We apply Proper Orthogonal Decomposition (POD) to characterise rotating, three dimensional, large scale coherent structures inside an unbaffled stirred tank agitated by a Rushton turbine at turbulent flow conditions (Re = 30000). The four leading POD modes come in pairs, with frequencies 0.6 and 0.2 times the impeller rotational frequency (in an inertial reference frame). Investigation of the spatial structure suggest that the two pairs correspond to precessing Macro-instabilities that rotate in a direction opposite to that of the impeller. Four Machine Learning methods are employed to reconstruct the dominant pair from sparse velocity measurements. The pair was reconstructed well by all algorithms using data from 1, 2, and 6 sensors. The performance improved with larger number of sensors. A reduced order model consisting of the mean and the first two modes reconstructs well the largest structures of the flow but, as expected, does not reproduce the finer features.