Time series data is perhaps the most frequently encountered type of data examined by the data mining community. Clustering is perhaps the most frequently used data mining algorithm, being useful in it’s own right as an exploratory technique, and also as a subroutine in more complex data mining algorithms such as rule discovery, indexing, summarization, anomaly detection, and classification. Given these two facts, it is hardly surprising that time series clustering has attracted much attention. The data to be clustered can be in one of two formats: many individual time series, or a single time series, from which individual time series are extracted with a sliding window. Given the recent explosion of interest in streaming data and online algorithms, the latter case has received much attention. In this work we make a surprising claim. Clustering of streaming time series is completely meaningless. More concretely, clusters extracted from streaming time series are forced to obey a certain constraint that is pathologically unlikely to be satisfied by any dataset, and because of this, the clusters extracted by any clustering algorithm are essentially random. While this constraint can be intuitively demonstrated with a simple illustration and is simple to prove, it has never appeared in the literature. We can justify calling our claim surprising, since it invalidates the contribution of dozens of previously published papers. We will justify our claim with a theorem, illustrative examples, and a comprehensive set of experiments on reimplementations of previous work. Although the primary contribution of our work is to draw attention to the fact that an apparent solution to an important problem is incorrect and should no longer be used, we also introduce a novel method which, based on the concept of time series motifs, is able to meaningfully cluster some streaming time series datasets.

Abstract. We apply a simple Learning Classifier System that has previously been shown to perform well on a number of difficult continuousvalued test problems to a foreign exchange trading problem. The performance of the Learning Classifier System is compared to that of a Genetic Programming approach from the literature. The simple Learning Classifier System is able to achieve a positive excess return in simulated trading, but results are not yet fully competitive because the Learning Classifier System trades too frequently. However, the Learning Classifier System approach shows potential because returns are obtained with no offline training and the technique is inherently adaptive, unlike many of the machine learning methods currently employed for financial trading. 1

Given the recent explosion of interest in streaming data and online algorithms, clustering of time series subsequences, extracted via a sliding window, has received much attention. In this work we make a surprising claim. Clustering of time series subsequences is meaningless. More concretely, clusters extracted from these time series are forced to obey a certain constraint that is pathologically unlikely to be satisfied by any dataset, and because of this, the clusters extracted by any clustering algorithm are essentially random.