Inspired by the use of random projections in biological sensing systems, we present a new algorithm
for processing data in classification problems. This is based on observations of the human brain
and the fruit fly’s olfactory system and involves randomly projecting data into a space of greatly
increased dimension before applying a cap operation to truncate the smaller entries. This leads to
a simple algorithm that is very computationally efficient and can be used to either give a sparse
representation with minimal loss in classification accuracy or give improved robustness, in the sense
that classification accuracy is improved when noise is added to the data. This is demonstrated with
numerical experiments, which supplement theoretical results demonstrating that the resulting signal
transform is continuous and invertible, in an appropriate sense.