A Survey on Session-based Recommender Systems <s> Factorization Machine-based Approaches <s> Abstract We consider specific additive decompositions d = d 1 + … + d n of metrics, defined on a finite set X (where a metric may give distance zero to pairs of distinct points). The simplest building stones are the slit metrics , associated to splits (i.e., bipartitions) of the given set X . While an additive decomposition of a Hamming metric into split metrics is in no way unique, we achieve uniqueness by restricting ourselves to coherent decompositions, that is, decompositions d = d 1 + … + d n such that for every map f : X → R with f ( x ) + f ( y ) ⩾ d ( x , y ) for all x , y ϵ X there exist maps f 1 , …, f n : X → R with f = f 1 + … + f n and f i ( x ) + f i ( y ) ⩾ d i ( x , y ) for all i = 1,…, n and all x , y ϵ X . These coherent decompositions are closely related to a geometric decomposition of the injective hull of the given metric. A metric with a coherent decomposition into a (weighted) sum of split metrics will be called totally split-decomposable . Tree metrics (and more generally, the sum of two tree metrics) are particular instances of totally split-decomposable metrics. Our main result confirms that every metric admits a coherent decomposition into a totally split-decomposable metric and a split-prime residue, where all the split summands and hence the decomposition can be determined in polynomial time, and that a family of splits can occur this way if and only if it does not induce on any four-point subset all three splits with block size two. <s> BIB001 </s> A Survey on Session-based Recommender Systems <s> Factorization Machine-based Approaches <s> 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. <s> BIB002 </s> A Survey on Session-based Recommender Systems <s> Factorization Machine-based Approaches <s> Typical recommender systems adopt a static view of the recommendation process and treat it as a prediction problem. We argue that it is more appropriate to view the problem of generating recommendations as a sequential optimization problem and, consequently, that Markov decision processes (MDPs) provide a more appropriate model for recommender systems. MDPs introduce two benefits: they take into account the long-term effects of each recommendation and the expected value of each recommendation. To succeed in practice, an MDP-based recommender system must employ a strong initial model, must be solvable quickly, and should not consume too much memory. In this paper, we describe our particular MDP model, its initialization using a predictive model, the solution and update algorithm, and its actual performance on a commercial site. We also describe the particular predictive model we used which outperforms previous models. Our system is one of a small number of commercially deployed recommender systems. As far as we know, it is the first to report experimental analysis conducted on a real commercial site. These results validate the commercial value of recommender systems, and in particular, of our MDP-based approach. <s> BIB003 </s> A Survey on Session-based Recommender Systems <s> Factorization Machine-based Approaches <s> With the increasing popularity of Location-based Social Networks, a vast amount of location check-ins have been accumulated. Though location prediction in terms of check-ins has been recently studied, the phenomena that users often check in novel locations has not been addressed. To this end, in this paper, we leveraged collaborative filtering techniques for check-in location prediction and proposed a short- and long-term preference model. We extensively evaluated it on two large-scale check-in datasets from Gowalla and Dianping with 6M and 1M check-ins, respectively, and showed that the proposed model can outperform the competing baselines. <s> BIB004 </s> A Survey on Session-based Recommender Systems <s> Factorization Machine-based Approaches <s> Personalized point-of-interest (POI) recommendation is a significant task in location-based social networks (LBSNs) as it can help provide better user experience as well as enable third-party services, e.g., launching advertisements. To provide a good recommendation, various research has been conducted in the literature. However, pervious efforts mainly consider the "check-ins" in a whole and omit their temporal relation. They can only recommend POI globally and cannot know where a user would like to go tomorrow or in the next few days. In this paper, we consider the task of successive personalized POI recommendation in LBSNs, which is a much harder task than standard personalized POI recommendation or prediction. To solve this task, we observe two prominent properties in the check-in sequence: personalized Markov chain and region localization. Hence, we propose a novel matrix factorization method, namely FPMC-LR, to embed the personalized Markov chains and the localized regions. Our proposed FPMC-LR not only exploits the personalized Markov chain in the check-in sequence, but also takes into account users' movement constraint, i.e., moving around a localized region. More importantly, utilizing the information of localized regions, we not only reduce the computation cost largely, but also discard the noisy information to boost recommendation. Results on two real-world LBSNs datasets demonstrate the merits of our proposed FPMC-LR. <s> BIB005 </s> A Survey on Session-based Recommender Systems <s> Factorization Machine-based Approaches <s> Location-based social networks (LBSNs) offer researchers rich data to study people's online activities and mobility patterns. One important application of such studies is to provide personalized point-of-interest (POI) recommendations to enhance user experience in LBSNs. Previous solutions directly predict users' preference on locations but fail to provide insights about users' preference transitions among locations. In this work, we propose a novel category-aware POI recommendation model, which exploits the transition patterns of users' preference over location categories to improve location recommendation accuracy. Our approach consists of two stages: (1) preference transition (over location