Title: Learning Random Fourier Features by Hybrid Constrained Optimization,
Abstract: The kernel embedding algorithm is an important component for adapting kernel
methods to large datasets. Since the algorithm consumes a major computation
cost in the testing phase, we propose a novel teacher-learner framework of
learning computation-efficient kernel embeddings from specific data. In the
framework, the high-precision embeddings (teacher) transfer the data
information to the computation-efficient kernel embeddings (learner). We
jointly select informative embedding functions and pursue an orthogonal
transformation between two embeddings. We propose a novel approach of
constrained variational expectation maximization (CVEM), where the alternate
direction method of multiplier (ADMM) is applied over a nonconvex domain in the
maximization step. We also propose two specific formulations based on the
prevalent Random Fourier Feature (RFF), the masked and blocked version of
Computation-Efficient RFF (CERF), by imposing a random binary mask or a block
structure on the transformation matrix. By empirical studies of several
applications on different real-world datasets, we demonstrate that the CERF
significantly improves the performance of kernel methods upon the RFF, under
certain arithmetic operation requirements, and suitable for structured matrix
multiplication in Fastfood type algorithms.