  We propose a novel Neyman-Pearson (NP) classifier that is both online and
nonlinear as the first time in the literature. The proposed classifier operates
on a binary labeled data stream in an online manner, and maximizes the
detection power about a user-specified and controllable false positive rate.
Our NP classifier is a single hidden layer feedforward neural network (SLFN),
which is initialized with random Fourier features (RFFs) to construct the
kernel space of the radial basis function at its hidden layer with sinusoidal
activation. Not only does this use of RFFs provide an excellent initialization
with great nonlinear modeling capability, but it also exponentially reduces the
parameter complexity and compactifies the network to mitigate overfitting while
improving the processing efficiency substantially. We sequentially learn the
SLFN with stochastic gradient descent updates based on a Lagrangian NP
objective. As a result, we obtain an expedited online adaptation and powerful
nonlinear Neyman-Pearson modeling. Our algorithm is appropriate for large scale
data applications and provides a decent false positive rate controllability
with real time processing since it only has O(N) computational and O(1) space
complexity (N: number of data instances). In our extensive set of experiments
on several real datasets, our algorithm is highly superior over the competing
state-of-the-art techniques, either by outperforming in terms of the NP
classification objective with a comparable computational as well as space
complexity or by achieving a comparable performance with significantly lower
complexity.
