Time Series Classification in Reservoir- and Model-Space: A Comparison
Learning in the space of Echo State Network (ESN) output weights, i.e. model space, has achieved excellent results in time series classification, visualization and modelling. This work presents a systematic comparison of time series classification in the
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Research Institute for Cognition and Robotics - CoR-Lab, Universit¨ asstraße 25, 33615 Bielefeld, Germany [email protected] 2 Fraunhofer Research Institution for Mechatronic Systems Design IEM, Zukunftsmeile 1, 33102 Paderborn, Germany
Abstract. Learning in the space of Echo State Network (ESN) output weights, i.e. model space, has achieved excellent results in time series classification, visualization and modelling. This work presents a systematic comparison of time series classification in the model space and the classical, discriminative approach with ESNs. We evaluate the approaches on 43 univariate and 18 multivariate time series. It turns out that classification in the model space achieves often better classification rates, especially for high-dimensional motion datasets. Keywords: Time series classification space
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Introduction
The idea of learning in the model space [6] is to train models on parts of the data and then use the model parameters for further processing. Recently, this approach was applied to learn parameterized skills in robotics [16,19,20], to model parameterized processes [2] and to classify [7,8] and to visualize [12,14] time series. While the idea to use parameters of linear models for time series classification appeared as early as in 1997 [10], only the more recent usage of non-linear, reservoir-based models allowed the method to achieve results similar or better as state-of-the-art methods [1,7,8]. The models used in the latter publications are variants of Echo State Networks (ESN, [13]). For each time series, an ESNmodel is trained and the model parameters are used as features in a consecutive classification stage [8]. Typically, the models are trained to minimize the onestep-ahead prediction error on the time series. The number of model parameters is independent of the length of the time series, which allows for the deployment of any feature-based classifier in the model space. Time series classification in the model space of ESNs was evaluated on a smaller number of datasets in [7,8], however, a systematic comparison to the classical, discriminative approach to time series classification with ESNs [15] is c Springer International Publishing AG 2016 F. Schwenker et al. (Eds.): ANNPR 2016, LNAI 9896, pp. 197–208, 2016. DOI: 10.1007/978-3-319-46182-3 17
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missing. Our contribution is the evaluation of a large number of datasets and the comparison of the classification performance in the model space with that of two discriminative ESN architectures. The results show that model space learning (MSL) is often superior to discriminative ESN training and on par with other state-of-the-art methods. The remainder of this paper is structured as follows. In Sect. 2, work related to learning in the model space is presented. In the following three sections, feature based time series classification is defined and the reservoir- and model-based feature creation presented. Section 6 describes the datasets and our approach to param
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