Statistical analysis of trajectories of multi-modality data

We develop a novel comprehensive Riemannian framework for analyzing, summarizing and clustering trajectories of multi-modality data. Our framework relies on using elastic representations of functions, curves and trajectories. The elastic representations not only provide proper distances, but also solve the problem of registration. We propose a proper Riemannian metric, which is a weighted average of distances on product spaces. The metric allows for joint comparison and registration of multi-modality data. Specifically, we apply our framework to detect stimulus-relevant fiber pathways and summarize projection pathways. We evaluate our method on two real data sets. Experimental results show that we can cluster fiber pathways correctly and compute better summaries of projection pathways. The proposed framework can also be easily generalized to various applications where multi-modality data exist.