  A closed-form solution exists in two-class linear discriminant analysis
(LDA), which discriminates two Gaussian-distributed classes in a
multi-dimensional feature space. In this work, we interpret the multilayer
perceptron (MLP) as a generalization of a two-class LDA system so that it can
handle an input composed by multiple Gaussian modalities belonging to multiple
classes. Besides input layer $l_{in}$ and output layer $l_{out}$, the MLP of
interest consists of two intermediate layers, $l_1$ and $l_2$. We propose a
feedforward design that has three stages: 1) from $l_{in}$ to $l_1$: half-space
partitionings accomplished by multiple parallel LDAs, 2) from $l_1$ to $l_2$:
subspace isolation where one Gaussian modality is represented by one neuron, 3)
from $l_2$ to $l_{out}$: class-wise subspace mergence, where each Gaussian
modality is connected to its target class. Through this process, we present an
automatic MLP design that can specify the network architecture (i.e., the layer
number and the neuron number at a layer) and all filter weights in a
feedforward one-pass fashion. This design can be generalized to an arbitrary
distribution by leveraging the Gaussian mixture model (GMM). Experiments are
conducted to compare the performance of the traditional backpropagation-based
MLP (BP-MLP) and the new feedforward MLP (FF-MLP).
