Diffusion map embedding and gradients of functional brain organization

The talk will overview conceptual and methodological advances to study gradients in functional brain organization. It will focus on diffusion map embedding, which is a widely used non-linear technique to reduce the dimensionality of large-scale brain mapping datasets. It works by computing eigenvectors and eigenvalues of a diffusion operator applied to the data. Diffusion map embedding thereby translates short- and long-range connectivity into distance relations within a lower dimensional embedding space, where regions with similar connectivity profiles and strong inter-connectivity are close together, while regions with little inter-connectivity are dissimilar connectivity profiles are further apart.

Diffusion map embedding has several strengths: (i) it can capture non-linear relationships between data points; (ii) it maintains the global structure of the underlying data and produces easily interpretable results (e.g., connectivity gradients); and (iii) compared to other methods, diffusion map embedding is relatively robust to noise and computationally inexpensive. Limitations of diffusion maps include ease of interpretability, stability, and simplicity compared to linear methods such as PCA, which have been found to often detect similar underlying patterns in large-scale brain mapping datasets.

This talk will cover the following specific aspects of the theory and implementation of diffusion map embedding, including a (very brief and accessible) overview into its mathematics, a differentiation from other dimensionality reductions techniques, the choice of related affinity kernels and alignment techniques, and its increasing adoption to study lower dimensional spatial patterns of functional as well as structural brain organization in both humans and non-human animals.

I will furthermore provide practical guidance on how to derive, align, and visualize brain gradients via the open access BrainSpace toolbox (http://brainspace.readthedocs.io). Here, we will provide a run through to demonstrate how a few lines of python (or matlab) code can suffice to identify lower-dimensional gradients of brain organization, based on open access neuroimaging datasets.