Extensive work has been done in the field of recommender systems to make use of the enormous online information of user activities for inferring user preference re- lationships about various products, books, web pages, or other information, which we generically refer to as objects. In the recommendation task, we are interested in predicting how likely a user is interested in a particular object, given informa- tion about this user, the other users’ historical behavior, and information about the objects.
The majority of recommender systems particularly exploit preferences of users for objects, which are usually expressed in the form of ratings. However, in the greater part of recommender systems, especially those positioned in an open Web setting, users provide only limited preference feedback. This leads to a very sparse rating matrix.
One mechanism that is recently studied in order to deal with such bottlenecks is to borrow useful knowledge from another domain. The category of techniques applying such an approach falls under the adaptive-based group of cross-domain recommender systems. By applying Transfer Learning - a subfield of Machine Learning - the research community has been able to extend collaborative filtering to cross-domain settings where there is sparseness of explicit user-object overlap between domains. Transfer learning aims at improving the learning and prediction task in one domain by exploiting knowledge transferred from other domains. This is also the theoretical foundation that we investigate in this work. We propose an approach for learning useful knowledge of user-object preferences in a source domain, then transfer this knowledge in a sparse, target domain in order to enable there accurate user recommendations. There is one particular deficiency of the related cross-domain recommenders that apply an adaptive learning approach: they boil down to analyzing the user-object rating matrix solely as tabular data.
Traditional approaches to the problem derive from classical algorithms in statistical pattern recognition and machine learning. The majority of the approaches assume a flat data representation for each object, and focus on a single dyadic relationship between the objects. In web usage analysis, for example, the information sources might include user access logs, the relationships between the web pages visited,
6.1. INTRODUCTION
reviews written by the user, meta-data on the site and additional information about the user. This information can be aggregated in an e-commerce setting, where we include customers’ buying patterns to make predictions about future purchases. In the Web context, where there is often much more relational information available than a single user-item relationship, we need added modeling power to capture richer relational information.
Therefore, our goal in this work is to formalize user preferential behavior with a richer model, which allows us to reason about many different relations at the same time. It takes advantage of the recent progress in statistical relational learn- ing (a.k.a. multi-relational data mining), which provides rich representations and efficient learning algorithms for non-i.i.d. data. We propose a first-order proba- bilistic model, which is based on a powerful formalism that combines logical and probabilistic reasoning. It makes possible to combine many different objects and relations into a comprehensive solution to the recommendation task.
(II) Adaptive Cross-domain Collaborative Filtering DomB 5 Book1 U1 4 Book2 U2 ? Movie1 Ui
Acquisition Formalization Semantic Enrichment Prediction &
Recommendation
Explicit Preference Feedback Knowledge Base
DomA
Semantically-enriched user behavior models
Probabilistic first-order logic model of user preference behavior Ratings Reviews e-Purchases Web Resources DomB DomA RQ3 RQ4
Figure 6.1: Framework overview: adaptive cross-domain collaborative filtering In Figure6.1, we graphically illustrate how the work presented in this chapter is positioned with respect to the overall thesis framework. The proposed approach captures the process starting with the acquisition of user preferential behavior in the form of explicit ratings, following with the probabilistic relational modeling of user behavior in each domain. In this stage, the meta-data harvested through the
semantic enrichment strategies described in Chapter4can be used to leverage the description of objects. The formal model we provide perfectly accomodates the representation of such knowledge, since it is based on an expressive logic formal- ism. In the next step, the modeled preferential behavior is used as basis for the transfer approach, which selects knowledge from the source domain and applies it for preference predictions in the target domain.
6.1.1 Research Questions and Contributions
There are two main research questions that we address in this chapter, each of them also marking the contributions of our work:
Research Question 3. Can we build a rich relational model of user behavior that can be used to accurately infer explicit user preferences to make recommendations? This research question addresses the challenge of finding an appropriate way of formalizing domain knowledge (or domain theory), so that we are able to capture multiple relations between objects and user preferences. The challenge here is to formalize the domain theory in a way that it provides user preferences representa- tion, collaborative filtering features, multiple relations and attributes of users and objects/items, and rigorous formulation of uncertainty.
Research Question 4. When user preference data for resources is very sparse, especially in an open Web setting, how can we transfer user behavior knowledge from one domain to better predict user preferences at a sparse target domain? This question addresses the data sparseness challenge. Our goal is to transfer knowledge from an auxiliary domain rich in training examples to a target domain which is highly sparse in user preferential feedback. At the same time, we need to provide a scalable learning and effective prediction approach.
