Related papers: Spectral Flow on the Manifold of SPD Matrices for …

While a common assumption in graph signal analysis is the smoothness of the signals or the band-limitedness of their spectrum, in many instances the spectrum of real graph data may be concentrated at multiple regions of the spectrum,…

We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…

Heterogeneous data fusion can enhance the robustness and accuracy of an algorithm on a given task. However, due to the difference in various modalities, aligning the sensors and embedding their information into discriminative and compact…

This paper introduces an efficient multi-linear nonparametric (kernel-based) approximation framework for data regression and imputation, and its application to dynamic magnetic-resonance imaging (dMRI). Data features are assumed to reside…

Geodesic distance serves as a reliable means of measuring distance in nonlinear spaces, and such nonlinear manifolds are prevalent in the current multimodal learning. In these scenarios, some samples may exhibit high similarity, yet they…

We introduce a new technique to visualize complex flowing phenomena by using concepts from shape analysis. Our approach uses techniques that examine the intrinsic geometry of manifolds through their heat kernel, to obtain representations of…

Graphs are ubiquitous, and learning on graphs has become a cornerstone in artificial intelligence and data mining communities. Unlike pixel grids in images or sequential structures in language, graphs exhibit a typical non-Euclidean…

Modern machine learning algorithms have been adopted in a range of signal-processing applications spanning computer vision, natural language processing, and artificial intelligence. Many relevant problems involve subspace-structured…

Data encoded as symmetric positive definite (SPD) matrices frequently arise in many areas of computer vision and machine learning. While these matrices form an open subset of the Euclidean space of symmetric matrices, viewing them through…

Feature learning in the presence of a mixed type of variables, numerical and categorical types, is an important issue for related modeling problems. For simple neighborhood queries under mixed data space, standard practice is to consider…

In this work, we address the problem of cross-modal comparison of aerial data streams. A variety of simulated automobile trajectories are sensed using two different modalities: full-motion video, and radio-frequency (RF) signals received by…

Many three-dimensional spatial fields are anisotropic, with directions of rapid and slow variation that need not align with the coordinate axes. Standard Gaussian process kernels with Automatic Relevance Determination (ARD) capture only…

A particularly interesting instance of supervised learning with kernels is when each training example is associated with two objects, as in pairwise classification (Brunner et al., 2012), and in supervised learning of preference relations…

There has been increasing interest in statistical analysis of data lying in manifolds. This paper generalizes a smoothing spline fitting method to Riemannian manifold data based on the technique of unrolling and unwrapping originally…

The use of geometric and symmetry techniques in quantum and classical information processing has a long tradition across the physical sciences as a means of theoretical discovery and applied problem solving. In the modern era, the emergent…

Remote sensing image classification exploiting multiple sensors is a very challenging problem: data from different modalities are affected by spectral distortions and mis-alignments of all kinds, and this hampers re-using models built for…

Implementations of symmetric positive definite (SPD) matrix-based neural networks for neural decoding remain fragmented across research codebases and Python packages. Existing implementations often employ ad hoc handling of manifold…

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…

In recent decades, advancements in motion learning have enabled robots to acquire new skills and adapt to unseen conditions in both structured and unstructured environments. In practice, motion learning methods capture relevant patterns and…

Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric,…