Clustering of time-series subsequences is meaningless: implications for previous and future research

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. 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 because 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 that, based on the concept of time-series motifs, is able to meaningfully cluster subsequences on some time-series datasets.