Recommender systems are an important component of many websites. Two of the most popular approaches are based on matrix factorization (MF) and Markov chains (MC). MF methods learn the general taste of a user by factorizing the matrix over observed user-item preferences. On the other hand, MC methods model sequential behavior by learning a transition graph over items that is used to predict the next action based on the recent actions of a user. In this paper, we present a method bringing both approaches together. Our method is based on personalized transition graphs over underlying Markov chains. That means for each user an own transition matrix is learned -thus in total the method uses a transition cube. As the observations for estimating the transitions are usually very limited, our method factorizes the transition cube with a pairwise interaction model which is a special case of the Tucker Decomposition. We show that our factorized personalized MC (FPMC) model subsumes both a common Markov chain and the normal matrix factorization model. For learning the model parameters, we introduce an adaption of the Bayesian Personalized Ranking (BPR) framework for sequential basket data. Empirically, we show that our FPMC model outperforms both the common matrix factorization and the unpersonalized MC model both learned with and without factorization.

Tagging plays an important role in many recent websites. Recommender systems can help to suggest a user the tags he might want to use for tagging a specific item. Factorization models based on the Tucker Decomposition (TD) model have been shown to provide high quality tag recommendations outperforming other approaches like PageRank, FolkRank, collaborative filtering, etc. The problem with TD models is the cubic core tensor resulting in a cubic runtime in the factorization dimension for prediction and learning.In this paper, we present the factorization model PITF (Pairwise Interaction Tensor Factorization) which is a special case of the TD model with linear runtime both for learning and prediction. PITF explicitly models the pairwise interactions between users, items and tags. The model is learned with an adaption of the Bayesian personalized ranking (BPR) criterion which originally has been introduced for item recommendation. Empirically, we show on real world datasets that this model outperforms TD largely in runtime and even can achieve better prediction quality. Besides our lab experiments, PITF has also won the ECML/PKDD Discovery Challenge 2009 for graph-based tag recommendation.

Shapelets are discriminative sub-sequences of time series that best predict the target variable. For this reason, shapelet discovery has recently attracted considerable interest within the time-series research community. Currently shapelets are found by evaluating the prediction qualities of numerous candidates extracted from the series segments. In contrast to the state-of-the-art, this paper proposes a novel perspective in terms of learning shapelets. A new mathematical formalization of the task via a classification objective function is proposed and a tailored stochastic gradient learning algorithm is applied. The proposed method enables learning nearto-optimal shapelets directly without the need to try out lots of candidates. Furthermore, our method can learn true top-K shapelets by capturing their interaction. Extensive experimentation demonstrates statistically significant improvement in terms of wins and ranks against 13 baselines over 28 time-series datasets.

Abstract. Collaborative tagging systems allow users to assign keywords-so called "tags"-to resources. Tags are used for navigation, finding resources and serendipitous browsing and thus provide an immediate benefit for users. These systems usually include tag recommendation mechanisms easing the process of finding good tags for a resource, but also consolidating the tag vocabulary across users. In practice, however, only very basic recommendation strategies are applied.In this paper we evaluate and compare two recommendation algorithms on large-scale real life datasets: an adaptation of user-based collaborative filtering and a graph-based recommender built on top of FolkRank. We show that both provide better results than non-personalized baseline methods. Especially the graphbased recommender outperforms existing methods considerably.

The situation in which a choice is made is an important information for recommender systems. Context-aware recommenders take this information into account to make predictions. So far, the best performing method for contextaware rating prediction in terms of predictive accuracy is Multiverse Recommendation based on the Tucker tensor factorization model. However this method has two drawbacks:(1) its model complexity is exponential in the number of context variables and polynomial in the size of the factorization and (2) it only works for categorical context variables. On the other hand there is a large variety of fast but specialized recommender methods which lack the generality of contextaware methods.We propose to apply Factorization Machines (FMs) to model contextual information and to provide context-aware rating predictions. This approach results in fast contextaware recommendations because the model equation of FMs can be computed in linear time both in the number of context variables and the factorization size. For learning FMs, we develop an iterative optimization method that analytically finds the least-square solution for one parameter given the other ones. Finally, we show empirically that our approach outperforms Multiverse Recommendation in prediction quality and runtime.