The high-dimensional data created by high-throughput technologies require visualization
tools that reveal data structure and patterns in an intuitive form. We present PHATE, a …

Finding meaningful representations and distances of hierarchical data is important in many
fields. This paper presents a new method for hierarchical data embedding and distance. Our …

The low-dimensional manifold of image patches has been introduced as regularizer term,
and shown effective in hyperspectral image inpainting. However, in this article, we find that …

Although data diffusion embeddings are ubiquitous in unsupervised learning and have
proven to be a viable technique for uncovering the underlying intrinsic geometry of data …

With the advent of high-throughput technologies measuring high-dimensional biological
data, there is a pressing need for visualization tools that reveal data structure and emergent …

In the era of 'Big Data'there is a pressing need for tools that provide human interpretable
visualizations of emergent patterns in high-throughput high-dimensional data. Further, to …

We prove an inequality with applications to solutions of the Schrödinger equation. There is a
universal constant c> 0 such that if is simply connected, vanishes on the boundary∂ Ω, and …

We describe a way of detecting the location of localized eigenvectors of the eigenvalue
problem Ax= λ x A x= λ x for eigenvalues λ λ with| λ|| λ| comparatively large. We define the …

The shortest-path, commute time, and diffusion distances on undirected graphs have been
widely employed in applications such as dimensionality reduction, link prediction, and trip …

Recent advances in experimental methods in neuroscience enable measuring in-vivo
activity of large populations of neurons at cellular level resolution. To leverage the full …