Partial Differential Equations (PDEs) and variational methods are widely used for many tasks in Image processing and analysis: filtering, segmentation, interpolation, etc. In this talk I will discuss recent works of their extension from Image processing to machine learning problems such as classification and clustering. These works are based on the framework of Partial difference Equations (PdEs) on graphs. I will show examples of applications in cytopathology such as filtering, segmentation for nucleus extraction, and nucleus classification, using the same framework.