In this study, we propose using an over-the-air computation (OAC) scheme for the federated k-means clustering algorithm to reduce the per-round communication latency when it is implemented over a wireless network. The OAC scheme relies on an encoder exploiting the representation of a number in a balanced number system and computes the sum of the updates for the federated k-means via signal superposition property of wireless multiple-access channels non-coherently to eliminate the need for precise phase and time synchronization. Also, a reinitialization method for ineffectively used centroids is proposed to improve the performance of the proposed method for heterogeneous data distribution. For a customer-location clustering scenario, we demonstrate the performance of the proposed algorithm and compare it with the standard k-means clustering. Our results show that the proposed approach performs similarly to the standard k-means while reducing communication latency.

翻译：本研究提出了一种基于空中计算（OAC）方案的联邦 $k$-均值聚类算法，以降低其在无线网络中实现时的每轮通信延迟。该OAC方案利用编码器基于平衡数制表示法，通过无线多址信道的信号叠加特性以非相干方式计算联邦 $k$-均值的更新和，从而无需精确的相位和时间同步。此外，针对无效使用的质心，提出了一种重初始化方法，以改善该算法在异构数据分布下的性能。在客户位置聚类场景中，我们展示了所提算法的性能，并将其与标准 $k$-均值聚类进行比较。结果表明，所提方法在降低通信延迟的同时，性能与标准 $k$-均值聚类相近。