Summary
In recent years, many techniques have been proposed to discover sequential patterns with temporal constraints from long sequences of categorical events. Central to these techniques is the concept of pattern occurrence. A rich set of measures based on pattern occurrence has been developed for sequential pattern discovery, filtering and ranking. Often, recurrences of patterns within the same sequence are ignored. However, the total number of pattern occurrences in each individual sequence can provide valuable insights, especially for applications with long sequences each containing many events.
In this chapter, we propose to use the maximum cardinality of all disjoint occurrence sets as the number of pattern occurrences in an individual sequence. In contrast to previous proposals, our de.nition (1) depends only on the sequence and the pattern, without requiring additional parameters such as a sliding window size; (2) ensures that patterns occur more often if their temporal constraints are relaxed; and (3) enables us to easily estimate the expected number of pattern occurrences, so that patterns whose counted occurrences deviate signi.cantly from their expectations can be regarded as surprising ones.
In addition, we (1) describe a greedy algorithm which e.ciently identi.es a single disjoint occurrence set that has the maximum cardinality; (2) develop a formula to calculate the expected value under a uniform distribution assumption; and (3) design an approximation process to e.ciently estimate the expected value. Our experiments show that the greedy algorithm is e.cient and the approximation is accurate.
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Wang, C., Kao, A., Choi, J., Tjoelker, R. (2008). Discovering Time-Constrained Patterns from Long Sequences. In: Liu, Y., Sun, A., Loh, H.T., Lu, W.F., Lim, EP. (eds) Advances of Computational Intelligence in Industrial Systems. Studies in Computational Intelligence, vol 116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78297-1_5
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DOI: https://doi.org/10.1007/978-3-540-78297-1_5
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