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TS-stream: clustering time series on data streams

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Abstract

The current ability to produce massive amounts of data and the impossibility in storing it motivated the development of data stream mining strategies. Despite the proposal of many techniques, this research area still lacks in approaches to mine data streams composed of multiple time series, which has applications in finance, medicine and science. Most of the current techniques for clustering streaming time series have a serious limitation in their similarity measure, which are based on the Pearson correlation. In this paper, we show the Pearson correlation is not capable of detecting similarities even for classic time series models, such as those by Box and Jenkins. This limitation motivated our proposal to cluster streaming time series based on their generating functions, which is achieved by considering features obtained using descriptive measures, such as Auto Mutual Information, the Hurst Exponent and several others. We present a new tree-based clustering algorithm, entitled TS-Stream, which uses the extracted features to produce partitions in better accordance to the time series generating functions. Experiments with synthetic data sets confirm TS-Stream outperforms ODAC, currently the most popular technique, in terms of clustering quality. Using real financial time series from the NYSE and NASDAQ, we conducted stock trading simulations employing TS-Stream to support the creation of diversified investment portfolios. Results confirmed TS-Stream increased the monetary returns in several orders of magnitude when compared to trading strategies simply based on the Moving Average Convergence Divergence financial indicator.

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Notes

  1. Determinism is a measure based on Recurrence Quantification Analysis (Marwan et al. 2007).

  2. Defined as \(\sigma ^{2}(X)~=~\sum _{i=1}^{n} p_{i}~\cdot ~(x_{i} - \mu )^{2}\) for a series X = (x 1, x 2, … , x n ), in which p i is the probability of observation x i and μ is the mean of the sequence.

  3. A deterministic, chaotic, nonlinear model.

  4. In this case outliers are simply exceptional gains, but when plotted hinder a better visualization of the distribution.

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Acknowledgments

This paper is based upon work supported by FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo)—Brazil under grant #2010/05062-6. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of FAPESP. We also thank the anonymous reviewers who suggested improvements to the presentation of this paper.

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  1. Institute of Mathematical and Computer Sciences–ICMC–USP, University of Sao Paulo, Av. Trabalhador são-carlense, São Carlos, 400 13566-590, SP, Brazil

    Cássio M. M. Pereira & Rodrigo F. de Mello

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  1. Cássio M. M. Pereira
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  2. Rodrigo F. de Mello
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Correspondence to Cássio M. M. Pereira.

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Pereira, C.M.M., de Mello, R.F. TS-stream: clustering time series on data streams. J Intell Inf Syst 42, 531–566 (2014). https://doi.org/10.1007/s10844-013-0290-3

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