  An interpretable generative model for handwritten digits synthesis is
proposed in this work. Modern image generative models, such as Generative
Adversarial Networks (GANs) and Variational Autoencoders (VAEs), are trained by
backpropagation (BP). The training process is complex and the underlying
mechanism is difficult to explain. We propose an interpretable multi-stage PCA
method to achieve the same goal and use handwritten digit images synthesis as
an illustrative example. First, we derive principal-component-analysis-based
(PCA-based) transform kernels at each stage based on the covariance of its
inputs. This results in a sequence of transforms that convert input images of
correlated pixels to spectral vectors of uncorrelated components. In other
words, it is a whitening process. Then, we can synthesize an image based on
random vectors and multi-stage transform kernels through a coloring process.
The generative model is a feedforward (FF) design since no BP is used in model
parameter determination. Its design complexity is significantly lower, and the
whole design process is explainable. Finally, we design an FF generative model
using the MNIST dataset, compare synthesis results with those obtained by
state-of-the-art GAN and VAE methods, and show that the proposed generative
model achieves comparable performance.
