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.

本研究中，我们提出了一种在无线网络上实现联邦 K - 均值聚类算法时减少每轮通信延迟的无线计算方案。该方案利用编码器利用平衡数系的数值表示和无线多址信道非相干超定位属性来计算联邦 K - 均值的更新总和，以消除对精确相位和时间同步的需求。此外，我们提出了一种重新初始化方法来改进处理异构数据分布的性能。通过客户位置聚类场景的实验证明了该算法的性能，并与标准 K - 均值聚类进行比较。结果显示，该方法在减少通信延迟的同时与标准 K - 均值聚类的性能相似。