We propose a scalable, divide-and-conquer decision tree framework for high-resolution imaging regression, which operates in two stages to handle cases where the input image has high resolution. Our framework offers an efficient approach to managing the complexity of high-resolution tensor data while maintaining interpretability. We show that our model outperforms other tensor regression models using simulated data and provide results from the application to a neuroimaging dataset.

Topology can extract the structural information in a dataset efficiently. In this paper, we attempt to incorporate topological information into a multiple output Gaussian process model for transfer learning purposes. To achieve this goal, we extend the framework of circular coordinates into a novel framework of mixed valued coordinates to take linear trends in the time series into consideration.One of the major challenges to learn from multiple time series effectively via a multiple output Gaussian process model is constructing a functional kernel. We propose to use topologically induced clustering to construct a cluster based kernel in a multiple output Gaussian process model. This kernel not only incorporates the topological structural information, but also allows us to put forward a unified framework using topological information in time and motion series.

We propose a method which jointly incorporates geometric and topological information to simultaneously estimate boundaries for objects in images with more complex topologies. We use a topological clustering-based method to assist the initialization of the Bayesian active contour model. When applied separately, the topological clustering is not robust to background noise, while active contour methods are known to be extremely sensitive to algorithm initialization. Our proposed topologically guided method provides an interpretable, principled initialization in these settings, which avoids potential pitfalls associated with these types of objects. We provide a simulation study comparing our initialization to boundary estimates obtained from standard segmentation algorithms on simulated images, and then demonstrate our method successfully on real-world applications with skin lesions and neural cellular images, for which multiple topological features can be identified automatically.