Related papers: Bounding the interleaving distance on concrete cat…

We are given the adjacency matrix of a geometric graph and the task of recovering the latent positions. We study one of the most popular approaches which consists in using the graph distances and derive error bounds under various…

Deep metric learning has yielded impressive results in tasks such as clustering and image retrieval by leveraging neural networks to obtain highly discriminative feature embeddings, which can be used to group samples into different classes.…

Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…

We investigate the distance function learned by message passing neural networks (MPNNs) in specific tasks, aiming to capture the functional distance between prediction targets that MPNNs implicitly learn. This contrasts with previous work,…

For multilayer structures, interfacial failure is one of the most important elements related to device reliability. For cohesive zone modelling, traction-separation relations represent the adhesive interactions across interfaces. However,…

Widely used loss functions for CNN segmentation, e.g., Dice or cross-entropy, are based on integrals over the segmentation regions. Unfortunately, for highly unbalanced segmentations, such regional summations have values that differ by…

Graphs are used in almost every scientific discipline to express relations among a set of objects. Algorithms that compare graphs, and output a closeness score, or a correspondence among their nodes, are thus extremely important. Despite…

This paper establishes connections between three of the most prominent metrics used in the analysis of persistence diagrams in topological data analysis: the bottleneck distance, Patel's erosion distance, and Bubenik's landscape distance.…

Loss functions are at the heart of deep learning, shaping how models learn and perform across diverse tasks. They are used to quantify the difference between predicted outputs and ground truth labels, guiding the optimization process to…

An added edge to a graph is called an inset edge. Predicting k inset edges which minimize the average distance of a graph is known to be NP-Hard. However, when k = 1 the complexity of the problem is polynomial. In this paper, some tools for…

This work incorporates topological features via persistence diagrams to classify point cloud data arising from materials science. Persistence diagrams are multisets summarizing the connectedness and holes of given data. A new distance on…

The stability of persistence diagrams is among the most important results in applied and computational topology. Most results in the literature phrase stability in terms of the bottleneck distance between diagrams and the $\infty$-norm of…

Longitudinal Multiple Sclerosis Lesion Segmentation is a particularly challenging problem that involves both input and output imbalance in the data and segmentation. Therefore in order to develop models that are practical, one of the…

We study the problem of how well a tree metric is able to preserve the sum of pairwise distances of an arbitrary metric. This problem is closely related to low-stretch metric embeddings and is interesting by its own flavor from the line of…

Cooking recipes are complex procedures that require not only a fluent and factual text, but also accurate timing, temperature, and procedural coherence, as well as the correct composition of ingredients. Standard training procedures are…

This paper prescribes a distance between learning tasks modeled as joint distributions on data and labels. Using tools in information geometry, the distance is defined to be the length of the shortest weight trajectory on a Riemannian…

3D cross-modal retrieval is gaining attention in the multimedia community. Central to this topic is learning a joint embedding space to represent data from different modalities, such as images, 3D point clouds, and polygon meshes, to…

Deep Metric Learning (DML) learns a non-linear semantic embedding from input data that brings similar pairs together while keeping dissimilar data away from each other. To this end, many different methods are proposed in the last decade…

Distance function is a main metrics of measuring the affinity between two data points in machine learning. Extant distance functions often provide unreachable distance values in real applications. This can lead to incorrect measure of the…

This paper brings together three distinct theories with the goal of quantifying shape textures with complex morphologies. Distance fields are central objects in shape representation, while topological data analysis uses algebraic topology…