Related papers: Neural Bregman Divergences for Distance Learning
Supervised learning requires the specification of a loss function to minimise. While the theory of admissible losses from both a computational and statistical perspective is well-developed, these offer a panoply of different choices. In…
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…
We present a Gaussian kernel loss function and training algorithm for convolutional neural networks that can be directly applied to both distance metric learning and image classification problems. Our method treats all training features…
Continual learning aims to efficiently learn from a non-stationary stream of data while avoiding forgetting the knowledge of old data. In many practical applications, data complies with non-Euclidean geometry. As such, the commonly used…
Unsupervised deep metric learning (UDML) focuses on learning a semantic representation space using only unlabeled data. This challenging problem requires accurately estimating the similarity between data points, which is used to supervise a…
We show that the Bregman divergence provides a rich framework to estimate unnormalized statistical models for continuous or discrete random variables, that is, models which do not integrate or sum to one, respectively. We prove that recent…
Distance metrics and their nonlinear variant play a crucial role in machine learning based real-world problem solving. We demonstrated how Euclidean and cosine distance measures differ not only theoretically but also in real-world medical…
Over the past few years, symmetric positive definite (SPD) matrices have been receiving considerable attention from computer vision community. Though various distance measures have been proposed in the past for comparing SPD matrices, the…
Many interesting machine learning problems are best posed by considering instances that are distributions, or sample sets drawn from distributions. Previous work devoted to machine learning tasks with distributional inputs has done so…
Distance metric learning (DML) is to learn the embeddings where examples from the same class are closer than examples from different classes. It can be cast as an optimization problem with triplet constraints. Due to the vast number of…
The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…
We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph…
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…
This paper proposes and analyzes a gradient-type algorithm based on Burer-Monteiro factorization, called the Asymmetric Projected Gradient Descent (APGD), for reconstructing the point set configuration from partial Euclidean distance…
Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in…
We present a deep learning approach for learning the joint semantic embeddings of images and captions in a Euclidean space, such that the semantic similarity is approximated by the L2 distances in the embedding space. For that, we introduce…
Graph comparison plays a major role in many network applications. We often need a similarity metric for comparing networks according to their structural properties. Various network features - such as degree distribution and clustering…
Gradient-based meta-learning methods leverage gradient descent to learn the commonalities among various tasks. While previous such methods have been successful in meta-learning tasks, they resort to simple gradient descent during…
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…
Metric embeddings are a widely used method in algorithm design, where generally a ``complex'' metric is embedded into a simpler, lower-dimensional one. Historically, the theoretical computer science community has focused on bi-Lipschitz…