Generating Dynamic Higher-Order Markov Models in Web Usage Mining

Abstract

Abstract. Markov models have been widely used for modelling users' web navigation behaviour. In previous work we have presented a dynamic clustering-based Markov model that accurately represents secondorder transition probabilities given by a collection of navigation sessions. Herein, we propose a generalisation of the method that takes into account higher-order conditional probabilities. The method makes use of the state cloning concept together with a clustering technique to separate the navigation paths that reveal differences in the conditional probabilities. We report on experiments conducted with three real world data sets. The results show that some pages require a long history to understand the users choice of link, while others require only a short history. We also show that the number of additional states induced by the method can be controlled through a probability threshold parameter.

Analysis of Users’ Web Navigation Behavior using GRPA with Variable Length Markov Chains

“…Higher-order Markov models have been widely used for modeling user records. For the task, we have proposed a Variable Length Markov Chain (VLMC) method [12] [1], which is an extension of a Markov chain that allows variable length history to be captured [13]. We note that, we have previously proposed (i) a novel approach to analyze the navigation behavior of Users' using GRPA [2] associated with Markov Chains (ii) a method to find the accuracy with which the model represents a collection of sessions.…”

“…A VLMC is a model extension that allows variable length history to be captured G. Bejerano [13]. J.Borges and Levene, [12] proposed a method that transforms a first-order model into a VLMC so that each transition probability between two states takes into account the path a user followed to reach the first state prior to choosing the out link corresponding to the transition to the second state. The method makes use of state cloning (where states are duplicated to distinguish between different paths leading to the same state) together with the K-Means clustering technique that separates paths revealing differences in their conditional probabilities.…”

Skipping-Based Collaborative Recommendations inspired from Statistical Language Modeling

“…In (Deshpande & Karypis, 2004), three pruning schemes are used to alleviate the state complexity: a support pruning scheme in which the same threshold is used for all of the Markov models, a confidence pruning scheme in which states are discarded if the difference of probability between the two most prominent resources is not statistically significant and an error pruning scheme using a validation dataset. (Borges & Levene, 2005) propose to transform first-order Markov models into a single model representing Markov models of variable orders by using cloning operations. This lowers time and space complexity while providing a full coverage and a good accuracy.…”

“…That is why it has been widely studied. Such studies do not necessarily include ratings, for instance sequential patterns (Nakagawa & Mobasher, 2003) or Markov models (Borges & Levene, 2005;Deshpande & Karypis, 2004;Eirinaki & Vazirgiannis, 2007;Pitkow & Pirolli, 1999), although some other do (Trousse, 2000). Web predictive modeling usually attempts to provide a tradeoff between accuracy, space and time complexity, and coverage (Deshpande & Karypis, 2004;Pitkow & Pirolli, 1999).…”

Sequence Mining Without Sequences: A New Way for Privacy Preserving

“…[5] exploited this idea defining the concept of composite association rule processed from a structured directed graph built from the log files of the Web site. More recently, [6] show how to use higher-level Markov models in order to process a weighted automaton to discover frequent paths of Web site users from log files. Nevertheless, these works are more restricted than our approach in the sense that first, they need the Web log files and second, they aim at discovering sequential patterns made up of consecutive Web pages while we are able to discover non consecutive ones.…”