A computer implemented method constructs a classifier for classifying test data. High-level features are generated from low-level features extracted from training data. The high level features are positive definite matrices in a form of an analytical manifold. A subset of the high-level features is selected. An intrinsic mean matrix is determined from the subset of the selected high-level features. Each high-level feature is mapped to a feature vector onto a tangent space of the analytical manifold using the intrinsic mean matrix. Then, an untrained classifier model can be trained with the feature vectors to obtain a trained classifier. Subsequently, the trained classifier can classify unknown test data.