  We consider the problem of computing the k-means centers for a large
high-dimensional dataset in the context of edge-based machine learning, where
data sources offload machine learning computation to nearby edge servers.
k-Means computation is fundamental to many data analytics, and the capability
of computing provably accurate k-means centers by leveraging the computation
power of the edge servers, at a low communication and computation cost to the
data sources, will greatly improve the performance of these analytics. We
propose to let the data sources send small summaries, generated by joint
dimensionality reduction (DR), cardinality reduction (CR), and quantization
(QT), to support approximate k-means computation at reduced complexity and
communication cost. By analyzing the complexity, the communication cost, and
the approximation error of k-means algorithms based on carefully designed
composition of DR/CR/QT methods, we show that: (i) it is possible to compute
near-optimal k-means centers at a near-linear complexity and a constant or
logarithmic communication cost, (ii) the order of applying DR and CR
significantly affects the complexity and the communication cost, and (iii)
combining DR/CR methods with a properly configured quantizer can further reduce
the communication cost without compromising the other performance metrics. Our
theoretical analysis has been validated through experiments based on real
datasets.
