Related papers: Bounding the Interleaving Distance for Mapper Grap…
The Reeb graph has been utilized in various applications including the analysis of scalar fields. Recently, research has been focused on using topological signatures such as the Reeb graph to compare multiple scalar fields by defining…
The challenge of describing model drift is an open question in unsupervised learning. It can be difficult to evaluate at what point an unsupervised model has deviated beyond what would be expected from a different sample from the same…
Many applications in pattern recognition represent patterns as a geometric graph. The geometric graph distance (GGD) has recently been studied as a meaningful measure of similarity between two geometric graphs. Since computing the GGD is…
This paper describes one objective function for learning semantically coherent feature embeddings in multi-output classification problems, i.e., when the response variables have dimension higher than one. In particular, we consider the…
Distance measures play an important role in shape classification and data analysis problems. Topological distances based on Reeb graphs and persistence diagrams have been employed to obtain effective algorithms in shape matching and scalar…
We propose a novel, connectivity-oriented loss function for training deep convolutional networks to reconstruct network-like structures, like roads and irrigation canals, from aerial images. The main idea behind our loss is to express the…
The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…
Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and…
One of the central notions to emerge from the study of persistent homology is that of interleaving distance. It has found recent applications in symplectic and contact geometry, sheaf theory, computational geometry, and phylogenetics. Here…
In this paper, we focus on the separability of classes with the cross-entropy loss function for classification problems by theoretically analyzing the intra-class distance and inter-class distance (i.e. the distance between any two points…
We consider the problem of constructing embeddings of large attributed graphs and supporting multiple downstream learning tasks. We develop a graph embedding method, which is based on extending deep metric and unbiased contrastive learning…
Since its introduction as a computable approximation of the Reeb graph, the Mapper graph has become one of the most popular tools from topological data analysis for performing data visualization and inference. However, finding an…
Large-scale graphs are widely used to represent object relationships in many real world applications. The occurrence of large-scale graphs presents significant computational challenges to process, analyze, and extract information. Graph…
While machine learning (ML) architectures have evolved rapidly to account for complex data, loss functions like cross-entropy remain mostly structure-agnostic in many real-world applications. However, the `class-symmetric' nature of these…
Understanding generalization and robustness of machine learning models fundamentally relies on assuming an appropriate metric on the data space. Identifying such a metric is particularly challenging for non-Euclidean data such as graphs.…
Despite significant advancements, Large Language Models (LLMs) exhibit blind spots that impair their ability to retrieve and process relevant contextual data effectively. We demonstrate that LLM performance in graph tasks with complexities…
The \textit{biharmonic distance} (BD) is a fundamental metric that measures the distance of two nodes in a graph. It has found applications in network coherence, machine learning, and computational graphics, among others. In spite of BD's…
We establish the link between Mathematical Morphology and the map of Asplund's distances between a probe and a grey scale function, using the Logarithmic Image Processing scalar multiplication. We demonstrate that the map is the logarithm…
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…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…