A new constraint for mining sets in sequences1

Discovering interesting episodes is a popular area in temporal or sequential data mining, examples of which are mining text or protein sequences. In such data, the order in which the events appear is being analysed and the user’s goal is to identify the regularities that may appear in the dataset, consisting of one or more sequences. The usual approach to episode discovery is to look for episodes consisting of events that frequently appear close to each other. Most of the current state-of-the-art methods first use a window of fixed length to find sufficiently cohesive episodes and then retrieve those that occur in more windows (or sequences) than a given minimum threshold. The frequency of an itemset X, fr(X), is thus defined as the number of windows X appears in divided by the total number of possible windows. The use of a window of fixed length is a major limitation of such approaches as no episodes longer than this window can ever be discovered. A different method that increases the window length proportionally to the size of the candidate set has been proposed in order to remove this limitation. Still, in this proposal, the window length remains fixed for a particular candidate when counting its frequency in the sequence. Hence, when the episode occurs in the sequence, but in a time frame larger than the window size, then such occurrences will be disregarded. The high frequency of a set of events appearing close together gives no guarantee that a subset of that set will not sometimes appear far away from the rest of the set. Take, for example, the following sequence: