Related papers: Geometric compression for progressive transmission

In this paper, we present a novel compression framework, TFZ, that preserves the topology of 2D symmetric and asymmetric second-order tensor fields defined on flat triangular meshes. A tensor field assigns a tensor - a multi-dimensional…

We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…

Meshes are widely used in 3D computer vision and graphics, but their irregular topology poses challenges in applying them to existing neural network architectures. Recent advances in mesh neural networks turn to remeshing and push the…

We present a geometric framework for regression on structured high-dimensional data that shifts the analysis from the ambient space to a geometric object capturing the data's intrinsic structure. The method addresses a fundamental challenge…

Today, with the growing demands of information storage and data transfer, data compression is becoming increasingly important. Data Compression is a technique which is used to decrease the size of data. This is very useful when some huge…

The encoding of input parameters is one of the fundamental building blocks of neural network algorithms. Its goal is to map the input data to a higher-dimensional space, typically supported by trained feature vectors. The mapping is crucial…

Utilizing patch-based transformers for unstructured geometric data such as polygon meshes presents significant challenges, primarily due to the absence of a canonical ordering and variations in input sizes. Prior approaches to handling 3D…

Applications that require Internet access to remote 3D datasets are often limited by the storage costs of 3D models. Several compression methods are available to address these limits for objects represented by triangle meshes. Many CAD and…

Relational representation learning transforms relational data into continuous and low-dimensional vector representations. However, vector-based representations fall short in capturing crucial properties of relational data that are complex…

Embedding tables are used by machine learning systems to work with categorical features. In modern Recommendation Systems, these tables can be very large, necessitating the development of new methods for fitting them in memory, even during…

Graph compression is a data analysis technique that consists in the replacement of parts of a graph by more general structural patterns in order to reduce its description length. It notably provides interesting exploration tools for the…

A matrix-compression algorithm is derived from a novel isogenic block decomposition for square matrices. The resulting compression and inflation operations possess strong functorial and spectral-permanence properties. The basic observation…

Various graphs such as web or social networks may contain up to trillions of edges. Compressing such datasets can accelerate graph processing by reducing the amount of I/O accesses and the pressure on the memory subsystem. Yet, selecting a…

A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…

Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…

Geometric trees are characterized by their tree-structured layout and spatially constrained nodes and edges, which significantly impacts their topological attributes. This inherent hierarchical structure plays a crucial role in domains such…

Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…

A textile structure is a periodic arrangement of threads in the thickened plane. A topological classification of textile structures is harder than for classical knots and links that are non-periodic and restricted to a bounded region. The…

Geometric relational embeddings map relational data as geometric objects that combine vector information suitable for machine learning and structured/relational information for structured/relational reasoning, typically in low dimensions.…

Meshes are ubiquitous in visual computing and simulation, yet most existing machine learning techniques represent meshes only indirectly, e.g. as the level set of a scalar field or deformation of a template, or as a disordered triangle soup…