arXiv research

New DR algorithm preserves both local and global structure.

Eigen-GNN enhances GNNs by preserving graph structures.

Projection-cost preservation is a low-rank approximation guarantee which ensures that the cost of any rank-$k$ projection can be preserved using a smaller sketch of the original data matrix. We present a general structural result outlining four sufficient conditions to achieve projection-cost preservation. These condit…

Reproduces IVFS for high-dimensional data structure preservation.

GCML preserves geometric structure in manifold clustering for diverse data types.

In this paper we extend some well-known rigidity results for conformal changes of Einstein metrics to the class of generalized quasi-Einstein (GQE) metrics, which includes gradient Ricci solitons. In order to do so, we introduce the notions of conformal diffeomorphisms and vector fields that preserve a GQE structure. W…

Geometric framework for SPD matrices preserving subspace structures.

Study preserves symplectic structure in forced discrete mechanical systems.

Paper proposes G-CRD to improve GNNs by preserving global graph topology.

DMT enhances deep neural networks to better preserve data structures.

New method preserves MHD equations on sphere without costly matrix exponentials.

Text style transfer aims to modify the style of a sentence while keeping its content unchanged. Recent style transfer systems often fail to faithfully preserve the content after changing the style. This paper proposes a structured content preserving model that leverages linguistic information in the structured fine-gra…

New integrators preserve geometric structure in Hamiltonian systems.

Method preserves correlations in synthetic data.

Establishes correspondence between Calabi-Yau and Landau-Ginzburg structures.

New saddle network architectures preserve convex-concave geometry in optimization problems.

We prove that certain volume preserving actions of Lie groups and their lattices do not preserve rigid geometric structures in the sense of Gromov. The actions considered are the "exotic" examples obtained by Katok and Lewis and the first author, by blowing up closed orbits in the well known actions on homogeneous spac…

Paper proposes a new method for supervised manifold learning using random forest proximities.

Domain adaptation aims to assist the modeling tasks of the target domain with knowledge of the source domain. The two domains often lie in different feature spaces due to diverse data collection methods, which leads to the more challenging task of heterogeneous domain adaptation (HDA). A core issue of HDA is how to pre…

Pluriclosed flow preserves Hermitian-symplectic structures and forms, with topological constraints.

We study a class of continuous deformations of branched complex projective structures on closed surfaces of genus $g\geq 2$, which preserve the holonomy representation of the structure and the order of the branch points. In the case of non-elementary holonomy we show that when the underlying complex structure is infini…

Structure-preserving GANs learn distributions with group symmetry efficiently.

Dimensionality reduction is an important operation in information visualization, feature extraction, clustering, regression, and classification, especially for processing noisy high dimensional data. However, most existing approaches preserve either the global or the local structure of the data, but not both. Approache…

Network embedding is the process of learning low-dimensional representations for nodes in a network, while preserving node features. Existing studies only leverage network structure information and focus on preserving structural features. However, nodes in real-world networks often have a rich set of attributes providi…

Optimal transport for vector Gaussian mixtures improves efficiency and structure preservation.

We present a numerical approach for approximating unknown Hamiltonian systems using observation data. A distinct feature of the proposed method is that it is structure-preserving, in the sense that it enforces conservation of the reconstructed Hamiltonian. This is achieved by directly approximating the underlying unkno…

Holonomy-preserving transformations help recover Alexander polynomials from graph zeta functions.

Study focuses on classifying special geometric structures.

In the last two decades, significant effort has been put in understanding and designing so-called structure-preserving numerical methods for the simulation of mechanical systems. Geometric integrators attempt to preserve the geometry associated to the original system as much as possible, such as the structure of the co…

In this article we introduce order preserving representations of fundamental groups of surfaces into Lie groups with bi-invariant orders. By relating order preserving representations to weakly maximal representations, introduced in arXiv:1305.2620, we show that order preserving representations into Lie groups of Hermit…

We prove an existence result for local and global G-structure preserving affine immersions between affine manifolds. Several examples are discussed in the context of Riemannian and semi-Riemannian geometry, including the case of isometric immersions into Lie groups endowed with a left-invariant metric, and the case of …

Every homeomorphism of Euclidean space is a commutator of two homeomorphisms.

Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have not been well studied. Our key contribution is to show that $2K$ projection vect…

PCA-Guided Quantile Sampling preserves data structure in large datasets.

We generalize the hyperkaehler quotient construction to the situation where there is no group action preserving the hyperkaehler structure but for each complex structure there is an action of a complex group preserving the corresponding complex symplectic structure. Many (known and new) hyperkaehler manifolds arise as …

Union of Subspaces (UoS) is a popular model to describe the underlying low-dimensional structure of data. The fine details of UoS structure can be described in terms of canonical angles (also known as principal angles) between subspaces, which is a well-known characterization for relative subspace positions. In this pa…

The Ricci flow preserves product structures with instantaneous curvature bounds.

Bispectral OT improves dataset comparison by preserving intrinsic coherence.

Let $\imath: M\to \RR^{p+2}$ be a smooth embedding from a connected, oriented, closed $p$-dimesional smooth manifold to $\RR^{p+2}$, then there is a spin structure $\imath^\sharp(ς^{p+2})$ on $M$ canonically induced from the embedding. If an orientation-preserving diffeomorphism $τ$ of $M$ extends over $\imath$ as an o…

Proof that m-shifted symplectic forms are preserved under Morita equivalence of Lie n-groupoids.

Enhances machine learning models by preserving data structure, addressing statistical distortions.

For actions with a dense orbit of a connected noncompact simple Lie group $G$, we obtain some global rigidity results when the actions preserve certain geometric structures. In particular, we prove that for a $G$-action to be equivalent to one on a space of the form $(G\times K\backslash H)/Γ$, it is necessary and suff…

A fast method learns plasma collision kernels from simulations, improving kinetic models.

The paper explores the connection between Poisson-Lie structures and invariant volume forms in Hamiltonian dynamics.

Brain networks have received considerable attention given the critical significance for understanding human brain organization, for investigating neurological disorders and for clinical diagnostic applications. Structural brain network (e.g. DTI) and functional brain network (e.g. fMRI) are the primary networks of inte…

This paper develops embeddings that preserve likelihood-based statistical inference.

Paper shows geometric properties preserved by compactifications in relation to coarse structures and group actions.

EPNE models evolving network patterns for better predictions.