Related papers: A Tutorial on Distance Metric Learning: Mathematic…

Visual Similarity plays an important role in many computer vision applications. Deep metric learning (DML) is a powerful framework for learning such similarities which not only generalize from training data to identically distributed test…

Deep metric learning has gained promising improvement in recent years following the success of deep learning. It has been successfully applied to problems in few-shot learning, image retrieval, and open-set classifications. However,…

Kernel-based learning algorithms are widely used in machine learning for problems that make use of the similarity between object pairs. Such algorithms first embed all data points into an alternative space, where the inner product between…

Density-based distances (DBDs) provide a principled approach to metric learning by defining distances in terms of the underlying data distribution. By employing a Riemannian metric that increases in regions of low probability density,…

Anomaly detection methods can be very useful in identifying unusual or interesting patterns in data. A recently proposed conditional anomaly detection framework extends anomaly detection to the problem of identifying anomalous patterns on a…

This book provides an introduction to the mathematical analysis of deep learning. It covers fundamental results in approximation theory, optimization theory, and statistical learning theory, which are the three main pillars of deep neural…

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…

Empirically, Deep Learning (DL) has demonstrated unprecedented success in practical applications. However, DL remains by and large a mysterious "black-box", spurring recent theoretical research to build its mathematical foundations. In this…

Machine learning is at the heart of managing the real-world problems associated with massive data. With the success of neural networks on such large-scale problems, more research in machine learning is being conducted now than ever before.…

In recent years, deep metric learning has achieved promising results in learning high dimensional semantic feature embeddings where the spatial relationships of the feature vectors match the visual similarities of the images. Similarity…

Metric magnitude is a measure of the "size" of point clouds with many desirable geometric properties. It has been adapted to various mathematical contexts and recent work suggests that it can enhance machine learning and optimization…

Metric learning algorithms aim to learn a distance function that brings the semantically similar data items together and keeps dissimilar ones at a distance. The traditional Mahalanobis distance learning is equivalent to find a linear…

Machine learning algorithms are used to construct a mathematical model for a system based on training data. Such a model is capable of making highly accurate predictions without being explicitly programmed to do so. These techniques have a…

Deep learning, a branch of artificial intelligence, is a data-driven method that uses multiple layers of interconnected units or neurons to learn intricate patterns and representations directly from raw input data. Empowered by this…

We study the problem of learning local metrics for nearest neighbor classification. Most previous works on local metric learning learn a number of local unrelated metrics. While this "independence" approach delivers an increased flexibility…

Distance measures have been recognized as one of the fundamental building blocks in time-series analysis tasks, e.g., querying, indexing, classification, clustering, anomaly detection, and similarity search. The vast proliferation of…

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…

Unsupervised machine learning lacks ground truth by definition. This poses a major difficulty when designing metrics to evaluate the performance of such algorithms. In sharp contrast with supervised learning, for which plenty of quality…

In this paper, we propose a metric on the space of finite sets of trajectories for assessing multi-target tracking algorithms in a mathematically sound way. The main use of the metric is to compare estimates of trajectories from different…

This paper relates parameter distance to gradient breakdown for a broad class of nonlinear compositional functions. The analysis leads to a new distance function called deep relative trust and a descent lemma for neural networks. Since the…