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## Über dieses Buch

Context-aware ranking is an important task with many applications. E.g. in recommender systems items (products, movies, ...) and for search engines webpages should be ranked. In all these applications, the ranking is not global (i.e. always the same) but depends on the context. Simple examples for context are the user for recommender systems and the query for search engines. More complicated context includes time, last actions, etc. The major problem is that typically the variable domains (e.g. customers, products) are categorical and huge, the observations are very sparse and only positive events are observed. In this book, a generic method for context-aware ranking as well as its application are presented. For modelling a new factorization based on pairwise interactions is proposed and compared to other tensor factorization approaches. For learning, the Bayesian Context-aware Ranking' framework consisting of an optimization criterion and algorithm is developed. The second main part of the book applies this general theory to the three scenarios of item, tag and sequential-set recommendation. Furthermore extensions of time-variant factors and one-class problems are studied. This book generalizes and builds on work that has received the WWW 2010 Best Paper Award', the WSDM 2010 Best Student Paper Award' and the ECML/PKDD 2009 Best Discovery Challenge Award'.

## Inhaltsverzeichnis

### Introduction

Abstract
With the emerging growth of the Internet, a huge amount of information is available to anyone. Even though everything could be accessed, the problem is to find relevant information.
Steffen Rendle

### Related Work

Related Work
In this chapter, we introduce the general related work for context-aware ranking with factorization models. Related work on specific issues like tag recommenders, Markov chains, etc. is discussed in detail in the corresponding chapters. Here, we discuss three general topics. The first one is recommender systems because the standard task of personalized item recommendation (a two mode problem) can be seen as context-aware ranking where the context is the user. Nevertheless in recommender systems, the term ‘context’ is usually used only for cases with at least three modes and furthermore the first mode is typically assumed to be the user. Thus, in the discussion about recommender systems we stick to the definition within the recommender community and use the term context − aware recommender system only for ranking problems with at least three modes. In contrast to this, in this book we use the term context − aware ranking for any number of modes. Secondly, we investigate factorization models on which our proposed approach is based. Finally, we discuss the literature about ranking in general and context-aware ranking in particular.
Steffen Rendle

### Ranking from Incomplete Data

Abstract
The most common classification setting is to predict labels from real-valued vectors, e.g. logistic regression or SupportVector Machines (SVM) are designed for this purpose. Our task differs from this: (1) The variables in our settings are defined over categorical domains with very many levels and there is no a priori knowledge about the space the variable instances lie in. (2) The observed data is highly sparse, nontrivial to interpret and it makes statements rather about pairs of instances than about a single instance. (3) The prediction problem is to rank the instances of one variable given an instance vector (the ‘context’) of the other variables. As the ranking should depend on the given instance vector, it is not a global ranking but a context dependent one. In this chapter, we discuss these three issues and develop a theory for context-aware ranking.
Steffen Rendle

### Learning Context-Aware Ranking

Learning Context-Aware Ranking
In this chapter, we propose a learning method for the problem setting of contextaware ranking. This problem setting has been investigated in detail in the last chapter. We have seen, that a context-aware ranking can be modelled by a real-valued function . Now, we will show how this function can be optimized. The optimization will be done with respect to the pairwise training data d s , that is inferred from the sparse and incomplete observations s. The whole chapter assumes, that y can be expressed as a differentiable, non-recursive function with a finite set of parameters Θ. This assumption holds for many models, including the factorization models that we will introduce in the next chapter.
Steffen Rendle

### Factorization Models

Abstract
In the last chapters, it was shown that a context-aware ranking $${\succ}\phantom{}$$ can be expressed by a function or equivalently by a tensor in case of finite categorical domains X i . Estimating the full parametrized tensor Y is infeasible because (1) for real-world problems, the number of parameters (i.e. ) would be too large – e.g. for the Netflix problem we would need billions of parameters – and (2) even more important, that the observations are typically very sparse which results in poor estimates without any generalization capabilities.
Steffen Rendle

