The multidimensional classification of multivariate time series deals with the assignment of multiple classes to time-ordered data described by a set of feature variables. Although this challenging task has received almost no attention in the literature, it is present in a wide variety of domains, such as medicine, finance or industry. The complexity of this problem lies in two nontrivial tasks, the learning with multivariate time series in continuous time and the simultaneous classification of multiple class variables that may show dependencies between them. These can be addressed with different strategies, but most of them may involve a difficult preprocessing of the data, high space and classification complexity or ignoring useful interclass dependencies. Additionally, no attention has been given to the development of new multidimensional classifiers of time series based on probabilistic graphical models, even though transparent models can facilitate further understanding of the domain. In this paper, a novel probabilistic graphical model is proposed, which is able to classify a discrete multivariate temporal sequence into multiple class variables while modeling their dependencies. This model extends continuous time Bayesian networks to the multidimensional classification problem, which are able to explicitly represent the behavior of time series that evolve over continuous time. Different methods for the learning of the parameters and structure of the model are presented, and numerical experiments on synthetic and real-world data show encouraging results in terms of performance and learning time with respect to independent classifiers, the current alternative approach under the continuous time Bayesian network paradigm.

中文翻译：

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多维连续时间贝叶斯网络分类器

多元时间序列的多维分类处理将多个类分配给由一组特征变量描述的时间顺序数据。尽管这项具有挑战性的任务在文献中几乎没有受到关注，但它存在于广泛的领域，例如医学、金融或工业。这个问题的复杂性在于两个非平凡的任务，在连续时间内对多元时间序列进行学习，以及对可能表现出它们之间依赖关系的多个类变量进行同时分类。这些可以通过不同的策略来解决，但其中大多数可能涉及对数据进行困难的预处理、高空间和分类复杂性或忽略有用的类间依赖关系。此外，尽管透明模型可以促进对该领域的进一步理解，但并未关注基于概率图形模型的时间序列的新多维分类器的开发。在本文中，提出了一种新的概率图模型，该模型能够将离散的多元时间序列分类为多个类变量，同时对其依赖项进行建模。该模型将连续时间贝叶斯网络扩展到多维分类问题，它能够明确表示随连续时间演化的时间序列的行为。介绍了学习模型参数和结构的不同方法，