categories) prediction, and (2) category-aware POI recommendation. Matrix factorization is employed to predict a user's preference transitions over categories and then her preference on locations in the corresponding categories. Real data based experiments demonstrate that our approach outperforms the state-of-the-art POI recommendation models by at least 39.75% in terms of recall. <s> BIB006 </s> A Survey on Session-based Recommender Systems <s> Factorization Machine-based Approaches <s> Context-aware recommendation algorithms focus on refining recommendations by considering additional information, available to the system. This topic has gained a lot of attention recently. Among others, several factorization methods were proposed to solve the problem, although most of them assume explicit feedback which strongly limits their real-world applicability. While these algorithms apply various loss functions and optimization strategies, the preference modeling under context is less explored due to the lack of tools allowing for easy experimentation with various models. As context dimensions are introduced beyond users and items, the space of possible preference models and the importance of proper modeling largely increases. In this paper we propose a general factorization framework (GFF), a single flexible algorithm that takes the preference model as an input and computes latent feature matrices for the input dimensions. GFF allows us to easily experiment with various linear models on any context-aware recommendation task, be it explicit or implicit feedback based. The scaling properties makes it usable under real life circumstances as well. We demonstrate the framework's potential by exploring various preference models on a 4-dimensional context-aware problem with contexts that are available for almost any real life datasets. We show in our experiments--performed on five real life, implicit feedback datasets--that proper preference modelling significantly increases recommendation accuracy, and previously unused models outperform the traditional ones. Novel models in GFF also outperform state-of-the-art factorization algorithms. We also extend the method to be fully compliant to the Multidimensional Dataspace Model, one of the most extensive data models of context-enriched data. Extended GFF allows the seamless incorporation of information into the factorization framework beyond context, like item metadata, social networks, session information, etc. Preliminary experiments show great potential of this capability. <s> BIB007 </s> A Survey on Session-based Recommender Systems <s> Factorization Machine-based Approaches <s> Matrix factorization (MF) models and their extensions are standard in modern recommender systems. MF models decompose the observed user-item interaction matrix into user and item latent factors. In this paper, we propose a co-factorization model, CoFactor, which jointly decomposes the user-item interaction matrix and the item-item co-occurrence matrix with shared item latent factors. For each pair of items, the co-occurrence matrix encodes the number of users that have consumed both items. CoFactor is inspired by the recent success of word embedding models (e.g., word2vec) which can be interpreted as factorizing the word co-occurrence matrix. We show that this model significantly improves the performance over MF models on several datasets with little additional computational overhead. We provide qualitative results that explain how CoFactor improves the quality of the inferred factors and characterize the circumstances where it provides the most significant improvements. <s> BIB008
Recently, factorization machines are adopted to factorize the observed transitions from the current item to the next one into latent representations of items or users. The resultant latent representations are used to estimate the unobserved transitions for recommendations BIB007 BIB004 BIB003 . Next, we first formalize the basic factorization machine-based SBRS and then review some variants. Once the personalized transition probability is achieved from the observed data, a transition matrix A u is built for each user u. Therefore, for all users a transition tensor A is built like A |U |×|I |×|I | , where each entry a u,i j ,i k indicates the transition probability from item i j to i k under user u. A general linear factorization model, the Tucker Decomposition, is used to factorize the transition cube and estimate the unobserved transitions. where C is a core tensor, V U is the feature matrix for users while V I j and V I k are the feature matrix for last items and the following items respectively. The Tucker Decomposition subsumes factorization models like the Canonical Decomposition BIB001 aka parallel factor analysis (PARAFAC). A special case of Canonical Decomposition is used to model the pairwise interactions because of the very spares transitions observed for A: where v u , v i j and v i k is the latent factor of user u, the current item i j and the next item i k respectively. Subsequently, a factorized personalized Markov chain (FPMC) model BIB002 is built for SBRS. Cheng etc. BIB005 extended FPMC into FPMC-LR model by adding a constraint to limit user movements into a localized region to be more consistent with the real-world tourism cases for next POI recommendations. The factorization models only built on item co-occurrence transition matrix actually only captures the sequential patterns over items while ignoring the user's individual preference which is captured by other RS like collaborative filtering. In BIB008 , the authors combines the matrix factorization used in collaborative filtering and the matrix factorization used in SBRS together to capture both the individual preference and the item transition patterns. Specifically, the authors proposed a co-factorization model, CoFactor, which jointly decomposes the user-item interaction matrix and the item-item co-occurrence matrix with shared latent factors for items. Other similar works include BIB006 which utilizes the matrix factorization model to learn the preference transitions from one location category to another and thus provides location recommendations.