In this study, the data analysis technique of proper orthogonal decomposition (POD) is applied to the numerical simulation solutions of two-dimensional unsteady cellular detonation. As a first stage to introduce the idea, the analysis is performed on the simulation results obtained numerically with the reactive Euler equations with a one-step Arrhenius kinetic model. Cases with different activation energies Ea are considered, yielding different degrees of cellular instability of the detonation frontal structure. The POD modes are obtained by performing a singular value decomposition (SVD) of the full ensemble matrix whose columns are the snapshots of time-dependent pressure fields from the stored numerical solutions. The dominant spatial flow features behind the detonation front with varying Ea are revealed by the resulting POD modes that represent flow structures with decreasing flow energy content. The accuracy of the pressure flow field reconstructed using different levels of POD basis modes for reduced-order modeling is demonstrated. The coherent structures and increasing complexity of the flow fields with higher Ea are elucidated with the use of Lagrangian descriptors (LD). The potential of the methods described in this work is discussed.