Manifold learning (ML), also known as nonlinear dimension reduction, is a set of methods to
find the low-dimensional structure of data. Dimension reduction for large, high-dimensional …

Graph theory is now becoming a standard tool in system-level neuroscience. However,
endowing observed brain anatomy and dynamics with a complex network structure does not …

Abstract Convolutional Neural Networks (CNNs) are a cornerstone of the Deep Learning
toolbox and have led to many breakthroughs in Artificial Intelligence. So far, these neural …

We study the convergence of the graph Laplacian of a random geometric graph generated
by an iid sample from am-dimensional submanifold MM in R^ d R d as the sample size n …

Gaussian processes are a versatile framework for learning unknown functions in a manner
that permits one to utilize prior information about their properties. Although many different …

Comparison among graphs is ubiquitous in graph analytics. However, it is a hard task in
terms of the expressiveness of the employed similarity measure and the efficiency of its …

Current methods for comparing single-cell RNA sequencing datasets collected in multiple
conditions focus on discrete regions of the transcriptional state space, such as clusters of …

We introduce vector diffusion maps (VDM), a new mathematical framework for organizing
and analyzing massive high‐dimensional data sets, images, and shapes. VDMis a …

We develop a framework for dimension reduction, mode decomposition, and nonparametric
forecasting of data generated by ergodic dynamical systems. This framework is based on a …

Designing a convolution for a spherical neural network requires a delicate tradeoff between
efficiency and rotation equivariance. DeepSphere, a method based on a graph …