Modern data science problems related to detection, estimation, clustering, and classification using data emanating from physical sensors (e.g. signals and images ) often pose difficult challenges due to nonlinearities present when modeling complex phenomena. When data is generated from processes related to transport phenomena, solutions based on optimal transport and other Lagrangian embeddings capable of yielding high accuracy solutions for low computational cost have emerged. We will define transport-based techniques are able to fully represent signals and image and can be viewed as mathematical transforms. We describe some of their mathematical properties related to partitioning data classes and nonlinear estimation problems, thus supporting high classification accuracy in certain signal and image processing-related data science problems. Results with simulated and real data are shown.