Abstract
We propose a data mining model that captures the user navigation behaviour patterns. The user navigation sessions are modelled as a hypertext probabilistic grammar whose higher probability strings correspond to the user's preferred trails. An algorithm to efficiently mine such trails is given. We make use of the N gram model which assumes that the last N pages browsed affect the probability of the next page to be visited. The model is based on the theory of probabilistic grammars providing it with a sound theoretical foundation for future enhancements. Moreover, we propose the use of entropy as an estimator of the grammar's statistical properties. Extensive experiments were conducted and the results show that the algorithm runs in linear time, the grammar's entropy is a good estimator of the number of mined trails and the real data rules confirm the effectiveness of the model. © Springer-Verlag Berlin Heidelberg 2000.

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Abstract
In this paper, we study the complexity of a data mining algorithm for extracting patterns from user web navigation data that was proposed in previous work.(3) The user web navigation sessions are inferred from log data and modeled as a Markov chain. The chain's higher probability trails correspond to the preferred trails on the web site. The algorithm implements a depth-first search that scans the Markov chain for the high probability trails. We show that the average behaviour of the algorithm is linear time in the number of web pages accessed.

Abstract
The problem of predicting the next request during a user's navigation session has been extensively studied. In this context, higher-order Markov models have been widely used to model navigation sessions and to predict the next navigation step, while prediction accuracy has been mainly evaluated with the hit and miss score. We claim that this score, although useful, is not sufficient for evaluating next link prediction models with the aim of finding a sufficient order of the model, the size of a recommendation set, and assessing the impact of unexpected events on the prediction accuracy. Herein, we make use of a variable length Markov model to compare the usefulness of three alternatives to the hit and miss score: the Mean Absolute Error, the Ignorance Score, and the Brier score. We present an extensive evaluation of the methods on real data sets and a comprehensive comparison of the scoring methods.

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