Related papers: A Graph Framework for Manifold-valued Data

In this paper, we propose a framework for graph signal processing using category theory. The aim is to generalize a few recent works on probabilistic approaches to graph signal processing, which handle signal and graph uncertainties.

Investment returns naturally reside on irregular domains, however, standard multivariate portfolio optimization methods are agnostic to data structure. To this end, we investigate ways for domain knowledge to be conveniently incorporated…

Multiscale transforms have become a key ingredient in many data processing tasks. With technological development, we observe a growing demand for methods to cope with non-linear data structures such as manifold values. In this paper, we…

In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and…

In this paper, we develop a novel weighted Laplacian method, which is partially inspired by the theory of graph Laplacian, to study recent popular graph problems, such as multilevel graph partitioning and balanced minimum cut problem, in a…

In the vast landscape of visualization research, Dimensionality Reduction (DR) and graph analysis are two popular subfields, often essential to most visual data analytics setups. DR aims to create representations to support neighborhood and…

Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying…

In the last decade or so, we have witnessed deep learning reinvigorating the machine learning field. It has solved many problems in the domains of computer vision, speech recognition, natural language processing, and various other tasks…

Graphs may be used to represent many different problem domains -- a concrete example is that of detecting communities in social networks, which are represented as graphs. With big data and more sophisticated applications becoming widespread…

This paper is devoted to signal processing on point-clouds by means of neural networks. Nowadays, state-of-the-art in image processing and computer vision is mostly based on training deep convolutional neural networks on large datasets.…

Representing and exploiting multivariate signals requires capturing relations between variables, which we can represent by graphs. Graph dictionaries allow to describe complex relational information as a sparse sum of simpler structures,…

Graph-structured data is a type of data to be obtained associated with a graph structure where vertices and edges describe some kind of data correlation. This paper proposes a regression method on graph-structured data, which is based on…

Theoretical analyses for graph learning methods often assume a complete observation of the input graph. Such an assumption might not be useful for handling any-size graphs due to the scalability issues in practice. In this work, we develop…

Graph-based variational methods have recently shown to be highly competitive for various classification problems of high-dimensional data, but are inherently difficult to handle from an optimization perspective. This paper proposes a convex…

Graphs are ubiquitous, and learning on graphs has become a cornerstone in artificial intelligence and data mining communities. Unlike pixel grids in images or sequential structures in language, graphs exhibit a typical non-Euclidean…

This paper uses the technology of weighted and regular triangulations to study discrete versions of the Laplacian on piecewise Euclidean manifolds. Regular triangulations are studied in some detail, including flip algorithms. The Laplacian…

Current image processing methods usually operate on the finest-granularity unit; that is, the pixel, which leads to challenges in terms of efficiency, robustness, and understandability in deep learning models. We present an improved…

The value of graph-based big data can be unlocked by exploring the topology and metrics of the networks they represent, and the computational approaches to this exploration take on many forms. The use-case of performing global computations…

The common graph Laplacian regularizer is well-established in semi-supervised learning and spectral dimensionality reduction. However, as a first-order regularizer, it can lead to degenerate functions in high-dimensional manifolds. The…

One of the main challenges in using deep learning-based methods for simulating physical systems and solving partial differential equations (PDEs) is formulating physics-based data in the desired structure for neural networks. Graph neural…