Abstracting Convolutional Autoencoders using A Compositional Subspace Representation Method for Autoassociative Mapping

In this paper, we propose a compositional subspace representation method to abstract the computational framework of convolutional autoencoders. The expected contribution is to provide a rigorous, understandable, and expressive explanation of the mathematical design and implementation of convolutional autoencoders. The proposed compositional subspace representation method involves structurally rigorous mathematical abstraction. It is based on the concept that complex nonlinear learning functions can be modeled by a composition of a set of continuous piecewise linear (CPL) learning functions. In this way, through a list of functional space projections, combinations, and sequential chaining, an inductive projection of hierarchical CPL learning chain space can finally be created to encapsulate the computational abstraction of generative autoencoding in a convolutional autoencoder. The paper concludes by presenting a two-layer convolutional autoencoder for an autoassociative mapping configuration with image reproduction application and experimental results to support our theoretical investigation.