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We present a latent diffusion-based differentiable inversion method (LD-DIM) for PDE-constrained inverse problems involving high-dimensional spatially distributed coefficients. LD-DIM couples a pretrained latent diffusion prior with an…
Multiple kernel learning (MKL) aims to find an optimal, consistent kernel function. In the hierarchical multiple kernel clustering (HMKC) algorithm, sample features are extracted layer by layer from a high-dimensional space to maximize the…
The geometric approach to diffeomorphic image registration known as "large deformation by diffeomorphic metric mapping" (LDDMM) is based on a left action of diffeomorphisms on images, and a right-invariant metric on a diffeomorphism group,…
Understanding the geometry of learned distributions is fundamental to improving and interpreting diffusion models, yet systematic tools for exploring their landscape remain limited. Standard latent-space interpolations fail to respect the…
We construct an extension of diffusion geometry to multiple modalities through joint approximate diagonalization of Laplacian matrices. This naturally extends classical data analysis tools based on spectral geometry, such as diffusion maps…
In this paper we describe an approach to complex Finsler metrics suitable to deal with global questions, and stressing the similarities between hermitian and complex Finsler metrics. Let $F$ be a smooth complex Finsler metric on a complex…
High-order Graph Neural Networks (HO-GNNs) have been developed to infer consistent latent spaces in the heterophilic regime, where the label distribution is not correlated with the graph structure. However, most of the existing HO-GNNs are…
Given only a collection of points sampled from a Riemannian manifold embedded in a Euclidean space, in this paper we propose a new method to solve elliptic partial differential equations (PDEs) supplemented with boundary conditions. Notice…
We consider a collection of $n$ points in $\mathbb{R}^d$ measured at $m$ times, which are encoded in an $n \times d \times m$ data tensor. Our objective is to define a single embedding of the $n$ points into Euclidean space which summarizes…
Motivated by distributed machine learning settings such as Federated Learning, we consider the problem of fitting a statistical model across a distributed collection of heterogeneous data sets whose similarity structure is encoded by a…
Recently a new feature representation and data analysis methodology based on a topological tool called persistent homology (and its corresponding persistence diagram summary) has started to attract momentum. A series of methods have been…
Graph diffusion models have made significant progress in learning structured graph data and have demonstrated strong potential for predictive tasks. Existing approaches typically embed node, edge, and graph-level features into a unified…
This paper provides a new similarity detection algorithm. Given an input set of multi-dimensional data points, where each data point is assumed to be multi-dimensional, and an additional reference data point for similarity finding, the…
Manifold learning now plays a very important role in machine learning and many relevant applications. Although its superior performance in dealing with nonlinear data distribution, data sparsity is always a thorny knot. There are few…
Let $g$ be locally homogeneous (LH) Riemannian metric on a differentiable compact manifold $M$, and $K$ be a compact Lie group endowed with an $\mathrm {ad}$-invariant inner product on its Lie algebra $\mathfrak{k}$. A connection $A$ on a…
Remote sensing pansharpening aims to reconstruct spatial-spectral properties during the fusion of panchromatic (PAN) images and low-resolution multi-spectral (LR-MS) images, finally generating the high-resolution multi-spectral (HR-MS)…
Due to the ever rising importance of the network paradigm across several areas of science, comparing and classifying graphs represent essential steps in the networks analysis of complex systems. Both tasks have been recently tackled via…
Diffusion, a fundamental internal mechanism emerging in many physical processes, describes the interaction among different objects. In many learning tasks with limited training samples, the diffusion connects the labeled and unlabeled data…
We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…
Hopfield networks (HNs) and Restricted Boltzmann Machines (RBMs) are two important models at the interface of statistical physics, machine learning, and neuroscience. Recently, there has been interest in the relationship between HNs and…