We consider the problem of classification of a pattern from multiple compressed observations that are collected in a sensor network. In particular, we exploit the properties of random projections in generic sensor devices and we take some first steps in introducing linear dimensionality reduction techniques in the compressed domain. We design a classification framework that consists in embedding the low dimensional classification space given by classical linear dimensionality reduction techniques in the compressed domain. The measurements of the multiple observations are then projected onto the new classification subspace and are finally aggregated in order to reach a classification decision. Simulation results verify the effectiveness of our scheme and illustrate that compressed measurements combined with information diversity lead to efficient dimensionality reduction in simple sensing architectures.