Related papers: Matched Topological Subspace Detector

Network Science provides a universal formalism for modelling and studying complex systems based on pairwise interactions between agents. However, many real networks in the social, biological or computer sciences involve interactions among…

The homology groups of a simplicial complex reveal fundamental properties of the topology of the data or the system and the notion of topological stability naturally poses an important yet not fully investigated question. In the current…

Community detection is a widely-studied unsupervised learning problem in which the task is to group similar entities together based on observed pairwise entity interactions. This problem has applications in diverse domains such as social…

To pinpoint the microscopic mechanism for superconductivity has proven to be one of the most outstanding challenges in the physics of correlated quantum matter. Thus far, the most direct evidence for an electronic pairing mechanism is the…

This paper presents an estimation method for time-varying graph signals among multiple sub-networks. In many sensor networks, signals observed are associated with nodes (i.e., sensors), and edges of the network represent the inter-node…

The problem of compressive detection of random subspace signals is studied. We consider signals modeled as $\mathbf{s} = \mathbf{H} \mathbf{x}$ where $\mathbf{H}$ is an $N \times K$ matrix with $K \le N$ and $\mathbf{x} \sim…

Real-world graphs have inherently complex and diverse topological patterns, known as topological heterogeneity. Most existing works learn graph representation in a single constant curvature space that is insufficient to match the complex…

To gain insight into reaction mechanism of activated processes, we introduce an exact approach for quantifying the topology of high-dimensional probability surfaces of the underlying dynamic processes. Instead of Morse indexes, we study the…

We consider the problem of classifying trajectories on a discrete or discretised 2-dimensional manifold modelled by a simplicial complex. Previous works have proposed to project the trajectories into the harmonic eigenspace of the Hodge…

We consider a network topology design problem in which an initial undirected graph underlying the network is given and the objective is to select a set of edges to add to the graph to optimize the coherence of the resulting network. We show…

Subgraph pattern detection aims to uncover complex interaction structures in graphs. However, state-of-the-art graph neural network (GNN)-based solutions assume centralized access to the entire graph. When graphs are instead distributed…

A novel, non-learning-based, saliency-aware, shape-cognizant correspondence determination technique is proposed for matching image pairs that are significantly disparate in nature. Images in the real world often exhibit high degrees of…

Grassmannian manifold offers a powerful carrier for geometric representation learning by modelling high-dimensional data as low-dimensional subspaces. However, existing approaches predominantly rely on static single-subspace…

Real-world problems, for example in climate applications, often require causal reasoning on spatially gridded time series data or data with comparable structure. While the underlying system is often believed to behave similarly at different…

Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and…

In this paper, we focus on fraud detection on a signed graph with only a small set of labeled training data. We propose a novel framework that combines deep neural networks and spectral graph analysis. In particular, we use the node…

Higher-order topological phases (HOTPs) host exotic topological states that go beyond the traditional bulk-boundary correspondence. Up to now, there is still a lack of experimentally measurable momentum-space topological characterization…

Simplicial distributions are combinatorial models describing distributions on spaces of measurements and outcomes that generalize non-signaling distributions on contextuality scenarios. This paper studies simplicial distributions on…

With the emergence of dynamic multiplex networks, corresponding to graphs where multiple types of edges evolve over time, a key inferential task is to determine whether the layers associated with different edge types differ in their…

Network topology is a fundamental aspect of network science that allows us to gather insights into the complicated relational architectures of the world we inhabit. We provide a first specific study of neighbourhood degree sequences in…