Related papers: Construction of Tight Frames on Graphs and Applica…
Abstract notions of convexity over the vertices of a graph, and corresponding notions of halfspaces, have recently gained attention from the machine learning community. In this work we study monophonic halfspaces, a notion of graph…
Geometric data analysis relies on graphs that are either given as input or inferred from data. These graphs are often treated as "correct" when solving downstream tasks such as graph signal denoising. But real-world graphs are known to…
Structured prediction tasks in machine learning involve the simultaneous prediction of multiple labels. This is typically done by maximizing a score function on the space of labels, which decomposes as a sum of pairwise elements, each…
We address the efficiency issue for the construction of a deep graph neural network (GNN). The approach exploits the idea of representing each input graph as a fixed point of a dynamical system (implemented through a recurrent neural…
The ability of deep neural networks to learn hierarchical features is widely regarded as a key mechanism underlying their success in high-dimensional learning. Existing theory partially supports this view by establishing approximation rates…
In this paper, a unified framework for representing uncertain information based on the notion of an interval structure is proposed. It is shown that the lower and upper approximations of the rough-set model, the lower and upper bounds of…
We introduce in this paper a new summarization method for large graphs. Our summarization approach retains only a user-specified proportion of the neighbors of each node in the graph. Our main aim is to simplify large graphs so that they…
We enhance the approximation capabilities of algebraic polynomials by composing them with homeomorphisms. This composition yields families of functions that remain dense in the space of continuous functions, while enabling more accurate…
By universal formulas we understand parameterized analytic expressions that have a fixed complexity, but nevertheless can approximate any continuous function on a compact set. There exist various examples of such formulas, including some in…
Dictionary learning is the task of determining a data-dependent transform that yields a sparse representation of some observed data. The dictionary learning problem is non-convex, and usually solved via computationally complex iterative…
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
Abstraction and refinement is widely used in software development. Such techniques are valuable since they allow to handle even more complex systems. One key point is the ability to decompose a large system into subsystems, analyze those…
When approaching graph signal processing tasks, graphs are usually assumed to be perfectly known. However, in many practical applications, the observed (inferred) network is prone to perturbations which, if ignored, will hinder performance.…
In this paper, we introduce robust and synergetic hand-crafted features and a simple but efficient deep feature from a convolutional neural network (CNN) architecture for defocus estimation. This paper systematically analyzes the…
Deep functional map frameworks are widely employed for 3D shape matching. However, most existing deep functional map methods cannot adaptively capture important frequency information for functional map estimation in specific matching…
A novel approach is put forth that utilizes data similarity, quantified on a graph, to improve upon the reconstruction performance of principal component analysis. The tasks of data dimensionality reduction and reconstruction are formulated…
This paper aims to provide a novel design of a multiscale framelet convolution for spectral graph neural networks (GNNs). While current spectral methods excel in various graph learning tasks, they often lack the flexibility to adapt to…
Frame theory provides a robust method for recovering vectors in a Hilbert space from inner product data, though the associated decomposition formula can be computationally demanding. We relax the frame condition by studying sequences that…
We introduce the Density Formula for (topological) drawings of graphs in the plane or on the sphere, which relates the number of edges, vertices, crossings, and sizes of cells in the drawing. We demonstrate its capability by providing…
The theory of sparse structures usually uses tree like structures as building blocks. In the context of sparse/dense dichotomy this role is played by graphs with bounded tree depth. In this paper we survey results related to this concept…