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Classification and clustering with continuous time Bayesian network models

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Abstract

Classification and clustering of streaming data are relevant in finance, computer science, and engineering while they are becoming increasingly important in medicine and biology. Streaming data are analyzed with algorithms and models capable to represent dynamics, sequences and time. Dynamic Bayesian networks and hidden Markov models are commonly used to analyze streaming data. However, they are concerned with evenly spaced time series data and thus suffer from several limitations. Indeed, it is not clear how timestamps should be discretized even if some approaches to mitigate this problem have been recently made available. In this paper we describe the class of continuous time Bayesian networks classifiers and develop algorithms for their parametric and structural learning to solve classification and clustering of multivariate discrete state continuous time trajectories. Numerical experiments on synthetic and real world data are used to compare the performance of continuous time Bayesian network models to that achieved by dynamic Bayesian networks. In particular, post-stroke rehabilitation data is used for the classification task while urban traffic data from continuous time loop is used for the clusteirng task. The achieved results confirm the effectiveness of the proposed approaches.

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Notes

  1. http://www.swarco.net/

  2. This definition differs from the one proposed in Stella and Amer (2012). In fact, this definition does not require the CTBNC graph \(\mathcal {G}\) to be connected. Therefore, feature selection is achieved as the product of any structural learning algorithm.

  3. Time count sufficient statistics refers to the time spent in a particular state by a variable given the state of its parents.

  4. With α y we refer to the hyperparameter associated with the class value y.

  5. For further experiments on continuous time Bayesian network classifiers for classification purposes refer to Codecasa and Stella (2013, 2014b).

  6. With α y we refer to the hyperparameter associated with the class value y.

  7. http://www.civitas.eu/archimedes

  8. For computational reasons a random subset of trajectories is used in the Monza road network tests.

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  1. DISCo, Università degli Studi di Milano-Bicocca, Viale Sarca 336, 20126, Milano, Italy

    Daniele Codecasa & Fabio Stella

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  1. Daniele Codecasa
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  2. Fabio Stella
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Correspondence to Fabio Stella.

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Codecasa, D., Stella, F. Classification and clustering with continuous time Bayesian network models. J Intell Inf Syst 45, 187–220 (2015). https://doi.org/10.1007/s10844-014-0345-0

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