763. Математичні машини і системи, 2014, № 1 123
with new characteristics. Still this group of methods can’t propose anything, if there are not
enough ratings in the system. Hybrid recommender systems use both collaborative and content-
based methods. Relatively new and very promising approach in the field of recommender systems
is Matrix Factorization, which belongs to the category of collaborative filtering [3].
In [4, 5] a novel Influence search algorithm, which is based on contrast analysis, was pro-
posed for solving the task of searching levers of influence on the human decision-making process
concerning such social problems as whether to bear a baby, whether to start studying etc. In [6]
authors provided a general scheme of this algorithm and described its adoption to the recom-
mender systems domain. Influence search algorithm essentially differs from traditional recom-
mending approaches as in stead of solving the task of matrix filling it searches for the patterns of
satisfied and dissatisfied users and provide recommendations how to improve their satisfaction.
2. Problem Formulation
In general, use of different nature methods can give essentially new and useful results. The pur-
pose of this paper is to investigate possibility of joint usage of traditional recommendation ap-
proaches with a new Influence search algorithm.
3. Contrast Analysis for Recommender Systems
General scheme of the Influence search algorithm was provided in [6]. In this paper, we will con-
sider its association rules based variant, which is presented in Fig. 2. Input of the proposed algo-
rithm is presented by a set of records revealing information about user’s interaction with the sys-
tem. These records can also contain additional data, such as information about content of the
items, user preferences, and demographic data.
Fig. 2. Influence search algorithm
Divide original dataset on
contrast subgroups
Define attributes, which can potentially
influence the value of contrast parameter
Define invariant attributes Define attributes the values of
which can be influenced exter-
nally
Perform association rules search
Define pairs of contrast rules
Compare contrast rules, make
conclusions
124 ISSN 1028-9763. Математичні машини і системи, 2014, № 1
On the first step of the proposed algorithm, original data set is divided into two contrast
groups basing on the value of contrast parameter. In the framework of recommender systems it is
natural to use user satisfaction rate for contrasting, which can be estimated basing on the previous
ratings.
The second step of the proposed approach is definition of attributes, which can potentially
influence value of contrast parameter that is the level of satisfaction (influencing attributes). Sa-
tisfaction level of the user depends on the recommended items and user preferences; also, it can
depend on the sequence of recommendations. So information about items (content) and users
(demographic information, preferences) and sequence of recommended items must to be consi-
dered as influencing attributes.
Next, the set of chosen attributes is divided on two subsets: invariant or independent
attributes and attributes the values of which can be influenced externally (that is by means of re-
commender system) or dependent attributes. It is obvious that among considered above attributes
only proposed items and sequence of recommendations can be influenced by the system. That
means that all other attributes (content, demographic information, preferences) belong to the in-
variant subset.
After that the search of contrast pairs of association rules is performed. A pair of associa-
tion rules is considered to be contrast if two rules have different values of contrast parameter as
conclusion of the rule and the bodies of the rules are constructed of premises with the same val-
ues of invariant attributes and different values of at least one influencing attribute. Contrast rules
must have high confidence and not necessarily large support.
Let’s examine the following example of contrast rules pair:
Rule 1. <sex=male>&<age=group1>&<preferences=actor1&actor2>&<recommended1 =
comedy&actor1>&<recommended2=adventure&actor2>�<satisfied=YES>(positive rule)
support = 2%, confidence = 78%
Rule 2. <sex=male>&<age=group1>&<preferences=actor1&actor2>&<recommended1 =
comedy&actor1>&<recommended2=comedy&actor2>�<satisfied=NO>(negative rule)
support=1,5%, confidence = 80%
Here sex, age, and preferences are invariant attributes and sequence of recommendations
(recommended1 and recommended2) belongs to the group of depended attributes. Analyzing
these 2 rules we can say that if we have a male user of age=group1, who likes actor1&actor2 and
we have previously recommended him a comedy with actor1 now we need to recommend him an
adventure with actor2 (but not a comedy with actor2), and with the probability of 78% (confi-
dence of positive rule) user will like it. Obtained recommendations remain general and don’t an-
swer the question which film exactly we should recommend.
4. Matrix Factorization for Recommender Systems
Matrix Factorization (MF) gained its wide popularity after 2009 when a team BellKor’s Pragmat-
ic Chaos used it to win Netflix Prize competition [7]. The objective of this approach is to present
rating matrix R (where ijr is a rating given by user i to the recommended item j ) as a product
of two matrices of a small rank (1).