### Item Recommendation

Abstract
Recommending content is an important task in many information systems. For example online shopping websites like Amazon give each customer personalized recommendations of products that the user might be interested in. Other examples are video portals like YouTube that recommend videos to visitors. Personalization is attractive both for content providers, who can increase sales or views, and for customers, who can find interesting content more easily. In this chapter, we focus on item recommendation where the task is to create a user-specific ranking for a set of items. Preferences of users about items are learned from the user’s past interaction with the system – e.g. his buying history, viewing history, etc. Thus, the context in item recommenders is the user and user-aware rankings should be generated.
Steffen Rendle

### Tag Recommendation

Abstract
Tagging is an important feature of the Web 2.0. It allows the user to annotate items/resources like songs, pictures, bookmarks, etc. with keywords. Tagging helps the user to organize his items and facilitate e.g. browsing and searching. Tag recommenders assist the tagging process of a user by suggesting him a set of tags that he is likely to use for an item. Personalized tag recommenders take the user’s tagging behaviour in the past into account when they recommend tags. That means each user is recommended a personalized list of tags – i.e. the suggested list of tags depends both on the user and the item. Personalization makes sense as people tend to use different tags for tagging the same item. This can be seen in systems like Last.fm that have a non-personalized tag recommender but still the people use different tags. For this, we will provide an empirical evaluation on a subset of Last.fm that shows, that our proposed personalized tag recommender outperform even the theoretical upper-bound for any non-personalized tag recommender.
Steffen Rendle

### Sequential-Set Recommendation

Abstract
Our methods so far ignore time which is an important variable that can be monitored in almost any application. In this chapter, we extend item recommendation (see chapter 6) with time information. In general, time is a continuous variable with infinite support. Thus, our factorization models in chapter 5 cannot be applied directly as they assume a categorical domain. Also simple discretization of the domain would not work because (1) factorization models assume no a priori relationship between two variable instances (e.g. two close points in time) and (2) the model could not predict in the future as no observations for these variables are present. Thus, our approach is different: we reformulate the problem with sequences and use the independence assumptions of Markov chains within our model. That means for each user, we see his action of the past as a sequence – e.g. what products he has bought. Typically, several products are bought at the same day and thus, we have per user a sequences of sets (=baskets/ shopping carts). The Markov chain assumption is now that the next action (=shopping cart) of the user depends only on a few of his previous ones.
Steffen Rendle

### Time-Variant Factorization Models

Abstract
All of our proposed factorization models so far do not model any time-variance within factors. In this chapter, we develop a non-parametric approach that allows to model changes in time for each factor. We will focus on the model itself which is generic and not limited to any optimization task like ranking, classification or regression. Even though, factor models for context-aware ranking can benefit from these extensions, this work is not limited to the ranking task, but is more general. That is why we describe the time-aware factorization models for typical problems instead of limiting the discussion to context-aware ranking.
Steffen Rendle

### One-Class Matrix Factorization

Abstract
The second topic, we are investigating is binary classification with matrix factorization models where only observations of one class are available. But in contrast to the problem settings we have discussed so far (see chapter 3), we now deal with a binary classification problem where the classes are more or less balanced. Context-aware ranking like item recommendation (see chapter 6) differs from this because it is a ranking task. Even when seeing it as a binary classification task, the problem differs substantially because the classes are typically hugely imbalanced: e.g. a customer buys much less books than he does not buy, a user listens to much less songs than he never listens to, etc.
Steffen Rendle

### Conclusion

Abstract
In this book, we have studied multi-mode prediction problems. The focus was on problem settings with large categorical domains and high sparsity. Due to the sparsity and usually high imbalance, we are not interested in classification but in ranking the entities of one of the modes. Instead of creating one global ranking, the rankings should be context-aware – i.e. we create many rankings that depend on a given context. Important applications for this setting are recommender systems. There exist several recommender tasks, two of the most well studied ones are personalization and tag recommendation. Our developed method of context-aware ranking subsumes both of them and includes also other settings like time-awareness. Moreover other well-known applications like web search or multi-label classification (e.g. annotation, wikipedia categorization) can be seen as an instance of context-aware ranking.
Steffen Rendle

### Backmatter

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