A well-defined distance is critical for the performance of time series classification. Existing distance measurements can be categorized into two branches. One is to utilize handmade features for calculating distance, e.g., dynamic time warping, which is limited to exploiting the dynamic information of time series. The other methods make use of the dynamic information by approximating the time series with a generative model, e.g., Fisher kernel. However, previous distance measurements for time series seldom exploit the label information, which is helpful for classification by distance metric learning. In order to attain the benefits of the dynamic information of time series and the label information simultaneously, this paper proposes a multiobjective learning algorithm for both time series approximation and classification, termed multiobjective model-metric (MOMM) learning. In MOMM, a recurrent network is exploited as the temporal filter, based on which, a generative model is learned for each time series as a representation of that series. The models span a non-Euclidean space, where the label information is utilized to learn the distance metric. The distance between time series is then calculated as the model distance weighted by the learned metric. The network size is also optimized to learn parsimonious representations. MOMM simultaneously optimizes the data representation, the time series model separation, and the network size. The experiments show that MOMM achieves not only superior overall performance on uni/multivariate time series classification but also promising time series prediction performance.

中文翻译：

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时间序列分类模型空间中的多目标学习


明确定义的距离对于时间序列分类的性能至关重要。现有的距离测量可以分为两个分支。一种是利用手工特征来计算距离，例如动态时间扭曲，这仅限于利用时间序列的动态信息。其他方法通过使用生成模型（例如费舍尔核）近似时间序列来利用动态信息。然而，以前的时间序列距离测量很少利用标签信息，这有助于通过距离度量学习进行分类。为了同时获得时间序列的动态信息和标签信息的好处，本文提出了一种用于时间序列逼近和分类的多目标学习算法，称为多目标模型度量（MOMM）学习。在 MOMM 中，循环网络被用作时间过滤器，基于此，为每个时间序列学习生成模型作为该序列的表示。这些模型跨越非欧几里得空间，其中标签信息用于学习距离度量。然后，时间序列之间的距离被计算为由学习指标加权的模型距离。网络大小也经过优化以学习简约的表示。 MOMM 同时优化数据表示、时间序列模型分离和网络大小。实验表明，MOMM 不仅在单变量/多变量时间序列分类上取得了优异的整体性能，而且在时间序列预测方面也取得了有前途的性能。