From Two-Class Linear Discriminant Analysis to Interpretable Multilayer Perceptron Design
This work addresses the challenge of interpretable and efficient MLP design for researchers and practitioners, though it is incremental as it builds on existing LDA and GMM methods.
The paper tackles the problem of designing multilayer perceptrons (MLPs) by interpreting them as a generalization of two-class linear discriminant analysis (LDA) to handle multiple Gaussian modalities and classes, resulting in an automatic feedforward design that specifies architecture and weights in one pass, with experiments showing competitive performance compared to backpropagation-based MLPs.
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).