Related papers: Irregular Shearlet Frames: Geometry and Approximat…

3D generative modeling is accelerating as the technology allowing the capture of geometric data is developing. However, the acquired data is often inconsistent, resulting in unregistered meshes or point clouds. Many generative learning…

We propose a means of computing fitted frames on the boundary and in the interior of objects and using them to provide the basis for producing geometric features from them that are not only alignment-free but most importantly can be made to…

Numerical simulations are a key tool to decipher the dynamics of gravitation. Yet, they fail to spatially reproduce the Universe we observe, limiting comparison between observations and simulations to a statistical level. This is highly…

This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…

The scattering transform is a multilayered, wavelet-based transform initially introduced as a model of convolutional neural networks (CNNs) that has played a foundational role in our understanding of these networks' stability and invariance…

Image classifiers are known to be difficult to interpret and therefore require explanation methods to understand their decisions. We present ShearletX, a novel mask explanation method for image classifiers based on the shearlet transform --…

In this paper, a novel unsupervised low-rank representation model, i.e., Auto-weighted Low-Rank Representation (ALRR), is proposed to construct a more favorable similarity graph (SG) for clustering. In particular, ALRR enhances the…

The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…

This paper presents a novel machine learning framework to consistently detect, localize and rate congenital cleft lip anomalies in human faces. The goal is to provide a universal, objective measure of facial differences and reconstructive…

Molecular self-assembly plays a very important role in various aspects of technology as well as in biological systems. Governed by the covalent, hydrogen or van der Waals interactions - self-assembly of alike molecules results in a large…

A geometric model of sparse signal representations is introduced for classes of signals. It is computed by optimizing co-occurrence groups with a maximum likelihood estimate calculated with a Bernoulli mixture model. Applications to face…

Recently, shearlet groups have received much attention in connection with shearlet transforms applied for orientation sensitive image analysis and restoration. The square integrable representations of the shearlet groups provide not only…

Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…

Following the development of weighted asymptotic approximation properties of matrices, we introduce the analogous uniform approximation properties (that is, study the improvability of Dirichlet's Theorem). An added feature is the use of…

Geometry can be used to explain many properties commonly observed in real networks. It is therefore often assumed that real networks, especially those with high average local clustering, live in an underlying hidden geometric space.…

This paper introduces a new shape-matching methodology, combinative matching, to combine interlocking parts for geometric shape assembly. Previous methods for geometric assembly typically rely on aligning parts by finding identical surfaces…

We present a novel shape-approximating anisotropic re-meshing algorithm as a geometric generalization of the adaptive moving mesh method. Conventional moving mesh methods reduce the interpolation error of a mesh that discretizes a given…

Sparse regression and classification estimators that respect group structures have application to an assortment of statistical and machine learning problems, from multitask learning to sparse additive modeling to hierarchical selection.…

The sparse representation of signals defined on Euclidean domains has been successfully applied in signal processing. Bringing the power of sparse representations to non-regular domains is still a challenge, but promising approaches have…