Markov models have been widely used to represent and analyse user web navigation data. In previous work we have proposed a method to dynamically extend the order of a Markov chain model and a complimentary method for assessing the predictive power of such a variable length Markov chain. Herein, we review these two methods and propose a novel method for measuring the ability of a variable length Markov model to summarise user web navigation sessions up to a given length. While the summarisation ability of a model is important to enable the identification of user navigation patterns, the ability to make predictions is important in order to foresee the next link choice of a user after following a given trail so as, for example, to personalise a web site. We present an extensive experimental evaluation providing strong evidence that prediction accuracy increases linearly with summarisation ability.
In Portugal the distribution of physicians is considered an appropriate proxy for the distribution of the actual hospital resources and additional information on hospital supply is mostly unavailable, while health care utilization data are also usually absent. A suitable method that can be used to analyze patients' access to hospital health care in countries with such characteristics is the two-step floating catchment area (2SFCA) method, since it requires only the number of physicians to represent supply and the population size to estimate demand. An improved version of the 2SFCA method is the kernel density 2SFCA (KD2SFCA) method. However, this method was not developed to analyze access to health care and it computes scores that express only the spatial access dimensions of proximity and availability. In this paper we present a new method, based on the KD2SFCA method, which improves health care access analysis and better identifies populations that are less empowered to use health care. We adapt the KD2SFCA method for the context of health care access analysis and extend it to capture additional access dimensions. We applied the extended method to the Portuguese hospital health care sector in a case study, and compared its results with those obtained with the KD2SFCA method. Our method was able to improve the identification of the less empowered populations and discovered that they represent 8.1% of the total population, instead of 4.6%, and reside in sixteen of the eighteen Portuguese districts, instead of in thirteen, as identified by the original KD2SFCA method. By improving the KD2SFCA method for the identification of the less empowered populations, our method can be a first step in an endeavor to identify opportunities to increase the health care supply or to redistribute supply resources, with the objective of increasing the access of those deprived populations.
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.
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