Transport Model for Feature Extraction

We present a new feature extraction method for noisy datasets with intricate spatio-temporal structures that is based on the concept of transport operators on graphs. The proposed approach generalizes and extends the many existing data representation methodologies built upon diffusion processes to a new domain where dynamical systems play a key role. The main advantage of this approach comes from the ability to exploit different relationships than those arising in the context of, e.g., graph Laplacians. Fundamental properties of the transport operators are proved. We demonstrate the flexibility of the method by introducing several diverse examples of transformations. We close the paper with a series of computational experiments and applications to the problem of image clustering and classification of hyperspectral data, to illustrate the practical implications of our algorithm and its ability to quantify new aspects of relationships within complicated datasets.