Classification in the hidden layer of a single layer neural network with random weights has shown high accuracy in recent experimental studies. We further explore its classification and clustering performance in a compressed hidden space on a large cohort of datasets from the UCI machine learning archive. We compress the hidden layer with a simple bit-encoding that yields a comparable error to the original hidden layer thus reducing memory requirements and allowing to study upÂ to a million random nodes. In comparison to the uncompressed hidden space we find classification error with the linear support vector machine to be statistically indistinguishable from that of the network’s compressed layer. We see that test error of the linear support vector machine in the compressed hidden layer improves marginally after 10,000 nodes and even rises when we reach one million nodes. We show that k-means clustering has an improved adjusted rand index and purity in the compressed hidden space compared to the original input space but only the latter by a statistically significant margin. We also see that semi-supervised k-nearest neighbor improves by a statistically significant margin when only 10% of labels are available. Finally we show that different classifiers have statistically significant lower error in the compressed hidden layer than the original space with the linear support vector machine reaching the lowest error. Overall our experiments show that while classification in our compressed hidden layer can achieve a low error competitive to the original space there is a saturation point beyond which the error does not improve, and that clustering and semi-supervised is better in the compressed hidden layer by a small yet statistically significant margin.