This paper focuses on the analysis of a rectangular supersonic multi-stream jet with aft deck using large eddy simulation (LES) and experimental data. Proper orthogonal decomposition (POD) and Dynamic mode decomposition (DMD) are applied to timeresolved schlieren, stereo particle image velocimetry (PIV), and LES data. The spatial eigenfunctions of the two datasets reveal similar trends in the flow field, where structures with high mean squared value propagate from the nozzle lip and mixing layer. In the schlieren, acoustic waves can also be seen radiating from the nozzle lip and edge of the aft deck. By combining the spatial eigenfunctions from the schlieren experiment and the time-dependent snapshots of the LES, low-dimensional time characteristics for the flow are reconstructed. Additionally, we compare the spatial modes from the PIV and LES to determine how well the coherent structures are being captured in the simulation.