We intend to provide advances in computational topology from a theoretical point of view together with applications that include, among others, computer vision applications and the study of neural networks in the context of topology, linking these areas. Our specific scientific aims are:
- To classify and recognize properties of very diverse datasets, such as, characterizing cell configurations in epithelial tissues, gait recognition, talking-face emotion recognition, to provide metrics to distinguish literary styles etc.
- To develop new computational topology tools that serve to extract new properties from data sets
- To provide a robust artificial neural network architecture based on Topology that allows to interpret and explain the decisions made by the network.