An Interpretable Generative Model for Handwritten Digits Synthesis

Abstract

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 stateof-the-art GAN and VAE methods, and show that the proposed generative model achieves comparable performance.

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“…Studies related to interpretabilities exist. For example, [118] uses encoder-decoder system to perform multistage PCA. Generative model is used to show that natural image distribution modeled using probability density is fundamentally difficult to interpret [119].…”

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“…audio, video, etc.) of categories they already know how to recognize and manipulate-such as faces [51], shapes [52], handwriting [53], speech, etc. These representations might serve as key enablers for explainable synthesized knowledge.…”

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“…Studies related to interpretabilities exist. For example [119] uses encoder-decoder system to perform multi-stage PCA. Generative model is used to show that natural image distribution modelled using probability density is fundamentally difficult to interpret [120].…”