  We present a method for radical linear compression of datasets where the data
are dependent on some number $M$ of parameters. We show that, if the noise in
the data is independent of the parameters, we can form $M$ linear combinations
of the data which contain as much information about all the parameters as the
entire dataset, in the sense that the Fisher information matrices are
identical; i.e. the method is lossless. We explore how these compressed numbers
fare when the noise is dependent on the parameters, and show that the method,
although not precisely lossless, increases errors by a very modest factor. The
method is general, but we illustrate it with a problem for which it is
well-suited: galaxy spectra, whose data typically consist of $\sim 10^3$
fluxes, and whose properties are set by a handful of parameters such as age,
brightness and a parametrised star formation history. The spectra are reduced
to a small number of data, which are connected to the physical processes
entering the problem. This data compression offers the possibility of a large
increase in the speed of determining physical parameters. This is an important
consideration as datasets of galaxy spectra reach $10^6$ in size, and the
complexity of model spectra increases. In addition to this practical advantage,
the compressed data may offer a classification scheme for galaxy spectra which
is based rather directly on physical processes.
