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Traditional methods employed in matrix volatility forecasting often overlook the inherent Riemannian manifold structure of symmetric positive definite matrices, treating them as elements of Euclidean space, which can lead to suboptimal…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
Machine unlearning methods have become increasingly important for selective concept removal in large pre-trained models. While recent work has explored unlearning in Euclidean contrastive vision-language models, the effectiveness of concept…
Unsupervised Deep Distance Metric Learning (UDML) aims to learn sample similarities in the embedding space from an unlabeled dataset. Traditional UDML methods usually use the triplet loss or pairwise loss which requires the mining of…
A robust and informative local shape descriptor plays an important role in mesh registration. In this regard, spectral descriptors that are based on the spectrum of the Laplace-Beltrami operator have been a popular subject of research for…
Deep metric learning (DML) is a cornerstone of many computer vision applications. It aims at learning a mapping from the input domain to an embedding space, where semantically similar objects are located nearby and dissimilar objects far…
This paper investigates the notion of learning user and item representations in non-Euclidean space. Specifically, we study the connection between metric learning in hyperbolic space and collaborative filtering by exploring Mobius…
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…
Learning for robot navigation presents a critical and challenging task. The scarcity and costliness of real-world datasets necessitate efficient learning approaches. In this letter, we exploit Euclidean symmetry in planning for 2D…
Neural networks have been successfully used as classification models yielding state-of-the-art results when trained on a large number of labeled samples. These models, however, are more difficult to train successfully for semi-supervised…
There is extensive interest in metric learning methods for image retrieval. Many metric learning loss functions focus on learning a correct ranking of training samples, but strongly overfit semantically inconsistent labels and require a…
In this paper, we propose a nonlinear dimensionality reduction algorithm for the manifold of Symmetric Positive Definite (SPD) matrices that considers the geometry of SPD matrices and provides a low dimensional representation of the…
Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…
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…
Riemannian metric learning is an emerging field in machine learning, unlocking new ways to encode complex data structures beyond traditional distance metric learning. While classical approaches rely on global distances in Euclidean space,…
Deep learning has been extensively utilized for PolSAR image classification. However, most existing methods transform the polarimetric covariance matrix into a real- or complex-valued vector to comply with standard deep learning frameworks…
This paper addresses the task of zero-shot image classification. The key contribution of the proposed approach is to control the semantic embedding of images -- one of the main ingredients of zero-shot learning -- by formulating it as a…
We consider the problem of learning distance-based Graph Convolutional Networks (GCNs) for relational data. Specifically, we first embed the original graph into the Euclidean space $\mathbb{R}^m$ using a relational density estimation…
In this paper, we explore the concept of metric-driven numerical methods as a powerful tool for solving various types of multiscale partial differential equations. Our focus is on computing constrained minimizers of functionals - or,…
This paper introduces a new metric and mean on the set of positive semidefinite matrices of fixed-rank. The proposed metric is derived from a well-chosen Riemannian quotient geometry that generalizes the reductive geometry of the positive…