{ }dim
dim & & min , ,
dim
T
T m k
m n k m n
k n
≈
= ×= ×
= ×
R U V
U
R
V
≪
(1)
where m is total number of users, n – total number of items, k – number of features.
ISSN 1028-9763. Математичні машини і системи, 2014, № 1 125
Values of the matrices U and V are usually calculated by a Gradient descend based or Al-
ternating least squares [8, 9] methods using only known values of matrix R . They minimize ob-
jective function (2)
2
min T −
R U V , (2)
Where i is usually a Frobenius norm.
MF approach belongs to the class of latent factor models and aims to represent interaction
between users and items with a small number of latent factors (features). It is obvious that if
{ }min ,k m n≪ the complexity of the model is reduced significantly. In addition, it is easy to
calculate unknown rating îjr using formulae (3).
ˆ T
ij i jr = u v , (3)
where iu and jv are column-vectors of matrices U and V respectively.
There exist a number of variations of MF techniques, which can be classified on 3 groups
(Fig. 3).The first group of methods builds model of the system using only one rating matrix. Such
techniques as Regularized MF (RMF), Non-Negative MF (NNMF) and Matrix Tri-Factorization
belong to this group. Second group analyses simultaneously two or more matrices (Collective MF
or CMF) and the third one provides different generalizations of the basic MF approach (Kernel
MF and Tensor Factorization).
Fig. 3. Classification of Matrix Factorization Techniques
While using Regularized Matrix Factorization [10] an additional constant λ is added in
order to avoid over fitting of the model, thus objective function is represented by equation (4).
Generalization
Matrix Factorization Techniques
Regularized MF
Non-Negative MF
1 matrix
Collective MF
Kernel MF
Tensor Factorization
2 or more matrices
Matrix Tri-Factorization
126 ISSN 1028-9763. Математичні машини і системи, 2014, № 1
2 22
min T
i j
i j
− + λ +
∑ ∑R U V u v . (4)
This approach is one of basic ones and it is widely used apart or in combination with other
MF techniques [11–13].
In Non-Negative Matrix Factorization values of both U and V must satisfy the condition
of positivity , 0li lju v ≥ . This approach decomposes an object into a sum of its parts (allowing
interpretation of the results). For example, for the task of image analysis it is possible to present a
face as a sum of eyes, nose, lips and so on [14]. In the frame of recommender systems, basic parts
can be considered as behavioral patterns [15] or groups of users [16].
Matrix Tri-Factorization [17] presents original rating matrix as a product of three matrices
(5). In this model matrix U represents interaction of m users and mk user-related features, ma-
trix V – interaction of n items and nk item-related features, and new matrix
S ( )( )dim m nk k= ×S reveals interdependence between user-related and item-related features.
Thus using Matrix Tri-Factorization it is possible to define different feature spaces for users and
items. If holds { }, min ,m nk k m n≤
complexity of the system is also reduced, as well as in the ba-
sic MF approach.
.T≈R U SV (5)
Collective Matrix Factorization was proposed by Singh and Gordon in 2008 [18]. It per-
forms simultaneous factorization of two or more matrices with condition of interdependence of
feature spaces (6).
( )
( )
( ) ( )
1 1 1
2 2 2
2 1 1 2 1 1, / , .
T
T
u vf and or f
≈
≈
= =
X U V
X U V
U U V V U V
(6)
CMF approaches are of particular interest, because depending on the nature of matrices
1X and 2X and dependences uf and vf it is possible to use additional information while building
the model of the system. For example, in [19] authors took two rating matrices from different
domains 1 src=X R (source domain) and 2 tgt=X R (target domain), thus using ratings from the
source domain in order to build the model in the target one. In [18] matrix 1X was represented by
a rating matrix and matrix 2X revealed information about item’s content (characteristics). Per-
forming collective factorization of these two matrices authors incorporated content information
into collaborative-based recommendation method, hereby implementing a hybrid technique.
Equation (3) can be written in a form of inner product (7) that means that interaction be-
tween users, features and items can be considered as a linear kernel.
ˆ ,ij i jr = u v . (7)
If dependence is more complex (not linear) it is possible to use other types of kernels, for
example polynomial or Gauss (8), and perform Kernel Matrix Factorization [11].
ISSN 1028-9763. Математичні машини і системи, 2014, № 1 127
( )
( ) ( )
( ) ( ) 2
2
, ,
, 1 ,
, exp .
2
g
l
d
p polynomial
K Ga
K lin
us
ear
K
s
=
= +
−
= −
σ
u v u v
u v u v
u v
u v
(8)
Provided each rating depends not only on user and item but also on other variables, MF
turns into tensor factorization, which was proposed in [20]. In this article, authors analyzed rat-
ings depending on context that is different conditions on which a certain item was proposed to a
specific user. For example, whether food was recommended when a person was hungry or not, or
in what season the system recommended a user to watch a comedy.
