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Recent progress in geometric deep learning has drawn increasing attention from the machine learning community toward domain adaptation on symmetric positive definite (SPD) manifolds, especially for neuroimaging data that often suffer from…

Recent work has shown a variety of ways in which machine learning can be used to accelerate the solution of constrained optimization problems. Increasing demand for real-time decision-making capabilities in applications such as artificial…

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…

One of the most fundamental problems in machine learning is to compare examples: Given a pair of objects we want to return a value which indicates degree of (dis)similarity. Similarity is often task specific, and pre-defined distances can…

Metric learning aims at finding a suitable distance metric over the input space, to improve the performance of distance-based learning algorithms. In high-dimensional settings, it can also serve as dimensionality reduction by imposing a…

The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…

Deep metric learning is an important area due to its applicability to many domains such as image retrieval and person re-identification. The main drawback of such models is the necessity for labeled data. In this work, we propose to…

We present a geometric formulation of the Multiple Kernel Learning (MKL) problem. To do so, we reinterpret the problem of learning kernel weights as searching for a kernel that maximizes the minimum (kernel) distance between two convex…

Deep metric learning has attracted much attention in recent years, due to seamlessly combining the distance metric learning and deep neural network. Many endeavors are devoted to design different pair-based angular loss functions, which…

Recent advances in Symmetric Positive Definite (SPD) matrix learning show that Riemannian metrics are fundamental to effective SPD neural networks. Motivated by this, we revisit the geometry of the Cholesky factors and uncover a simple…

We study the problem of recovering a globally consistent Euclidean embedding of data, given only a local distance graph and propose a method that optimally represents these distances. The method operates solely on a neighborhood graph…

Deep-learning metrics have recently demonstrated extremely good performance to match image patches for stereo reconstruction. However, training such metrics requires large amount of labeled stereo images, which can be difficult or costly to…

Classical linear metric learning methods have recently been extended along two distinct lines: deep metric learning methods for learning embeddings of the data using neural networks, and Bregman divergence learning approaches for extending…

Metric learning methods for dimensionality reduction in combination with k-Nearest Neighbors (kNN) have been extensively deployed in many classification, data embedding, and information retrieval applications. However, most of these…

The constraint of neighborhood consistency or local consistency is widely used for robust image matching. In this paper, we focus on learning neighborhood topology consistent descriptors (TCDesc), while former works of learning descriptors,…

Stochastic-gradient sampling methods are often used to perform Bayesian inference on neural networks. It has been observed that the methods in which notions of differential geometry are included tend to have better performances, with the…

In many robot control problems, factors such as stiffness and damping matrices and manipulability ellipsoids are naturally represented as symmetric positive definite (SPD) matrices, which capture the specific geometric characteristics of…

Estimating the parameters of a model describing a set of observations using a neural network is in general solved in a supervised way. In cases when we do not have access to the model's true parameters this approach can not be applied.…

We study the problem of similarity learning and its application to image retrieval with large-scale data. The similarity between pairs of images can be measured by the distances between their high dimensional representations, and the…

Despite successful use in a wide variety of disciplines for data analysis and prediction, machine learning (ML) methods suffer from a lack of understanding of the reliability of predictions due to the lack of transparency and black-box…