  The hashing trick is a machine learning technique used to encode categorical
features into a numerical vector representation of pre-defined fixed length. It
works by using the categorical hash values as vector indices, and updating the
vector values at those indices. Here we discuss a different approach based on
additive-hashing and the "almost orthogonal" property of high-dimensional
random vectors. That is, we show that additive feature hashing can be performed
directly by adding the hash values and converting them into high-dimensional
numerical vectors. We show that the performance of additive feature hashing is
similar to the hashing trick, and we illustrate the results numerically using
synthetic, language recognition, and SMS spam detection data.
