Related papers: Articulated Shape Matching Using Laplacian Eigenfu…

Graph alignment, the problem of identifying corresponding nodes across multiple graphs, is fundamental to numerous applications. Most existing unsupervised methods embed node features into latent representations to enable cross-graph…

Modern data introduces new challenges to classic signal processing approaches, leading to a growing interest in the field of graph signal processing. A powerful and well established model for real world signals in various domains is sparse…

The standard approach to representation learning on attributed graphs -- i.e., simultaneously reconstructing node attributes and graph structure -- is geometrically flawed, as it merges two potentially incompatible metric spaces. This…

Graph matching---aligning a pair of graphs to minimize their edge disagreements---has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and…

The Laplacian eigenvalues of a network play an important role in the analysis of many structural and dynamical network problems. In this paper, we study the relationship between the eigenvalue spectrum of the normalized Laplacian matrix and…

Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its…

This paper presents a new axis-based shape representation scheme along with a matching framework to address the problem of generic shape recognition. The main idea is to define the relative spatial arrangement of local symmetry axes and…

A fundamental tool in shape analysis is the virtual embedding of the Riemannian manifold describing the geometry of a shape into Euclidean space. Several methods have been proposed to embed isometric shapes in flat domains while preserving…

In this paper we propose a new approach to detect clusters in undirected graphs with attributed vertices. We incorporate structural and attribute similarities between the vertices in an augmented graph by creating additional vertices and…

Spectral embedding is a procedure which can be used to obtain vector representations of the nodes of a graph. This paper proposes a generalisation of the latent position network model known as the random dot product graph, to allow…

In this paper we generalise the results on eigenvalues and eigenvectors of unnormalized (combinatorial) Laplacian of two-dimensional grid presented by Edwards:2013 first to a grid graph of any dimension, and second also to other types of…

Generating computational anatomical models of cerebrovascular networks is vital for improving clinical practice and understanding brain oxygen transport. This is achieved by extracting graph-based representations based on pre-mapping of…

We propose a principled approach for non-isometric landmark-preserving non-rigid shape matching. Our method is based on the functional maps framework, but rather than promoting isometries we focus instead on near-conformal maps that…

An automatic elastic registration method suited for vascularized organs is proposed. The vasculature in both the preoperative and intra-operative images is represented as a graph. A typical application of this method is the fusion of…

Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…

Many natural shapes have most of their characterizing features concentrated over a few regions in space. For example, humans and animals have distinctive head shapes, while inorganic objects like chairs and airplanes are made of…

For a regular polyhedron (or polygon) centered at the origin, the coordinates of the vertices are eigenvectors of the graph Laplacian for the skeleton of that polyhedron (or polygon) associated with the first (non-trivial) eigenvalue. In…

We analyze the spectral clustering procedure for identifying coarse structure in a data set $x_1, \dots, x_n$, and in particular study the geometry of graph Laplacian embeddings which form the basis for spectral clustering algorithms. More…

This paper introduces a new extension of Riemannian elastic curve matching to a general class of geometric structures, which we call (weighted) shape graphs, that allows for shape registration with partial matching constraints and…

The construction of a meaningful graph plays a crucial role in the success of many graph-based representations and algorithms for handling structured data, especially in the emerging field of graph signal processing. However, a meaningful…