Related papers: SNEkhorn: Dimension Reduction with Symmetric Entro…
Optimal transport (OT) serves as a natural framework for comparing probability measures, with applications in statistics, machine learning, and applied mathematics. Alas, statistical estimation and exact computation of the OT distances…
Seeking the equivalent entities among multi-source Knowledge Graphs (KGs) is the pivotal step to KGs integration, also known as \emph{entity alignment} (EA). However, most existing EA methods are inefficient and poor in scalability. A…
We study the optimal transport problem for $d>2$ discrete measures. This is a linear programming problem on $d$-tensors. It gives a way to compute a "distance" between two sets of discrete measures. We introduce an entropic regularization…
An attributed hypergraph comprises nodes with attributes and hyperedges that connect varying numbers of nodes. Attributed hypergraph node and hyperedge embedding (AHNEE) maps nodes and hyperedges to compact vectors for use in important…
The remarkable success of deep neural networks (DNNs) in various applications is accompanied by a significant increase in network parameters and arithmetic operations. Such increases in memory and computational demands make deep learning…
The central goal of this paper is to establish two commonly available dimensionality reduction (DR) methods i.e. t-distributed Stochastic Neighbor Embedding (t-SNE) and Multidimensional Scaling (MDS) in Matlab and to observe their…
This article presents a novel application of the t-distributed Stochastic Neighbor Embedding (t-SNE) clustering algorithm to the telecommunication field. t-SNE is a dimensionality reduction (DR) algorithm that allows the visualization of…
Entity alignment (EA) aims to find equivalent entities in different knowledge graphs (KGs). State-of-the-art EA approaches generally use Graph Neural Networks (GNNs) to encode entities. However, most of them train the models and evaluate…
Subgraph matching query is a fundamental problem in graph data management and has a variety of real-world applications. Several recent works utilize deep learning (DL) techniques to process subgraph matching queries. Most of them find…
Multimarginal optimal transport (MOT) is a powerful framework for modeling interactions between multiple distributions, yet its applicability is bottlenecked by a high computational overhead. Entropic regularization provides computational…
Entity alignment (EA) aims to identify entities across different knowledge graphs that represent the same real-world objects. Recent embedding-based EA methods have achieved state-of-the-art performance in EA yet faced interpretability…
Doubly-stochastic matrices (DSM) are increasingly utilized in structure-preserving deep architectures -- such as Optimal Transport layers and Sinkhorn-based attention -- to enforce numerical stability and probabilistic interpretability. In…
The t-distributed Stochastic Neighbor Embedding (t-SNE) algorithm is a ubiquitously employed dimensionality reduction (DR) method. Its non-parametric nature and impressive efficacy motivated its parametric extension. It is however bounded…
As the complexity of modern control systems increases, it becomes challenging to derive an accurate model of the uncertainty that affects their dynamics. Wasserstein Distributionally Robust Optimization (DRO) provides a powerful framework…
Soft, porous mechanical metamaterials exhibit pattern transformations that may have important applications in soft robotics, sound reduction and biomedicine. To design these innovative materials, it is important to be able to simulate them…
We develop a new methodology for model-based clustering. Optimizing the log-likelihood provides a principled statistical framework for clustering, with solutions found via the EM algorithm. However, because the log-likelihood is nonconvex,…
The rise of graph representation learning as the primary solution for many different network science tasks led to a surge of interest in the fairness of this family of methods. Link prediction, in particular, has a substantial social…
Matrix scaling problems with sparse cost matrices arise frequently in various domains, such as optimal transport, image processing, and machine learning. The Sinkhorn-Knopp algorithm is a popular iterative method for solving these problems,…
Dimension reduction (DR) methods provide systematic approaches for analyzing high-dimensional data. A key requirement for DR is to incorporate global dependencies among original and embedded samples while preserving clusters in the…
This paper aims to overcome a fundamental problem in the theory and application of deep neural networks (DNNs). We propose a method to solve the local minimum problem in training DNNs directly. Our method is based on the cross-entropy loss…