Related papers: Supervised LogEuclidean Metric Learning for Symmet…

Data classification without access to labeled samples remains a challenging problem. It usually depends on an appropriately chosen distance between features, a topic addressed in metric learning. Recently, Huizing, Cantini and Peyr\'e…

In this contribution, we augment the metric learning setting by introducing a parametric pseudo-distance, trained jointly with the encoder. Several interpretations are thus drawn for the learned distance-like model's output. We first show…

We study the problem of testing whether a matrix $\mathbf{A} \in \mathbb{R}^{n \times n}$ with bounded entries ($\|\mathbf{A}\|_\infty \leq 1$) is positive semi-definite (PSD), or $\epsilon$-far in Euclidean distance from the PSD cone,…

The accuracy and complexity of machine learning algorithms based on kernel optimization are determined by the set of kernels over which they are able to optimize. An ideal set of kernels should: admit a linear parameterization (for…

In this paper, we attempts to learn a single metric across two heterogeneous domains where source domain is fully labeled and has many samples while target domain has only a few labeled samples but abundant unlabeled samples. To the best of…

In the domain of image-set based classification, a considerable advance has been made by representing original image sets as covariance matrices which typical lie in a Riemannian manifold. Specifically, it is a Symmetric Positive Definite…

Meta-learning, or "learning to learn," aims to enable models to quickly adapt to new tasks with minimal data. While traditional methods like Model-Agnostic Meta-Learning (MAML) optimize parameters in Euclidean space, they often struggle to…

Image classification is an essential part of computer vision which assigns a given input image to a specific category based on the similarity evaluation within given criteria. While promising classifiers can be obtained through deep…

Typical learning curves for Soft Margin Classifiers (SMCs) learning both realizable and unrealizable tasks are determined using the tools of Statistical Mechanics. We derive the analytical behaviour of the learning curves in the regimes of…

The Euclidean distance geometry problem arises in a wide variety of applications, from determining molecular conformations in computational chemistry to localization in sensor networks. When the distance information is incomplete, the…

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…

We propose to learn multiple local Mahalanobis distance metrics to perform k-nearest neighbor (kNN) classification of temporal sequences. Temporal sequences are first aligned by dynamic time warping (DTW); given the alignment path,…

The choice of good distances and similarity measures between objects is important for many machine learning methods. Therefore, many metric learning algorithms have been developed in recent years, mainly for Euclidean data in order to…

Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…

Distance metric learning (DML) is an important task that has found applications in many domains. The high computational cost of DML arises from the large number of variables to be determined and the constraint that a distance metric has to…

Estimating matrices in the symmetric positive-definite (SPD) cone is of interest for many applications ranging from computer vision to graph learning. While there exist various convex optimization-based estimators, they remain limited in…

We propose a new method for local distance metric learning based on sample similarity as side information. These local metrics, which utilize conical combinations of metric weight matrices, are learned from the pooled spatial…

Metric learning methods have been shown to perform well on different learning tasks. Many of them rely on target neighborhood relationships that are computed in the original feature space and remain fixed throughout learning. As a result,…

Matrix Factorization plays an important role in machine learning such as Non-negative Matrix Factorization, Principal Component Analysis, Dictionary Learning, etc. However, most of the studies aim to minimize the loss by measuring the…

The crucial importance of metrics in machine learning algorithms has led to an increasing interest in optimizing distance and similarity functions, an area of research known as metric learning. When data consist of feature vectors, a large…