In their recent paper, Wang et al. propose a few updates to the Graph Attention Network (GAT) neural network algorithm (if you want to skip the technical bit and get to the code, click here). Briefly, GATs are a recently-developed neural network architecture applied to data distributed over a graph domain. We can think of graph convolutional networks as progressively transforming and aggregating signals from within a local neighborhood of a node. At each iteration of this process, we implicitly merge signals from larger and larger neighborhoods of the node of interest, and thereby learn unique representations of nodes that are dependent on their surroundings.
As I mentioned in my previous post, I work with cortical surface segmentation data. Due to the biology of the human brain, there is considerable reproducible structure and function across individuals (thankfully!). One manifestation of this reproducibility is exemplified by the neocortex a.k.a. the thin (~2.5mm) gray matter layer of cell-bodies at the periphery of the brain. The neocortex is well known to have local homogeneity in terms of types of neuronal cells, protein and gene expression, and large-scale function, for example. Naturally, researchers have been trying to identify discrete delineations of the cortex for nearly 100 years, by looking for regions of local homogeneity of various features along the cortical manifold.
I’m using graph convolutional networks as a tool to segment the cortical surface of the brain. This research resides in the domain of node classification using inductive learning. By node classification, I mean that we wish to assign a discrete label to cortical surface locations (nodes / vertices in a graph) on the basis of some feature data and brain network topology. By inductive learning, I mean that we will train, validate, and test on datasets with possibly different graph topologies – this is in contrast to transductive learning that learns models that do not generalize to arbitrary network topology.
I’m working with some multi-dimensional float-valued data – I’ll call a single instance of this data $X \in \mathbb{R}^{n \times k}$. I have multiple samples $X_{1}, X_{2}…X_{t}$, and want to compare these subspaces – namely, I want to compute the distance between pairs of subspaces.
What follows are the contents of part of a lab meeting presentation I gave recently. The topic of the meeting was “Python for Neuroimaging”, where I covered basic software development tools that brain imaging scientists might be interested in.
I’m fortunate enought to work in a lab with some high-level computing infrastructure. We have a cluster of machines using the
Sun Grid Engine (SGE) software system for distributed resource management. The other day, I was searching for how to wrap my Python scripts with qsub so that I could submit a batch of jobs to our cluster. Eventually, I want to be able to submit jobs with dependencies between them, but we’ll start here.
I’m applying some methods developed in this paper for testing purposes in my own thesis research. Specifically, I have some float-valued data, $F$, that varies along the cortical surface of the brain. Visually, I can see that there are areas where these scalar maps change abruptly. I want to identify these boundaries – eventually, I’ll segment out the regions I’m interested in.
The other day, one of my friends and colleagues (I’ll refer to him as “Dr. A”) asked me if I knew anything about assessing biomarker diagnostic power. He went on to describe his clinical problem, which I’ll try to recount here (but will likely mess up some of the relevant detail – his research pertains to generating induced pluripotent cardiac stem cells, which I have little to no experience with):
Here, we’ll look at various applications of the Delta Method, especially in the context of variance stabilizing transformations, along with looking at the confidence intervals of estimates.
The Delta Method is used as a way to approximate the Standard Error of transformations of random variables, and is based on a Taylor Series approximation.
For one of the projects I’m working on, I have an array of multivariate data relating to brain connectivity patterns. Briefly, each brain is represented as a surface mesh, which we represent as a graph $G = (V,E)$, where $V$ is a set of $n$ vertices, and $E$ is the set of edges between vertices.