The investigation of these research questions led to the following contributions: Contribution III. Probabilistic first-order model for hybrid recommendations. We present an expressive multi-relational model that makes it possible to combine many different objects and relations into a comprehensive solution to the recom-
6.2. RELATED WORK
mendation task. We deploy a hybrid approach for generating recommendations, based on a content/collaborative merging scheme through feature combination. Contribution IV. Adaptive cross-domain collaborative filtering with probabilistic first-order knowledge transfer.
We extend the expressive relational model of user-object preferences, provided in Contribution III, to build a new technique for knowledge transfer from one source domain to another sparse target domain. We contribute with a mechanism for gen- erating accurate recommendations to users in a target domain that is unknown to them.
6.1.2 Outline
We refer in Section6.2 to a set of works related to ours. We then proceed with our problem statement in Section6.3. In Section6.4, we introduce the first-order probabilistic model for formalizing domain knowledge and capturing user prefer- ential behavior. In Section6.5, we introduce the overall framework to learn useful knowledge in a source domain and transfer it to a sparse, target domain to en- able accurate user preference predictions. Details on the inference mechanism and transfer process are given in Section6.6and Section6.7, accordingly.
We have performed various experiments to evaluate the formalization and recom- mendation approach both in single domain and cross-domain setting. The experi- mental setup and evaluation results are shown in Section6.8. We draw conclusions in Section6.9.
6.2
Related Work
The general recommendation problem is built on the user-item matrix R of U users and I items, where the element rij is the rating given by user u to item
i. In the matrix, a large scale of ratings are typically missing. Thus the recom-
mendation task is formalized to predict the missing values in the matrix. The techniques are divided into content-based methods [MOONEYand ROY2000] and collaborating filtering (CF) methods [MAet al. 2007,ZHANGand KOREN2007].
There has been a plethora of collaborative filtering approaches introduced in the recommender systems field, but the factorization-based method has been demon- strated as most successful in performing the recommendation task with large-scale datasets [AGARWALand CHEN2009, KORENet al. 2009]. Matrix factorization (MF) techniques learn hidden features from the observed ratings in a user-item matrix, also referred to as latent features of users and items. These latent features are used as basis for predicting the unobserved ratings in the matrix. A compet- itive representative of one of the state-of-the-art works is the probabilistic matrix factorization (PMF) model [SALAKHUTDINOVand MNIH2007]. PMF follows a
probabilistic approach for factorization in a single domain.
There is another line of works based on relational learning to analyze the prob- abilistic constraints between the attributes of entities and relationships. Xu et al. [XUet al. 2010] extend the expressiveness of relational models by in- troducing for each entity (or object) an infinite dimensional latent variable as part of a Dirichlet process mixture model. In an earlier work, Getoor et al.[GETOORand SAHAMI1999] present a conceptual model that allows one to reason about many different relations in a domain based on probabilistic relational models (PRMs). Yet, this work remains conceptual in describing how PRMs can be applied to CF and its efficacy is not experimentally verified.
Recently, there have been several cross-domain CF approaches proposed for deal- ing with recommendation across domains. Probabilistic matrix factorization is ex- tended from single domain to multiple domains, such as in the work of Zhang et al.[ZHANGet al. 2010]. The authors propose a CF learning model that identifies correlations of ratings in a latent factor space. Thereby, rating matrices from dif- ferent domains are transformed into user and item latent factors, which are then used for recommendations across domains. However, the approach requires that the sets of users in the different domains are the same. Shi et al. [SHIet al. 2011b]
propose another interesting approach based on a graphical model for improving cross-domain CF by connecting multiple domains via user-assigned tags. They extend a matrix factorization approach to collaborative filtering by exploiting the tags given by users as source of valuable information that links users and items across various domains. In both these cases, it is assumed that there is information
6.3. PROBLEM STATEMENT
shared in both domains, such as in the form of tags, or more explicitly the sets of users/items.
However, our focus is particularly set on related works that apply an adaptive approach without requiring domain bridges. Like ours, these approaches aim to learn useful knowledge in an auxiliary domain, transfer it to another sparse do- main in order to make better predictions there. Transfer Learning is an active research field in Machine Learning, which aims to improve a particular learn- ing task in a specific domain by exploiting knowledge transferred from other do- mains [PANand YANG2010]. Transfer learning methods have been applied in the
field of recommender systems to improve collaborative filtering.
Li et al. [LIet al. 2009b] propose a method referred to as codebook transfer (CBT), which consists of first compressing the ratings in the user-item matrix of an auxil- iary domain into a compact cluster-level rating pattern. This structure is the code- book, which is then expanded in another sparse, target domain leading to the re- construction of the respective rating matrix. The authors extend the approach by means of a probabilistic model, presenting in Li et al. [LIet al. 2009d] a common model built from the ratings of all the domains that does not need a dense source matrix to learn the implicit cluster-level pattern.
