  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.
