  This work demonstrates a hardware-efficient support vector machine (SVM)
training algorithm via the alternative direction method of multipliers (ADMM)
optimizer. Low-rank approximation is exploited to reduce the dimension of the
kernel matrix by employing the Nystr\"{o}m method. Verified in four datasets,
the proposed ADMM-based training algorithm with rank approximation reduces
32$\times$ of matrix dimension with only 2% drop in inference accuracy.
Compared to the conventional sequential minimal optimization (SMO) algorithm,
the ADMM-based training algorithm is able to achieve a 9.8$\times$10$^7$
shorter latency for training 2048 samples. Hardware design techniques,
including pre-computation and memory sharing, are proposed to reduce the
computational complexity by 62% and the memory usage by 60%. As a proof of
concept, an epileptic seizure detector chip is designed to demonstrate the
effectiveness of the proposed hardware-efficient training algorithm. The chip
achieves a 153,310$\times$ higher energy efficiency and a 364$\times$ higher
throughput-to-area ratio for SVM training than a high-end CPU. This work
provides a promising solution for edge devices which require low-power and
real-time training.
