Massive lossless data compression and multiple parameter estimation from galaxy spectra

We present a method for radical linear compression of data sets where the d ata are dependent on some number M of parameters. We show that, if the nois e in the data is independent of the parameters, we can form M linear combin ations of the data which contain as much information about all the paramete rs as the entire data set, in the sense that the Fisher information matrice s are identical; i.e. the method is lossless. We explore how these compress ed numbers fare when the noise is dependent on the parameters, and show tha t the method, though not precisely lossless, increases errors by a very mod est factor. The method is general, but we illustrate it with a problem for which it is well-suited: galaxy spectra, the data for which typically consi st of similar to 10(3) fluxes, and the properties of which are set by a han dful of parameters such as age, and a parametrized star formation history. The spectra are reduced to a small number of data, which are connected to t he physical processes entering the problem. This data compression offers th e possibility of a large increase in the speed of determining physical para meters. This is an important consideration as data sets of galaxy spectra r each 10(6) in size, and the complexity of model spectra increases. In addit ion to this practical advantage, the compressed data may offer a classifica tion scheme for galaxy spectra which is based rather directly on physical p rocesses.