Representing videos by densely extracted local space-time features has recently become a popular approach for analysing actions. In this study, the authors tackle the problem of categorising human actions by devising bag of words (BoWs) models based on covariance matrices of spatiotemporal features, with the features formed from histograms of optical flow. Since covariance matrices form a special type of Riemannian manifold, the space of symmetric positive definite (SPD) matrices, non-Euclidean geometry should be taken into account while discriminating between covariance matrices. To this end, the authors propose to embed SPD manifolds to Euclidean spaces via a diffeomorphism and extend the BoW approach to its Riemannian version. The proposed BoW approach takes into account the manifold geometry of SPD matrices during the generation of the codebook and histograms. Experiments on challenging human action datasets show that the proposed method obtains notable improvements in discrimination accuracy, in comparison with several state-of-the-art methods.