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 …

In applications such as social, energy, transportation, sensor, and neuronal networks, high-
dimensional data naturally reside on the vertices of weighted graphs. The emerging field of …

High-throughput mapping of cellular differentiation hierarchies from single-cell data
promises to empower systematic interrogations of vertebrate development and disease …

This handbook provides a comprehensive and unified account of the main research
developments in cluster analysis. Written by active, distinguished researchers in this area …

Single-cell expression profiling reveals the molecular states of individual cells with
unprecedented detail. Because these methods destroy cells in the process of analysis, they …

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 …

Inverse imaging problems are inherently underdetermined, and hence, it is important to
employ appropriate image priors for regularization. One recent popular prior-the graph …

Attention based models such as Transformers involve pairwise interactions between data
points, modeled with a learnable attention matrix. Importantly, this attention matrix is …

In this paper we improve the spectral convergence rates for graph-based approximations of
weighted Laplace-Beltrami operators constructed from random data. We utilize regularity of …

We investigate a family of regression problems in a semisupervised setting. The task is to
assign real-valued labels to a set of n sample points provided a small training subset of N …