DATA COMPRESSION AND MULTIPLE PARAMETER ESTIMATION

A method for radical linear compression of datasets where the data are dependent on some number M of parameters. If the noise in the data is independent of the parameters, M linear combinations of the data can be formed, 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. When the noise is dependent on the parameters, the method, although not precisely lossless, increases errors by a very modest factor. The method is general, but is illustrated with a problem for which it is well-suited: galaxy spectra, whose data typically consist of about 1000 fluxes, and whose properties are set by a handful of parameters such as age, brightness and a parameterized 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 106 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.