Kernel-based methods are powerful tools that are widely applied in many applications and fields of research. In recent years, methods from computational topology have emerged for characterizing the intrinsic geometry of data. Persistence homology is a central tool in topological data analysis, which allows to capture the evolution of topological features of the data. Persistence diagrams represent a natural way to summarize these features, but they can not be directly used in machine learning algorithms. To deal with them, we first analyse various kernel-based methods of recent development, then we propose and apply Variable Scaled Kernels (VSKs) to the persistence diagrams framework. We therefore discuss the application of these kernels in medical imaging in the context of Alzheimer’s Disease classification. Taking into account the
cortical thickness measures on the cortical surface, we build the
persistence diagrams upon different MRI subjects and we perform some classification tests using the support vector machines classifier.ope
