A method constructs a classifier from training data and detects moving objects in test data using the trained classifier. High-level features are generated from low-level features extracted from training data. The high level features are positive definite matrices on an analytical manifold. A subset of the high-level features is selected, and an intrinsic mean matrix is determined. Each high-level feature is mapped to a feature vector on a tangent space of the analytical manifold using the intrinsic mean matrix. An untrained classifier is trained with the feature vectors to obtain a trained classifier. Test high-level features are similarly generated from test low-level features. The test high-level features are classified using the trained classifier to detect moving objects in the test data.