Exploring, understanding and utilizing geometric structures of big data can be of crucial importance in data analysis and machine learning algorithms. For example, the set of image patches or 3D surfaces usually stays near a low dimensional manifold. This manifold structure can be used to efficiently characterize similarities and dissimilarities. It is also desirable to design features that are invariant under certain transformations or group actions. When these features are used as input or desired properties are incorporated into learning structures and algorithms, the accuracy, efficiency, and interpretability of the whole process is significantly enhanced. In this workshop, we aim to investigate and study the possibilities and potential of the integration of geometry, modeling, and learning from theory and principle to practice and implementation in order to take advantage of both model-based and learning-based approaches.