Multivariate Time-Series (MTS) clustering is crucial for signal processing and data analysis. Although deep learning approaches, particularly those leveraging Contrastive Learning (CL), are prominent for MTS representation, existing CL-based models face two key limitations: 1) neglecting clustering information during positive/negative sample pair construction, and 2) introducing unreasonable inductive biases, e.g., destroying time dependence and periodicity through augmentation strategies, compromising representation quality. This paper, therefore, proposes a Temporal-Frequency Enhanced Contrastive (TFEC) learning framework. To preserve temporal structure while generating low-distortion representations, a temporal-frequency Co-EnHancement (CoEH) mechanism is introduced. Accordingly, a synergistic dual-path representation and cluster distribution learning framework is designed to jointly optimize cluster structure and representation fidelity. Experiments on six real-world benchmark datasets demonstrate TFEC's superiority, achieving 4.48% average NMI gains over SOTA methods, with ablation studies validating the design. The code of the paper is available at: https://github.com/yueliangy/TFEC.

翻译：多元时间序列（MTS）聚类在信号处理与数据分析中至关重要。尽管深度学习方法，尤其是利用对比学习（CL）的方法，在MTS表征学习中占据主导地位，但现有的基于CL的模型面临两个关键局限：1）在正/负样本对构建过程中忽略聚类信息；2）引入不合理的归纳偏置，例如通过增强策略破坏时间依赖性与周期性，从而损害表征质量。为此，本文提出一种时频增强对比学习（TFEC）框架。为在生成低失真表征的同时保持时序结构，本文引入了时频协同增强（CoEH）机制。相应地，设计了一种协同的双路径表征与聚类分布学习框架，以联合优化聚类结构与表征保真度。在六个真实世界基准数据集上的实验证明了TFEC的优越性，其平均归一化互信息（NMI）相较于最先进（SOTA）方法提升了4.48%，消融研究验证了设计有效性。本文代码已公开于：https://github.com/yueliangy/TFEC。