Additional conditions imposed by each discussed above method are not always mutually
exclusive. So it is possible to use different approaches simultaneously depending on the solved
task and nature of the data. For example, authors of [17] used non-negative matrix tri-
factorization and in [13] collective regularized MF was performed.
5. Joint Use of Matrix Factorization and Contrast Analysis
Because usually rating matrices are very sparse over fitting remains a problem for MF approach-
es. In addition, if available information is not fully representative (doesn’t correctly represent all
interaction between users and items), built model will lack for accuracy. That is why it seems
promising to divide original rating matrix on sub-matrices depending on the nature of the data
and perform sub-matrix factorization. It is also possible to use different MF approaches for dif-
ferent sub-matrices according to their properties.
We can use Influence search algorithm for the task of identification of essentially different
sub-matrices because it extracts groups of related users. So these two methods can be used as
complements to each other. For example, considering pair of contrast rules discussed above, we
can identify what film exactly we should recommend with the help of MF approach used for sub-
matrix consisting of users <sex=male>&<age=group1>&<preferences=actor1&actor2> and items
with <content=adventure&actor2>.Thus we can consider a two-step recommender system, where
first more general recommendation is generated by means of contrast analysis and after that,
whenever possible, recommendation is personalized by means of Matrix Factorization.
6. Conclusion
In this paper, we discussed peculiarities of Influence search algorithm usage in the frame of re-
commender systems. We also presented a brief overview of Matrix Factorization approaches and
outlined advantages of each of them. In the end we proposed a two-step recommender system
model, which incorporates Contrast Analysis and Matrix Factorization and allows generate more
general recommendation with possibility of their further personalization.
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Стаття надійшла до редакції 20.01.2014
|
| id | nasplib_isofts_kiev_ua-123456789-84339 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1028-9763 |
| language | English |
| last_indexed | 2025-12-01T16:16:18Z |
| publishDate | 2014 |
| publisher | Інститут проблем математичних машин і систем НАН України |
| record_format | dspace |
| spelling | Aleksandrova, M. Brun, A. Boyer, A. Chertov, O. 2015-07-06T16:18:00Z 2015-07-06T16:18:00Z 2014 Two-step recommendations: contrast analysis and matrix factorization techniques / M. Aleksandrova, A. Brun, A. Boyer, O. Chertov // Математичні машини і системи. — 2014. — № 1. — С. 122-128. — Бібліогр.: 20 назв. — англ. 1028-9763 https://nasplib.isofts.kiev.ua/handle/123456789/84339 004.942 In this paper we present a two-step recommendation model based on Contrast Analysis and Matrix Factorization techniques which mutually complement each other. We also provide a brief overview of different Matrix Factorization approaches. У даній статті представлена двокрокова модель рекомендаційної системи, що використовує взаємодоповнюючим чином техніки контрастного аналізу та матричної факторизації. Також наданий короткий огляд варіацій методу матричної факторизації. В данной статье представлена двушаговая модель рекомендационной системы, которая использует взаимодополняющим образом техники контрастного анализа и матричной факторизации. Также приведен краткий обзор вариаций метода матричной факторизации. en Інститут проблем математичних машин і систем НАН України Математичні машини і системи Моделювання і управління Two-step recommendations: contrast analysis and matrix factorization techniques Двокрокові рекомендації: контрастний аналіз і методи матричної факторизації Двушаговые рекомендации: контрастный анализ и методы матричной факторизации Article published earlier |
| spellingShingle | Two-step recommendations: contrast analysis and matrix factorization techniques Aleksandrova, M. Brun, A. Boyer, A. Chertov, O. Моделювання і управління |
| title | Two-step recommendations: contrast analysis and matrix factorization techniques |
| title_alt | Двокрокові рекомендації: контрастний аналіз і методи матричної факторизації Двушаговые рекомендации: контрастный анализ и методы матричной факторизации |
| title_full | Two-step recommendations: contrast analysis and matrix factorization techniques |
| title_fullStr | Two-step recommendations: contrast analysis and matrix factorization techniques |
| title_full_unstemmed | Two-step recommendations: contrast analysis and matrix factorization techniques |
| title_short | Two-step recommendations: contrast analysis and matrix factorization techniques |
| title_sort | two-step recommendations: contrast analysis and matrix factorization techniques |
| topic | Моделювання і управління |
| topic_facet | Моделювання і управління |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/84339 |
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