The time series classification literature has expanded rapidly over the last decade, with many new classification approaches published each year. Prior research has mostly focused on improving the accuracy and efficiency of classifiers, with interpretability being somewhat neglected. This aspect of classifiers has become critical for many application domains and the introduction of the EU GDPR legislation in 2018 is likely to further emphasize the importance of interpretable learning algorithms. Currently, state-of-the-art classification accuracy is achieved with very complex models based on large ensembles (COTE) or deep neural networks (FCN). These approaches are not efficient with regard to either time or space, are difficult to interpret and cannot be applied to variable-length time series, requiring pre-processing of the original series to a set fixed-length. In this paper we propose new time series classification algorithms to address these gaps. Our approach is based on symbolic representations of time series, efficient sequence mining algorithms and linear classification models. Our linear models are as accurate as deep learning models but are more efficient regarding running time and memory, can work with variable-length time series and can be interpreted by highlighting the discriminative symbolic features on the original time series. We show that our multi-resolution multi-domain linear classifier (mtSS-SEQL+LR) achieves a similar accuracy to the state-of-the-art COTE ensemble, and to recent deep learning methods (FCN, ResNet), but uses a fraction of the time and memory required by either COTE or deep models. To further analyse the interpretability of our classifier, we present a case study on a human motion dataset collected by the authors. We release all the results, source code and data to encourage reproducibility.
Explainable and Interpretable Diabetic Retinopathy Classification Based on Neural-Symbolic Learning
Massachusetts General Hospital（麻省总医院）；Harvard Medical School（哈佛医学院）；Singapore Eye Research Institute（新加坡眼科研究所）；Duke-NUS Medical School（杜克-新加坡国立大学医学院）；Institute for Molecular and Clinical Ophthalmology（分子与临床眼科研究所）；National University of Singapore（新加坡国立大学）
The Shape of Consumer Behavior: A Symbolic and Topological Analysis of Time Series
Maastricht University, School of Business and Economics（马斯特里赫特大学商学院）；Department of Data Analytics and Digitalisation（数据分析与数字化部门）；Department of Data Analytics（数据分析部门）
本研究评估了 SAX、eSAX 和 TDA 三种无监督聚类方法在 Google Trends 时间序列数据上的表现，发现 TDA 通过持续同调能更好地捕捉全局结构特征，实现比符号方法更均衡且有意义的分组。
Embedded Polygon Symbolic Transfer Entropy (EPSTE): A Geometric Token and Deep Learning Approach to Estimating Transfer Entropy in Neuroimaging Time Series
Towards symbolic regression for interpretable clinical decision scores
Federal University of ABC（ABC联邦大学）；University of Pennsylvania（宾夕法尼亚大学）；Institute for Biomedical Informatics, University of Pennsylvania（宾夕法尼亚大学生物医学信息学研究所）；Boston Children's Hospital, Harvard Medical School（哈佛医学院波士顿儿童医院）
Turning Time Series into Algebraic Equations: Symbolic Machine Learning for Interpretable Modeling of Chaotic Time Series
SAFIR, Sorbonne University Abu Dhabi, UAE（SAFIR，索邦大学阿布扎赫德分校）；Sorbonne Center for Artificial Intelligence, Sorbonne University, Paris, France（索邦人工智能中心，索邦大学巴黎分校）
Symbolic--KAN: Kolmogorov-Arnold Networks with Discrete Symbolic Structure for Interpretable Learning
Energy \& Intelligence Lab, Department of Chemical Engineering, University of Utah, Salt Lake City, Utah, 84112, USA；Department of Mechanical Engineering, University of Utah, Salt Lake City, Utah, 84112, USA；Imaging Institute, University of Utah, Salt Lake City, Utah, 84112, USA；Department of Biomedical Engineering, University of Utah, Salt Lake City, Utah, 84112, USA；Department of Mechanical Engineering, School of Engineering, Urmia University of Technology, Urmia, Iran
Interpretable and Explainable Logical Policies via Neurally Guided Symbolic Abstraction
Technical University of Darmstadt（达姆施塔特工业大学）；National Research Center for Applied Cybersecurity（国家应用网络安全研究中心）；Eindhoven University of Technology（埃因霍温理工大学）；Hessian Center for AI (hessian.AI)（黑森人工智能中心）；German Research Center for AI (DFKI)（德国人工智能研究中心）
Structured Kolmogorov-Arnold Neural ODEs for Interpretable Learning and Symbolic Discovery of Nonlinear Dynamics
Department of Industrial Systems Engineering and Management, National University of Singapore（工业系统工程与管理系，新加坡国立大学）；Department of Civil, Environmental and Geomatic Engineering, ETH Zürich（土木、环境与测绘工程系，苏黎世联邦理工学院）；Future Resilient Systems, Singapore-ETH Centre（未来韧性系统，新加坡-苏黎世中心）
Interpretable Robotic Friction Learning via Symbolic Regression
Ludwig-Maximilians-Universität München（慕尼黑路易斯-马克西米利安大学）；German Aerospace Center（德国航空航天中心）；University of Tromsø（特罗姆瑟大学）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）
Learning Interpretable Network Dynamics via Universal Neural Symbolic Regression
College of Computer Science and Technology, Jilin University（吉林大学计算机科学与技术学院）；Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University（吉林大学符号计算与知识工程教育部重点实验室）
University of Cambridge（剑桥大学）；Université Côte d’Azur（蔚蓝海岸大学）；CNRS（法国国家科学研究中心）；Inria（法国国家信息与自动化研究所）；University of Siena（锡耶纳大学）；INRA（法国国家农业食品与环境研究院）；Université Paris-Saclay（巴黎萨克雷大学）；KU Leuven（鲁汶大学）
Closing the Loop: PID Feedback Control for Interpretable Activation Steering in Symbolic Music Generation
Athens University of Economics and Business（雅典经济与商业大学）；Orfium Research（Orfium 研究）；Hellenic Mediterranean University（希腊地中海大学）；Archimedes / Athena Research Center（阿基米德/雅典娜研究中心）
Mathematics & Statistics, University of Vermont（数学与统计学系，佛蒙特大学）；Vermont Complex Systems Center, University of Vermont（佛蒙特复杂系统中心，佛蒙特大学）；Computer Science, University of Vermont（计算机科学系，佛蒙特大学）
Latent Space Disentanglement via Activation Steering for Interpretable Attribute Control in Symbolic Music Generation
Athens University of Economics；Innovation Lab Orfium Athens, Greece；Department of Music Technology；Acoustics Hellenic Mediterranean University Rethymno, Greece；Institute of Informatics \& Telecommunications National Center for Scientific Research “Demokritos” Athens, Greece；Department of Informatics Athens University of Economics
Discovering an interpretable mathematical expression for a full wind-turbine wake with artificial intelligence enhanced symbolic regression
School of Ocean and Civil Engineering, Shanghai Jiao Tong University（上海交通大学海洋与土木工程学院）；Ningbo Institute of Digital Twin, Eastern Institute of Technology（东方理工大学宁波数字孪生研究院）
