  Principal component analysis, dictionary learning, and auto-encoders are all
unsupervised methods for learning representations from a large amount of
training data. In all these methods, the higher the dimensions of the input
data, the longer it takes to learn. We introduce a class of neural networks,
termed RandNet, for learning representations using compressed random
measurements of data of interest, such as images. RandNet extends the
convolutional recurrent sparse auto-encoder architecture to dense networks and,
more importantly, to the case when the input data are compressed random
measurements of the original data. Compressing the input data makes it possible
to fit a larger number of batches in memory during training. Moreover, in the
case of sparse measurements,training is more efficient computationally. We
demonstrate that, in unsupervised settings, RandNet performs dictionary
learning using compressed data. In supervised settings, we show that RandNet
can classify MNIST images with minimal loss in accuracy, despite being trained
with random projections of the images that result in a 50% reduction in size.
Overall, our results provide a general principled framework for training neural
networks using compressed data.
