Time series prediction is of great significance in many applications and has attracted extensive attention from the data mining community. Existing work suggests that for many problems, the shape in the current time series may correlate an upcoming shape in the same or another series. Therefore, it is a promising strategy to associate two recurring patterns as a rule's antecedent and consequent: the occurrence of the antecedent can foretell the occurrence of the consequent, and the learned shape of consequent will give accurate predictions. Earlier work employs symbolization methods, but the symbolized representation maintains too little information of the original series to mine valid rules. The state-of-the-art work, though directly manipulating the series, fails to segment the series precisely for seeking antecedents consequents, resulting in inaccurate rules in common scenarios. In this paper, we propose a novel motif-based rule discovery method, which utilizes motif discovery to accurately extract frequently occurring consecutive subsequences, i.e. motifs, as antecedents consequents. It then investigates the underlying relationships between motifs by matching motifs as rule candidates and ranking them based on the similarities. Experimental results on real open datasets show that the proposed approach outperforms the baseline method by 23.9 . Furthermore, it extends the applicability from single time series to multiple ones.
Early work extracts association rules from frequent patterns in the transactional database @cite_16 . are the first to study the problem of finding rules from real-valued time series in a symbolization-based perspective @cite_0 , followed by a series of work @cite_3 @cite_14 .
@cite_0 @cite_14 @cite_16 @cite_3
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We consider the problem of finding rules relating patterns in a time series to other patterns in that series, or patterns in one series to patterns in another series. A simple example is a rule such as "a period of low telephone call activity is usually followed by a sharp rise in call volume". Examples of rules relating two or more time series are "if the Microsoft stock price goes up and Intel falls, then IBM goes up the next day," and "if Microsoft goes up strongly for one day, then declines strongly on the next day, and on the same days Intel stays about level, then IBM stays about level." Our emphasis is in the discovery of local patterns in multivariate time series, in contrast to traditional time series analysis which largely focuses on global models. Thus, we search for rules whose conditions refer to patterns in time series. However, we do not want to define beforehand which patterns are to be used; rather, we want the patterns to be formed from the data in the context of rule discovery. We describe adaptive methods for finding rules of the above type from time-series data. The methods are based on discretizing the sequence by methods resembling vector quantization. We first form subsequences by sliding a window through the time series, and then cluster these subsequences by using a suitable measure of time-series similarity. The discretized version of the time series is obtained by taking the cluster identifiers corresponding to the subsequence. Once the time-series is discretized, we use simple rule finding methods to obtain rules from the sequence. We present empirical results on the behavior of the method. The increasing volume of data in modern business and science calls for more complex and sophisticated tools. Although advances in data mining technology have made extensive data collection much easier, it's still always evolving and there is a constant need for new techniques and tools that can help us transform this data into useful information and knowledge. Since the previous edition's publication, great advances have been made in the field of data mining. Not only does the third of edition of Data Mining: Concepts and Techniques continue the tradition of equipping you with an understanding and application of the theory and practice of discovering patterns hidden in large data sets, it also focuses on new, important topics in the field: data warehouses and data cube technology, mining stream, mining social networks, and mining spatial, multimedia and other complex data. Each chapter is a stand-alone guide to a critical topic, presenting proven algorithms and sound implementations ready to be used directly or with strategic modification against live data. This is the resource you need if you want to apply today's most powerful data mining techniques to meet real business challenges. * Presents dozens of algorithms and implementation examples, all in pseudo-code and suitable for use in real-world, large-scale data mining projects. * Addresses advanced topics such as mining object-relational databases, spatial databases, multimedia databases, time-series databases, text databases, the World Wide Web, and applications in several fields. *Provides a comprehensive, practical look at the concepts and techniques you need to get the most out of real business data This paper presents techniques for discovering and matching rules with elastic patterns. Elastic patterns are ordered lists of elements that can be stretched along the time axis. Elastic patterns are useful for discovering rules from data sequences with different sampling rates. For fast discovery of rules whose heads (left-hand sides) and bodies (right-hand sides) are elastic patterns, we construct a trimmed suffix tree from succinct forms of data sequences and keep the tree as a compact representation of rules. The trimmed suffix tree is also used as an index structure for finding rules matched to a target head sequence. When matched rules cannot be found, the concept of rule relaxation is introduced. Using a cluster hierarchy and relaxation error as a new distance function, we find the least relaxed rules that provide the most specific information on a target head sequence. Experiments on synthetic data sequences reveal the effectiveness of our proposed approach.