  Autoencoders have been widely used for dimensional reduction and feature
extraction. Various types of autoencoders have been proposed by introducing
regularization terms. Most of these regularizations improve representation
learning by constraining the weights in the encoder part, which maps input into
hidden nodes and affects the generation of features. In this study, we show
that a constraint to the decoder can also significantly improve its performance
because the decoder determines how the latent variables contribute to the
reconstruction of input. Inspired by the structural modal analysis method in
mechanical engineering, a new modal autoencoder (MAE) is proposed by
othogonalising the columns of the readout weight matrix. The new regularization
helps to disentangle explanatory factors of variation and forces the MAE to
extract fundamental modes in data. The learned representations are functionally
independent in the reconstruction of input and perform better in consecutive
classification tasks. The results were validated on the MNIST variations and
USPS classification benchmark suite. Comparative experiments clearly show that
the new algorithm has a surprising advantage. The new MAE introduces a very
simple training principle for autoencoders and could be promising for the
pre-training of deep neural networks.
