Related papers: Triangular Alignment (TAME): A Tensor-based Approa…
The apparent ``black box'' nature of neural networks is a barrier to adoption in applications where explainability is essential. This paper presents TAME (Trainable Attention Mechanism for Explanations), a method for generating explanation…
Additive models can be used for interpretable machine learning for their clarity and simplicity. However, In the classical models for high-order data, the vectorization operation disrupts the data structure, which may lead to degenerated…
Network alignment is the problem of matching the nodes of two graphs, maximizing the similarity of the matched nodes and the edges between them. This problem is encountered in a wide array of applications-from biological networks to social…
Network alignment can be used to transfer functional knowledge between conserved regions of different networks. Typically, existing methods use a node cost function (NCF) to compute similarity between nodes in different networks and an…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
Tensor network contractions are widely used in statistical physics, quantum computing, and computer science. We introduce a method to efficiently approximate tensor network contractions using low-rank approximations, where each intermediate…
Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…
Network alignment, the process of finding correspondences between nodes in different graphs, has many scientific and industrial applications. Existing unsupervised network alignment methods find suboptimal alignments that break up node…
Multiple network alignment is the problem of identifying similar and related regions in a given set of networks. While there are a large number of effective techniques for pairwise problems with two networks that scale in terms of edges,…
Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows to integrate higher-order geometric information. Hypergraph matching can be formulated as a third-order…
Higher-order low-rank tensor arises in many data processing applications and has attracted great interests. Inspired by low-rank approximation theory, researchers have proposed a series of effective tensor completion methods. However, most…
Understanding the evolutionary patterns of real-world evolving complex systems such as human interactions, transport networks, biological interactions, and computer networks has important implications in our daily lives. Predicting future…
Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models…
Network alignment is the task of establishing one-to-one correspondences between the nodes of different graphs. Although finding a plethora of applications in high-impact domains, this task is known to be NP-hard in its general form.…
Network alignment, in general, seeks to discover the hidden underlying correspondence between nodes across two (or more) networks when given their network structure. However, most existing network alignment methods have added assumptions of…
Network alignment aims to find regions of topological or functional similarities between networks. In computational biology, it can be used to transfer biological knowledge from a well-studied species to a poorly-studied species between…
Higher-order tensors are becoming prevalent in many scientific areas such as computer vision, social network analysis, data mining and neuroscience. Traditional tensor decomposition approaches face three major challenges: model selecting,…
This work presents a novel method for task optimization in industrial plants using quantum-inspired tensor network technology. This method obtains the best possible combination of tasks on a set of machines with directed constraints while…
Tensor Kronecker products, the natural generalization of the matrix Kronecker product, are independently emerging in multiple research communities. Like their matrix counterpart, the tensor generalization gives structure for implicit…
This paper aims to maximize algebraic connectivity of networks via topology design under the presence of constraints and an adversary. We are concerned with three problems. First, we formulate the concave maximization topology design…