  This paper explores how to customize time series classification (TSC) methods
with the help of external data in a privacy-preserving federated learning (FL)
scenario. To the best of our knowledge, we are the first to study on this
essential topic. Achieving this goal requires us to seamlessly integrate the
techniques from multiple fields including Data Mining, Machine Learning, and
Security. In this paper, we systematically investigate existing TSC solutions
for the centralized scenario and propose FedST, a novel FL-enabled TSC
framework based on a shapelet transformation method. We recognize the federated
shapelet search step as the kernel of FedST. Thus, we design a basic protocol
for the FedST kernel that we prove to be secure and accurate. However, we
identify that the basic protocol suffers from efficiency bottlenecks and the
centralized acceleration techniques lose their efficacy due to the security
issues. To speed up the federated protocol with security guarantee, we propose
several optimizations tailored for the FL setting. Our theoretical analysis
shows that the proposed methods are secure and more efficient. We conduct
extensive experiments using both synthetic and real-world datasets. Empirical
results show that our FedST solution is effective in terms of TSC accuracy, and
the proposed optimizations can achieve three orders of magnitude of speedup.
