  In the era of big data, it is desired to develop efficient machine learning
algorithms to tackle massive data challenges such as storage bottleneck,
algorithmic scalability, and interpretability. In this paper, we develop a
novel efficient classification algorithm, called fast polynomial kernel
classification (FPC), to conquer the scalability and storage challenges. Our
main tools are a suitable selected feature mapping based on polynomial kernels
and an alternating direction method of multipliers (ADMM) algorithm for a
related non-smooth convex optimization problem. Fast learning rates as well as
feasibility verifications including the efficiency of an ADMM solver with
convergence guarantees and the selection of center points are established to
justify theoretical behaviors of FPC. Our theoretical assertions are verified
by a series of simulations and real data applications. Numerical results
demonstrate that FPC significantly reduces the computational burden and storage
memory of existing learning schemes such as support vector machines,
Nystr\"{o}m and random feature methods, without sacrificing their
generalization abilities much.
