Related papers: Spectral Flow on the Manifold of SPD Matrices for …
We introduce a novel framework that directly learns a spectral basis for shape and manifold analysis from unstructured data, eliminating the need for traditional operator selection, discretization, and eigensolvers. Grounded in…
Spectral subspaces of a linear dynamical system identify a large class of invariant structures that highlight/isolate the dynamics associated to select subsets of the spectrum. The corresponding notion for nonlinear systems is that of…
Autoencoding is a popular method in representation learning. Conventional autoencoders employ symmetric encoding-decoding procedures and a simple Euclidean latent space to detect hidden low-dimensional structures in an unsupervised way.…
We propose a framework for 2D shape analysis using positive definite kernels defined on Kendall's shape manifold. Different representations of 2D shapes are known to generate different nonlinear spaces. Due to the nonlinearity of these…
Generative modeling is typically framed as learning mapping rules, but from an observer's perspective without access to these rules, the task becomes disentangling the geometric support from the probability distribution. We propose that…
This paper introduces the sigma flow model for the prediction of structured labelings of data observed on Riemannian manifolds, including Euclidean image domains as special case. The approach combines the Laplace-Beltrami framework for…
We propose an approach for capturing the signal variability in hyperspectral imagery using the framework of the Grassmann manifold. Labeled points from each class are sampled and used to form abstract points on the Grassmannian. The…
This paper presents an overview of recent developments in the analysis of shapes such as curves and surfaces through Riemannian metrics. We show that several constructions of metrics on spaces of submanifolds can be unified through the…
The simultaneous capture of imaging data at multiple wavelengths across the electromagnetic spectrum is highly challenging, requiring complex and costly multispectral image sensors. In this study, we introduce a comprehensive framework for…
The concepts of spread and spread dimension of a metric space were introduced by Willerton in the context of quantifying biodiversity of ecosystems. This paper develops practical applications of spread dimension in the context of machine…
As a pivotal branch of machine learning, manifold learning uncovers the intrinsic low-dimensional structure within complex nonlinear manifolds in high-dimensional space for visualization, classification, clustering, and gaining key…
Symmetric Positive Definite (SPD) matrices have received wide attention in machine learning due to their intrinsic capacity to encode underlying structural correlation in data. Many successful Riemannian metrics have been proposed to…
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…
The increasing use of machine-learning (ML) enabled systems in critical tasks fuels the quest for novel verification and validation techniques yet grounded in accepted system assurance principles. In traditional system development,…
The generalization performance of kernel methods is largely determined by the kernel, but common kernels are stationary thus input-independent and output-independent, that limits their applications on complicated tasks. In this paper, we…
Learning shared representations is a primary area of multimodal representation learning. The current approaches to achieve a shared embedding space rely heavily on paired samples from each modality, which are significantly harder to obtain…
Motivated by inverse problems with a single passive measurement, we introduce and analyze a new class of inverse spectral problems on closed Riemannian manifolds. Specifically, we establish two general uniqueness results for the recovery of…
Multimodal datasets, where measurements are obtained from multiple sensors, have become central to many scientific domains. In unsupervised settings, most representation learning methods focus on identifying shared latent structures, such…
Diffusion-based manifold learning methods have proven useful in representation learning and dimensionality reduction of modern high dimensional, high throughput, noisy datasets. Such datasets are especially present in fields like biology…
We study the problem of learning local metrics for nearest neighbor classification. Most previous works on local metric learning learn a number of local unrelated metrics. While this "independence" approach delivers an increased flexibility…