We present an analysis and characterization of the coherent dynamics of bubble clouds. The study is two folds. First, through analysis of the Rayleigh-Plesset equation, we systematically show that the diagonal dominance of the virtual-mass matrix of the system of Lagrangian bubbles is parametrized by the cloud interaction parameter that controls the coherent dynamics of bubbles (d'Agostino and Brennen, J. Fluid. Mech., 1989). Second, based on this insight, we introduce the principal component analysis (PCA) of a time series of Lagrangian bubble dynamic data. Through PCA of test data, we show that the variance of the principal component can be directly correlated with the interaction parameter when a proper normalization (weighting) of the data is made. We further show that the incoherence of the bubble dynamics due to the initial polydispersity and the nonlinear oscillations of bubbles can appear in the slope of the decay of the variances. These results may help further understand the interaction parameter as well as suggest that the weighted PCA can be a simple, systematic means to characterize the coherent dynamics of bubbles with various parameters.