Sparse Autoencoders Using Non-smooth Regularization

Autoencoder, at the heart of a deep learning structure, plays an important role in extracting abstract representation of a set of input training patterns. Abstract representation contains informative features to demonstrate a large set of data patterns in an optimal way in certain applications. It is shown that through sparse regularization of outputs of the hidden units (codes) in an autoencoder, the quality of codes can be enhanced that leads to a higher learning performance in applications like classification. Almost all methods trying to achieve code sparsity in an autoencoder use a smooth approximation of l₁ norm, as the best convex approximation of pseudo l₀ norm. In this paper, we incorporate sparsity to autoencoder training optimization process using non-smooth convex l₁ norm and propose an efficient algorithm to train the structure. The non-smooth l₁ regularization have shown its efficiency in imposing sparsity in various applications including feature selection via lasso and sparse representation using basis pursuit. Our experimental results on three benchmark datasets show superiority of this term in training a sparse autoencoder over previously proposed ones. As a byproduct of the proposed method, it can also be used to apply different types of non-smooth regularizers to autoencoder training problem.