Multivariate time series are common in many application domains, particularly in industrial processes with a large number of sensors installed for process monitoring and control. Often, such data encapsulate complex relations among individual series. This paper presents a new type of patterns in multivariate time series, referred to as temporal associations, to capture a wide range of local relations along and across individual series. A scalable algorithm is developed to discover frequent associations by incorporating (1) redundancy pruning of patterns in single time series and (2) two conditions to avoid over-counting the occurrences of associations, thus greatly reducing the space and runtime complexity of the discovery process. A statistical significance measure is also introduced for ranking and post-pruning discovered associations. To evaluate the proposed method, synthetic data sets and a real world data set taken from the time series mining repository as well as a large data set obtained from a delayed coking plant are used. The experiments demonstrated that the discovered associations capture the local relations in multiple time series and that the proposed method is scalable to large data sets.

Discovering patterns from sequence data has significant impact in many aspects of science and society, especially in genomics and proteomics. Here we consider multiple strings as input sequence data and substrings as patterns. In the real world, usually a large set of patterns could be discovered yet many of them are redundant, thus degrading the output quality. This paper improves the output quality by removing two types of redundant patterns. First, the notion of delta tolerance closed itemset is employed to remove redundant patterns that are not delta closed. Second, the concept of statistically induced patterns is proposed to capture redundant patterns which seem to be statistically significant yet their significance is induced by their strong significant subpatterns. It is computationally intense to mine these nonredundant patterns (delta closed patterns and noninduced patterns). To efficiently discover these patterns in very large sequence data, two efficient algorithms have been developed through innovative use of suffix tree. Three sets of experiments were conducted to evaluate their performance. They render excellent results when applying to genomics. The experiments confirm that the proposed algorithms are efficient and that they produce a relatively small set of patterns which reveal interesting information in the sequences.