Related papers: Adaptive Log-Euclidean Metrics for SPD Matrix Lear…
Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions. Here we consider an alternative, which embeds data as discrete…
Since the popularization of the Stiefel manifold for numerical applications in 1998 in a seminal paper from Edelman et al., it has been exhibited to be a key to solve many problems from optimization, statistics and machine learning. In…
In this paper, we consider a class of optimization problems constrained to the generalized Stiefel manifold. Such problems are fundamental to a wide range of real-world applications, including generalized canonical correlation analysis,…
Model-based paradigms for decision-making and control are becoming ubiquitous in robotics. They rely on the ability to efficiently learn a model of the system from data. Structured Mechanical Models (SMMs) are a data-efficient black-box…
Log Anomaly Detection (LAD) seeks to identify atypical patterns in log data that are crucial to assessing the security and condition of systems. Although Large Language Models (LLMs) have shown tremendous success in various fields, the use…
The problem of determining the configuration of points from partial distance information, known as the Euclidean Distance Geometry (EDG) problem, is fundamental to many tasks in the applied sciences. In this paper, we propose two algorithms…
Symmetric positive definite (SPD) matrices arising from functional connectivity analysis of neuroimaging data can be endowed with a Riemannian geometric structure that standard methods fail to respect. While existing R packages provide some…
We address the problem of distribution shift in unsupervised domain adaptation with a moment-matching approach. Existing methods typically align low-order statistical moments of the source and target distributions in an embedding space…
In this paper, we revamp the forgotten classical Semi-Supervised Distance Metric Learning (SSDML) problem from a Riemannian geometric lens, to leverage stochastic optimization within a end-to-end deep framework. The motivation comes from…
In this paper, we target the problem of sufficient dimension reduction with symmetric positive definite matrices valued responses. We propose the intrinsic minimum average variance estimation method and the intrinsic outer product gradient…
Stochastic minimax optimization on Riemannian manifolds has recently attracted significant attention due to its broad range of applications, such as robust training of neural networks and robust maximum likelihood estimation. Existing…
Distance metric learning aims to learn from the given training data a valid distance metric, with which the similarity between data samples can be more effectively evaluated for classification. Metric learning is often formulated as a…
Distance metric learning (DML) approaches learn a transformation to a representation space where distance is in correspondence with a predefined notion of similarity. While such models offer a number of compelling benefits, it has been…
Compressed Deep Learning (DL) models are essential for deployment in resource-constrained environments. But their performance often lags behind their large-scale counterparts. To bridge this gap, we propose Alignment Adapter (AlAd): a…
We examine a wide class of stochastic approximation algorithms for solving (stochastic) nonlinear problems on Riemannian manifolds. Such algorithms arise naturally in the study of Riemannian optimization, game theory and optimal transport,…
Unsupervised anomaly detection aims to build models to effectively detect unseen anomalies by only training on the normal data. Although previous reconstruction-based methods have made fruitful progress, their generalization ability is…
The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The…
The goal of this paper is to show how different machine learning tools on the Riemannian manifold $\mathcal{P}_d$ of Symmetric Positive Definite (SPD) matrices can be united under a probabilistic framework. For this, we will need several…
We explore the use of a topological manifold, represented as a collection of charts, as the target space of neural network based representation learning tasks. This is achieved by a simple adjustment to the output of an encoder's network…
Spectral clustering is one of the most popular clustering approaches with the capability to handle some challenging clustering problems. Most spectral clustering methods provide a nonlinear map from the data manifold to a subspace. Only a…