text: In this work, we propose a new approach for discovering various relationships among keywords over the scientific publications based on a Markov Chain model. It is an important problem since keywords are the basic elements for representing abstract objects such as documents, user profiles, topics and many things else. Our model is very effective since it combines four important factors in scientific publications: content, publicity, impact and randomness. Particularly, a recommendation system (called SciRecSys) has been presented to support users to efficiently find out relevant articles.
  @cite_7: The author describes four different methods to rank teams in uneven paired competition and shows how each of these methods depends in some fundamental way on the Perron–Frobenius theorem.
  @cite_8: Ranking has been applied in many domains using recommendation systems such as search engine, e-commerce, and so on. We will introduce and study N-linear mutual ranking, which can rank n classes of objects at once. The ranking scores of these classes are dependent to the others. For instance, PageRank by Google is a 2-linear mutual ranking, which ranks the webpages and links at once. Particularly, we focus to N-star ranking model and demonstrate it in ranking conference and journal problems. We have conducted the experiments for the models in which the citations are not considered. The experimental results are based on the DBLP dataset, which contains more than one million papers, authors and thousands of conferences and journals in computer science. Finally, N-star ranking is a very strong ranking algorithm can be applied in many real-world problems.
  @cite_3: This work presents a new perspective on characterizing the similarity between elements of a database or, more generally, nodes of a weighted and undirected graph. It is based on a Markov-chain model of random walk through the database. More precisely, we compute quantities (the average commute time, the pseudoinverse of the Laplacian matrix of the graph, etc.) that provide similarities between any pair of nodes, having the nice property of increasing when the number of paths connecting those elements increases and when the "length" of paths decreases. It turns out that the square root of the average commute time is a Euclidean distance and that the pseudoinverse of the Laplacian matrix is a kernel matrix (its elements are inner products closely related to commute times). A principal component analysis (PCA) of the graph is introduced for computing the subspace projection of the node vectors in a manner that preserves as much variance as possible in terms of the Euclidean commute-time distance. This graph PCA provides a nice interpretation to the "Fiedler vector," widely used for graph partitioning. The model is evaluated on a collaborative-recommendation task where suggestions are made about which movies people should watch based upon what they watched in the past. Experimental results on the MovieLens database show that the Laplacian-based similarities perform well in comparison with other methods. The model, which nicely fits into the so-called "statistical relational learning" framework, could also be used to compute document or word similarities, and, more generally, it could be applied to machine-learning and pattern-recognition tasks involving a relational database
  @cite_0: Received November 04, 2008Abstract. Problems which have a huge database always issue challenges to scientists.Evaluating importance of Webs is an interesting example. This problem should be verydiﬃcult about not only computation, but also storage since the Web environment con-tains around 10 billions Web pages. Basing on the “random surfer” idea of PageRankalgorithm, MPageRank greatly improves results of Web search by applying a proba-bilistic model on the link structure of Webs to evaluate “authority” of Webs. UnlikePageRank, in MPageRank, a Web now has diﬀerent ranking scores which depend onthe given multi topics. By assigning a value characterizing a relationship between con-tent of pages and a popular topic, we would like to introduce some new notions suchas the inﬂuence of page and the stability of rank score vector to evaluate the stabilityof Web environment. However, the main idea of establishing the MPageRank modelis to partition our Web graph into smaller-size Web subgraphs. As a consequence ofevaluation and rejection about pages inﬂuence weakly to other pages, the rank scoreof pages of the original Web graph can be approximated from the rank score of pagesin the new partition Web graph.2000 Mathematics Subject Classiﬁcation: ————————–.Key words: —————————————-.
  @cite_2: Recommender systems have the effect of guiding users in a personal- ized way to interesting objects in a large space of possible options. Content-based recommendation systems try to recommend items similar to those a given user has liked in the past. Indeed, the basic process performed by a content-based recom- mender consists in matching up the attributes of a user profile in which preferences and interests are stored, with the attributes of a content object (item), in order to recommend to the user new interesting items. This chapter provides an overview of content-based recommender systems, with the aim of imposing a degree of order on the diversity of the different aspects involved in their design and implementation. The first part of the chapter presents the basic concepts and terminology of content- based recommender systems, a high level architecture, and their main advantages and drawbacks. The second part of the chapter provides a review of the state of the art of systems adopted in several application domains, by thoroughly describ- ing both classical and advanced techniques for representing items and user profiles. The most widely adopted techniques for learning user profiles are also presented. The last part of the chapter discusses trends and future research which might lead towards the next generation of systems, by describing the role of User Generated Content as a way for taking into account evolving vocabularies, and the challenge of feeding users with serendipitous recommendations, that is to say surprisingly interesting items that they might not have otherwise discovered.
summary: Markov Chain model which properties are studied in @cite_7 @cite_0 is used for computing the similarity and ranking @cite_3 @cite_8 . @cite_3 use a stochastic random-walk model to compute similarities between nodes of a graph for recommendation. @cite_8 introduce an N-star model, and demonstrate it in ranking conference and journal problems. Finally, @cite_2 do a thorough review on state-of-the-art and trends of content-based recommender systems.