Manifold learning methods play a prominent role in nonlinear dimensionality reduction and other tasks involving high-dimensional data sets with low intrinsic dimensionality. Many of these are graph-based: they associate vertex each point weighted edge pair. Existing theory shows that the Laplacian matrix graph converges to Laplace–Beltrami operator manifold, under assumption pairwise affinities...

Graph convolutional neural networks (GCNs) have become increasingly popular in recent times due to the emerging graph data scenes such as social and recommendation systems. However, engineering are often noisy incomplete or even unavailable, making it challenging impossible implement de facto GCNs method directly on them. Current efforts for tackling this issue either require an overparameteriz...

Machine learning and deep methods have been employed in the hyperspectral image (HSI) classification field. Of methods, convolution neural network (CNN) has widely used achieved promising results. However, CNN its limitations modeling sample relations. Graph (GCN) introduced to HSI due demonstrated ability processing Introducing GCN into classification, key issue is how transform HSI, a typical...

Introduction: Appropriate definition of the distance measure between diffusion tensors has a deep impact on Diffusion Tensor Image (DTI) segmentation results. The geodesic metric is the best distance measure since it yields high-quality segmentation results. However, the important problem with the geodesic metric is a high computational cost of the algorithms based on it. The main goal of this ...

A faithful (unit) distance graph in Rd is a graph whose set of vertices is a finite subset of the d-dimensional Euclidean space, where two vertices are adjacent if and only if the Euclidean distance between them is exactly 1. A (unit) distance graph in Rd is any subgraph of such a graph. In the first part of the paper we focus on the differences between these two classes of graphs. In particula...

introduction: appropriate definition of the distance measure between diffusion tensors has a deep impact on diffusion tensor image (dti) segmentation results. the geodesic metric is the best distance measure since it yields high-quality segmentation results. however, the important problem with the geodesic metric is a high computational cost of the algorithms based on it. the main goal of this ...

Deterministic equilibrium flows in transport networks can be investigated by means of Markov's processes defined on the dual graph representations of the network. Sustained movement patterns are generated by a subset of automorphisms of the graph spanning the spatial network of a city naturally interpreted as random walks. Random walks assign absolute scores to all nodes of a graph and embed sp...

Unit-Disk Graphs (UDGs) are intersection graphs of equal diameter (or unit diameter w.l.o.g.) circles in the Euclidean plane. In the geometric (or disk) representation, each circle is specified by the coordinates of its center. Three equivalent graph models can be defined with vertices representing the circles [18]. In the intersection graph model, two vertices are adjacent if the corresponding...

Recent studies on a computationally hard visual optimization problem, the Traveling Salesperson Problem (TSP), indicate that humans are capable of finding close to optimal solutions in near-linear time. The current study is a preliminary step in investigating human performance on another hard problem, the Minimum Vertex Cover Problem, in which solvers attempt to find a smallest set of vertices ...

A greedy embedding of a graph G = (V, E) into a metric space (X, d) is a function x : V (G) → X such that in the embedding for every pair of non-adjacent vertices x(s), x(t) there exists another vertex x(u) adjacent to x(s) which is closer to x(t) than x(s). This notion of greedy embedding was defined by Papadimitriou and Ratajczak (Theor. Comput. Sci. 2005), where authors conjectured that ever...