Early classification on time series has emerged as an active research area in the field of machine learning. It covers a wide range of applications in agriculture, medical and multimedia systems, including drought prediction, health monitoring, event detection, and many more. The early classification aims to predict the class label of a time series as soon as possible without waiting for the complete series. A critical issue in early classification is the learning of decision policy that determines the adequacy of the collected data required for reliable class prediction. It is more challenging for Multivariate Time Series (MTS) data, where the decision depends on multiple variables to achieve a trade-off between earliness and accuracy. Therefore, this work proposes an optimization-based early classification model for MTS data based on optimal decision rule learning. The proposed model adopts a two-layered approach. The first layer employs the Gaussian process probabilistic classifiers for each variable in MTS that provides the class probabilities at the successive time steps in the series. The second layer defines Early Stopping Rule (ESR) that performs the class prediction task. The ESR learns its parameters through the particle swarm optimization by simultaneously minimizing the misclassification cost and delaying the decision cost. This work has utilized publicly available MTS datasets to validate the proposed early classification model. The experimental results show that the proposed model achieves promising results in terms of accuracy and earliness compared to existing methods.

时间序列的早期分类已成为机器学习领域的活跃研究领域。它涵盖了农业，医疗和多媒体系统中的广泛应用，包括干旱预测，健康监测，事件检测等。早期分类的目的是在不等待整个序列的情况下，尽快预测时间序列的类标签。早期分类中的一个关键问题是学习决策策略，该决策策略确定可靠的类别预测所需的收集数据是否足够。对于多变量时间序列（MTS）数据而言，更具挑战性，因为决策取决于多个变量才能在早期性和准确性之间进行权衡。因此，这项工作提出了一个基于优化决策规则学习的基于优化的MTS数据早期分类模型。提出的模型采用了两层方法。第一层为MTS中的每个变量采用高斯过程概率分类器，该分类器在序列的连续时间步长提供类概率。第二层定义执行类预测任务的早期停止规则（ESR）。ESR通过最小化分类错误成本并延迟决策成本，通过粒子群优化学习其参数。这项工作已利用公开可用的MTS数据集来验证建议的早期分类模型。实验结果表明，与现有方法相比，该模型在准确性和早期性方面均取得了可喜的成果。