Related papers: Heat Kernel Smoothing in Irregular Image Domains

Networks constitute fundamental organizational structures across biological systems, although conventional graph-theoretic analyses capture exclusively pairwise interactions, thereby omitting the intricate higher-order relationships that…

Tree kernels have demonstrated their ability to deal with hierarchical data, as the intrinsic tree structure often plays a discriminative role. While such kernels have been successfully applied to various domains such as nature language…

A diagramatic heat kernel expansion technique is presented. The method is especially well suited to the small-derivative expansion of the heat kernel, but it can also be used to reproduce the results obtained by the approach known as…

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression…

Under the assumption that data lie on a compact (unknown) manifold without boundary, we derive finite sample bounds for kernel smoothing and its (first and second) derivatives, and we establish asymptotic normality through Berry-Esseen type…

This paper proposes nonparametric kernel-smoothing estimation for panel data to examine the degree of heterogeneity across cross-sectional units. We first estimate the sample mean, autocovariances, and autocorrelations for each unit and…

Graph convolutional networks gain remarkable success in semi-supervised learning on graph structured data. The key to graph-based semisupervised learning is capturing the smoothness of labels or features over nodes exerted by graph…

We introduce a new technique to visualize complex flowing phenomena by using concepts from shape analysis. Our approach uses techniques that examine the intrinsic geometry of manifolds through their heat kernel, to obtain representations of…

Shape-based regularization has proven to be a useful method for delineating objects within noisy images where one has prior knowledge of the shape of the targeted object. When a collection of possible shapes is available, the specification…

The availability of graph data with node attributes that can be either discrete or real-valued is constantly increasing. While existing kernel methods are effective techniques for dealing with graphs having discrete node labels, their…

Among the available perturbative approaches in quantum field theory, heat kernel techniques provide a powerful and geometrically transparent framework for computing effective actions in nontrivial backgrounds. In this work, resummation…

Topological data analysis is an emerging mathematical concept for characterizing shapes in multi-scale data. In this field, persistence diagrams are widely used as a descriptor of the input data, and can distinguish robust and noisy…

Directional data consist of observations distributed on a (hyper)sphere, and appear in many applied fields, such as astronomy, ecology, and environmental science. This paper studies both statistical and computational problems of kernel…

High dimensional structured data such as text and images is often poorly understood and misrepresented in statistical modeling. The standard histogram representation suffers from high variance and performs poorly in general. We explore…

We propose a spherical kernel for efficient graph convolution of 3D point clouds. Our metric-based kernels systematically quantize the local 3D space to identify distinctive geometric relationships in the data. Similar to the regular grid…

We establish a new formula for the heat kernel on regular trees in terms of classical I-Bessel functions. Although the formula is explicit, and a proof is given through direct computation, we also provide a conceptual viewpoint using the…

Network theory provides a principled abstraction of the human brain: reducing a complex system into a simpler representation from which to investigate brain organisation. Recent advancement in the neuroimaging field are towards representing…

In recent years, quantities derived from the heat equation have become popular in shape processing and analysis of triangulated surfaces. Such measures are often robust with respect to different kinds of perturbations, including…

This paper introduces a novel, non-deterministic method for embedding data in low-dimensional Euclidean space based on computing realizations of a Gaussian process depending on the geometry of the data. This type of embedding first appeared…

We propose a neural network for 3D point cloud processing that exploits `spherical' convolution kernels and octree partitioning of space. The proposed metric-based spherical kernels systematically quantize point neighborhoods to identify…