A Survey on Session-based Recommender Systems <s> Basic Markov <s> Markov models have been widely used for modelling users' navigational behaviour in the Web graph, using the transitional probabilities between web pages, as recorded in the web logs. The recorded users' navigation is used to extract popular web paths and predict current users' next steps. Such purely usage-based probabilistic models, however, present certain shortcomings. Since the prediction of users' navigational behaviour is based solely on the usage data, structural properties of the Web graph are ignored. Thus important - in terms of pagerank authority score - paths may be underrated. In this paper we present a hybrid probabilistic predictive model extending the properties of Markov models by incorporating link analysis methods. More specifically, we propose the use of a PageRank-style algorithm for assigning prior probabilities to the web pages based on their importance in the web site's graph. We prove, through experimentation, that this approach results in more objective and representative predictions than the ones produced from the pure usage-based approaches. <s> BIB001 </s> A Survey on Session-based Recommender Systems <s> Basic Markov <s> In this paper, we present novel methods that combine (1) Markov models and (2) Web page content search techniques to generate Web navigation recommendations. For click-stream modeling, both first-order and second-order Markov models were studied and a compact storage format for Markov transition matrices was used. For content-based search, a search engine was used to obtain similar-content pages for recommendation to compensate for the sparsity of the Markov model and thus improve coverage. Experiments were conducted on real Web clickstream logs, and confirmed the efficiency of the proposed methods. <s> BIB002 </s> A Survey on Session-based Recommender Systems <s> Basic Markov <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> BIB003 </s> A Survey on Session-based Recommender Systems <s> Basic Markov <s> Predicting personalized sequential behavior is a key task for recommender systems. In order to predict user actions such as the next product to purchase, movie to watch, or place to visit, it is essential to take into account both long-term user preferences and sequential patterns (i.e., short-term dynamics). Matrix Factorization and Markov Chain methods have emerged as two separate but powerful paradigms for modeling the two respectively. Combining these ideas has led to unified methods that accommodate long- and short-term dynamics simultaneously by modeling pairwise user-item and item-item interactions. ::: In spite of the success of such methods for tackling dense data, they are challenged by sparsity issues, which are prevalent in real-world datasets. In recent years, similarity-based methods have been proposed for (sequentially-unaware) item recommendation with promising results on sparse datasets. In this paper, we propose to fuse such methods with Markov Chains to make personalized sequential recommendations. We evaluate our method, Fossil, on a variety of large, real-world datasets. We show quantitatively that Fossil outperforms alternative algorithms, especially on sparse datasets, and qualitatively that it captures personalized dynamics and is able to make meaningful recommendations. <s> BIB004 </s> A Survey on Session-based Recommender Systems <s> Basic Markov <s> Users express their preferences for items in diverse forms, through their liking for items, as well as through the sequence in which they consume items. The latter, referred to as “sequential preference”, manifests itself in scenarios such as song or video playlists, topics one reads or writes about in social media, etc. The current approach to modeling sequential preferences relies primarily on the sequence information, i.e., which item follows another item. However, there are other important factors, due to either the user or the context, which may dynamically affect the way a sequence unfolds. In this work, we develop generative modeling of sequences, incorporating dynamic user-biased emission and context-biased transition for sequential preference. Experiments on publicly-available real-life datasets as well as synthetic data show significant improvements in accuracy at predicting the next item in a sequence. <s> BIB005
Chain-based Approaches. Generally speaking, the process of a basic Markov chain-based RS is simple: first calculating the transition probability over a sequence of items from the training data, and then matching a user's shopping sequence to the sequence with calculated transition probability for prediction and recommendations. Those candidate items with high probability are put into the recommendation list BIB001 . Given a session set S as defined in Definition 2.2, each session s ∈ S is a sequence of items with strict order. A Markov chain synopsis is built to encode all sessions into a directed graph G by taking each item as a node and the co-occurrence between each pair of items as an edge. The frequency of each item and the co-occurrence times of each item pair correspond to the node weight and edge weight respectively. Therefore, each session is described by a path in G. The Markov chain model is defined as a set of tuples {ST , P t , P 0 }, where ST is the state space including all distinct nodes in G, P t is the m * m one-step transition probability matrix between m distinct items, and P 0 is the initial probability of each state in ST . The first-order transitional probability from item i j to i k is defined as: Then we can estimate the probability of a shopping path {i 1 → i 2 → i 3 } by using the aforementioned first-order Markov chain model: Given a sequence of chosen items, we chose the shopping paths with high probabilities and take the given sequence as the prefix. Those items occurred in these paths and after the given sequence are put into the recommendation list. Except for the basic Markov chain-based RS defined above, there are many variants like BIB004 . For example, Zhang etc. combined first-and second-order Markov model together to make more accurate web recommendations BIB002 , while Le etc. developed a hidden Markov model-based probabilistic model for next item recommendations by incorporating additional factors like context features to leverage the recommendation accuracy BIB005 . Another important variant is to adopt a factorization method on the transition probability to estimate those unobserved transitions BIB003 , which will be introduced in Section 7.2.