Clustering of streaming time series is meaningless

Abstract

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.

Logical Clustering and Learning for Time-Series Data

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Coconut: sortable summarizations for scalable indexes over static and streaming data series

“…Constant Approximation (PCA), and Adaptive Piecewise Constant Approximation (APCA) [11], as well as data series specific techniques such as Piecewise Aggregate Approximation (PAA) [27], Symbolic Aggregate approXimation (SAX) [36] and the indexable Symbolic Aggregate approXimation (iSAX) [67,9]. These smaller summarizations can be scanned and filtered [23,33], or indexed and pruned [76,66,67,74,75,19,7,69,71,38,53,37,72] to avoid accessing parts of the data that do not contain the nearest neighbor.…”

“…We now discuss the state-of-the-art in data series indexing. We concentrate on SAX summarizations [67,36], which have been shown to outperform other summarizations in terms of pruning power using the same amount of bytes [77]. We illustrate the construction of a SAX summarization in Figure 1.…”

A Review of Subsequence Time Series Clustering

“…Lin et al [ 27 ] prove the claim of meaningless results in 2003 and explain that all previous claims are false because they have the same results and are unacceptable [ 14 ]. Thus, researchers have tried to find a solution to this issue and answer the question of why it is meaningless (from 2005 to 2011) [ 13 , 14 , 28 – 30 ].…”