6.3
Problem Statement
The research problem we study in this paper is the effective generation of rec- ommendations in a domain that is highly sparse in user preferential feedback by applying knowledge learned and transferred from an auxiliary domain. We adhere to again the definition [WINOTOand TANG2008] of a domain as the set of similar items with the same characteristics that can be easily differentiated, e.g. movies, concerts, songs, news, books, etc.1
In the following, we give the definition of our cross-domain recommendation task. Without loss of generality, we define the task when two domains are involved. We use the notation introduced in [CREMONESIet al. 2011].
1
Definition 13. (Adaptive Cross-domain Recommendation Task) Let UA be the
set of users andIAthe set of items in domainA, as well as UBthe set of users and
IB the sets of items in a domainB that is very sparse on user-item ratings. Our
task is to makeseparate recommendations of items in RB to users inUB, given
information on users inUA, itemsRA, and the respective ratings. We assume that
UA∩ UB = ∅ and IA∩ IB = ∅.
Our approach tackles the most challenging case when there is no user overlap and no resource overlap among domains (i.e. each domain has its own separate users and items). The task consists in transferring rules that capture user preference patterns data from a dense auxiliary rating domain (e.g. a popular book rating website) to a sparse rating domain (e.g. a new movie rating website). The goal is to improve recommendations of one domain from knowledge learned in other domains and alleviate the sparsity problem.
We illustrate our reseach problem with an example in Figure6.2. Suppose we are given information on users, objects, and their explicit ratings in a source domain
DS, which is rather dense in terms of the ratings that users have expressed. At the
same time, we also deal with another separate domain DT, referred to as the target
domain, which is highly sparse in user ratings.
In each domain, each user has attributes, such as address and age, and expresses own preferential feedback on objects (in this case books) via ratings. For example, user U1S in the source domain has rated Book1 with a score of 5. The book has
as author another object, which is from the country U S. Similar relations are also occuring for user U2T, who rates Book1 with score 5. We could potentially
learn a pattern in this domain, such as intuitively this would be similar to “users of the same age like the same books” or “users from the same country like the same books”. More importantly, we could learn in this domain how strong is this pattern, i.e. learn a weight.
In the target domain, we also have information on users and items, but in this setting the ratings are very sparse. The task is now to predict which score user U2T would give for M ovie2. We want to consider the rating similarities of this user to the other
users (i.e. collaborative-filtering features), as well as the attributes of the book and the attributes of the user (i.e. content-based features). We are also interested to
6.3. PROBLEM STATEMENT
consider relations of this user to other objects, e.g. the tags assigned and how they are similar to those of other users. Since we have very few ratings available here to learn meaningful patterns between users and objects, we rely on potentially useful knowledge that can be transferred from the source domain S. Precisely, the recommendation task consists in predicting the probability of the existence of a relation rij between user uTi and object oTj (e.g. rates(uT2, movie2), and then
choosing as recommendations the set of objects with the highest probability value.
El Palacio de La Luna title 1999 date Paul Auster author 155 id Rumors title 1992 date Kate William author 843 id Book1 5 1 Book2 El Palacio de La Luna title 1999 date Paul Auster author 155 id 5 Book1 27 age
barcelona, granollers, spain
address
27 age
premià de dalt, barcelona, spain
address Book2 ? U1S U2S Link Prediction U1T Kafka title 1991 date Drama genre Sci-fi genre 7001 id Hudson Hawk title 1991 date Adventure genre Comedy genre 7000 id Movie1 1 ? Movie2 U2T Kafka title 1991 date Drama genre Sci-fi genre 7001 id 1 Movie1 Movie2
Source Domain DS Target Domain D
T ? 1 transfer from US
Figure 6.2: Example of cross-domain recommendation task in two domains In our first step, we aim to expressively model the domain knowledge and respec- tive relationships. This would allow us to consider more information and yield correct prediction values of the missing relations (in this case rating of user U2T for
M ovie2). Therefore, we start by introducing a model for formalizing the theory
i.e. objects, users, and relations in one domain. This is model is referred to as hMLN and is presented next in Section6.4.
Since user and item profiles are distributed and do not overlap in these two do- mains, we have to establish a mechanism to learn meaningful knowledge about user preference ratings in one domain, and then transfer it to the other domain in a way that it enables us to make there accurate rating predictions. Section6.5 presents the transfer approach that we propose for tackling this problem.