Context Prediction by Alignment Methods

Context prediction is the approach to provide applications with information about future contexts. Some work has already been done on predicting future contexts based on the observed context history. The observed context timeline is analysed for typical patterns in the context history. Based on this knowledge the most probable future contexts are forecast. The authors of [1] and [2] study prediction based on GSM cell location histories. To describe the transition probabilities from one location to the other they use a Markov predictor and a weighted graph respectively. In [3] Unix shell commands are predicted by a simple pattern matching method. The authors in [4] propose a state predictor method which is a variation of a Markov predictor. A decent overview of context prediction is given by Mayrhofer in [5]. Mayrhofer proposes an architecture for context prediction and indicates some of its benefits and challenges. He chooses an approach called growing neural gas to predict arbitrary future contexts. In [4] various context prediction methods that have been mentioned above are compared. Only minor variations in the prediction accuracy have been discovered. This is not surprising since all these methods suffer from general properties in ubiquitous computing environments. The observed context patterns are highly fluctuating since a user typically not conserves the exact behaviour pattern for several executions of the pattern. A typical behaviour pattern is at most similar to all other repetitions of this pattern. The methods mentioned above are not able to abstract from slight fluctuations in typical behaviour patterns. We propose a context prediction scheme that ignores changes in the user behaviour to some extent. Another characteristic in ubiquitous computing environments is the weak computational power available. Considering for example a Markov predictor the running time may be estimated as follows. Let k be the number of different context elements known to the algorithm. Each of these is considered a state in the Markov chain. The arcs between the states describe the probability to traverse from one state to another. The future states with highest probability are desired. The time to find the most probable next element is O(k) in the worst case. To find the most probable m/c elements for any constant c the computation time is O(m). We propose a time series based local alignment search method that has a worst case running time of O(m|S|) to predict context time series of maximum length m, where |S| denotes the number of typical time series known to the prediction method.