Related papers: Nonlinear Metric Learning through Geodesic Interpo…

Fusion learning refers to synthesizing inferences from multiple sources or studies to provide more effective inference and prediction than from any individual source or study alone. Most existing methods for synthesizing inferences rely on…

In this work, we propose to study the global geometrical properties of generative models. We introduce a new Riemannian metric to assess the similarity between any two data points. Importantly, our metric is agnostic to the parametrization…

Deep metric learning has yielded impressive results in tasks such as clustering and image retrieval by leveraging neural networks to obtain highly discriminative feature embeddings, which can be used to group samples into different classes.…

Deep metric learning maps visually similar images onto nearby locations and visually dissimilar images apart from each other in an embedding manifold. The learning process is mainly based on the supplied image negative and positive training…

Development of comprehensive prediction models are often of great interest in many disciplines of science, but datasets with information on all desired features often have small sample sizes. We describe a transfer learning approach for…

A basic problem in machine learning is to find a mapping $f$ from a low dimensional latent space $\mathcal{Y}$ to a high dimensional observation space $\mathcal{X}$. Modern tools such as deep neural networks are capable to represent general…

Many recent efforts have been devoted to designing sophisticated deep learning structures, obtaining revolutionary results on benchmark datasets. The success of these deep learning methods mostly relies on an enormous volume of labeled…

We present parameter-interpolated dynamic mode decomposition (piDMD), a parametric reduced-order modeling framework that embeds known parameter-affine structure directly into the DMD regression step. Unlike existing parametric DMD methods…

We introduce a generative learning framework to model high-dimensional parametric systems using gradient guidance and virtual observations. We consider systems described by Partial Differential Equations (PDEs) discretized with structured…

A wide range of applications require learning image generation models whose latent space effectively captures the high-level factors of variation present in the data distribution. The extent to which a model represents such variations…

This paper prescribes a distance between learning tasks modeled as joint distributions on data and labels. Using tools in information geometry, the distance is defined to be the length of the shortest weight trajectory on a Riemannian…

Locally Linear Embedding (LLE) is a nonlinear spectral dimensionality reduction and manifold learning method. It has two main steps which are linear reconstruction and linear embedding of points in the input space and embedding space,…

Non-linear dimensionality reduction can be performed by \textit{manifold learning} approaches, such as Stochastic Neighbour Embedding (SNE), Locally Linear Embedding (LLE) and Isometric Feature Mapping (ISOMAP). These methods aim to produce…

Given a graph or similarity matrix, we consider the problem of recovering a notion of true distance between the nodes, and so their true positions. We show that this can be accomplished in two steps: matrix factorisation, followed by…

This paper presents a novel method, named geodesic deformable networks (GDN), that for the first time enables the learning of geodesic flows of deformation fields derived from images. In particular, the capability of our proposed GDN being…

Dilated Convolution with Learnable Spacings (DCLS) is a recently proposed variation of the dilated convolution in which the spacings between the non-zero elements in the kernel, or equivalently their positions, are learnable. Non-integer…

We present $\texttt{LAMINAR}$, a novel unsupervised machine learning pipeline designed to enhance the representation of structure within data via producing a more-informative distance metric. Analysis methods in the physical sciences often…

In this paper we devise a systematic procedure to obtain nonlocal symmetries of a class of scalar nonlinear ordinary differential equations (ODEs) of arbitrary order related to linear ODEs through nonlocal relations. The procedure makes use…

In the article, we discuss the architecture of the polynomial neural network that corresponds to the matrix representation of Lie transform. The matrix form of Lie transform is an approximation of the general solution of the nonlinear…

For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its…