In artificial-intelligence-aided signal processing, existing deep learning models often exhibit a black-box structure. Here, conceptually beyond spectral analysis, we demonstrate that topological methods not only effectively capture intrinsic and complex structural information but can also enhance neural networks. We provide a transparent methodology, TopCap, to capture topological features inherent in time series for basic machine learning.
Compared to prior approaches, we obtain descriptors that probe finer information such as the vibration of a time series. Notably, in classifying voiced and voiceless consonants, TopCap achieves an accuracy consistently standing in comparison with neural network models. Moreover, by integrating TopCap features into those neural networks, our approach improves upon state-of-the-art methods in terms of robustness against noise, as well as accuracy, stability, convergence of loss function, and interpretability.
The authors would like to thank Meng Yu of Tencent AI Lab for his mentorship on audio and speech signal processing, on neural networks and deep learning, as well as for his comments and suggestions on an earlier draft of this manuscript. The authors would also like to thank Andrew Blumberg, Gunnar Carlsson, Fangyi Chen, Haibao Duan, Houhong Fan, Fuquan Fang, Yulia Gel, Yunan He, Wenfei Jin, Tyler Lawson, Fengchun Lei, Jingyan Li, Yanlin Li, Hongwei Lin, Andy Luchuan Liu, Tao Luo, Zhi Lü, Jianxin Pan, Yuhe Qin, Qi Sun, Yujiao Jennifer Sun, Guoliang Tian, Jie Wu, Rongling Wu, Kelin Xia, Tony Xiaochen Xiao, Jiang Yang, Jin Zhang, and Zhen Zhang for discussions and encouragement. This work was partly supported by the National Natural Science Foundation of China grant 12371069, Guangdong Basic and Applied Basic Research Foundation grant 2023A1515030289, and the Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science (2022B1212010006, UICR0600008-7).
Present address: Department of Mathematics, North Carolina State University, Raleigh, NC, USA Present address: School of Intelligence Science and Engineering, Harbin Institute of Technology (Shenzhen), Shenzhen, China Present address: School of Mathematics and Systems Science, Shenyang Normal University, Shenyang, China These authors contributed equally: Pingyao Feng, Qingrui Qu. Department of Mathematics, Southern University of Science and Technology, Shenzhen, China Pingyao Feng, Qingrui Qu, Haiyu Zhang, Siheng Yi, Zhiwang Yu, Zeyang Ding & Yifei Zhu The authors declare no competing interests. Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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