相关论文: Persistent reachability homology in machine learni…

We abstract and study \emph{reachability preservers}, a graph-theoretic primitive that has been implicit in prior work on network design. Given a directed graph $G = (V, E)$ and a set of \emph{demand pairs} $P \subseteq V \times V$, a…

Persistent homology (PH) studies the topology of data across multiple scales by building nested collections of topological spaces called filtrations, computing homology and returning an algebraic object that can be vizualised as a…

Deep hashing methods have received much attention recently, which achieve promising results by taking advantage of the strong representation power of deep networks. However, most existing deep hashing methods learn a whole set of hashing…

Long lived topological features are distinguished from short lived ones (considered as topological noise) in simplicial complexes constructed from complex networks. A new topological invariant, persistent homology, is determined and…

In this paper, the efficient hinging hyperplanes (EHH) neural network is proposed based on the model of hinging hyperplanes (HH). The EHH neural network is a distributed representation, the training of which involves solving several convex…

Topological data analysis combines machine learning with methods from algebraic topology. Persistent homology, a method to characterize topological features occurring in data at multiple scales is of particular interest. A major obstacle to…

Heterogeneous information network has been widely used to alleviate sparsity and cold start problems in recommender systems since it can model rich context information in user-item interactions. Graph neural network is able to encode this…

Graphs are commonly used to encode relationships among entities, yet their abstractness makes them difficult to analyze. Node-link diagrams are popular for drawing graphs, and force-directed layouts provide a flexible method for node…

Persistent homology is a popular method for computing topological features of (metric) data. Standard approaches based on the \v{C}ech or Rips filtration are stable under small perturbations of the data, but highly sensitive to outliers.…

While many approaches to make neural networks more fathomable have been proposed, they are restricted to interrogating the network with input data. Measures for characterizing and monitoring structural properties, however, have not been…

Topological data analysis (TDA) is gaining prominence across a wide spectrum of machine learning tasks that spans from manifold learning to graph classification. A pivotal technique within TDA is persistent homology (PH), which furnishes an…

Wearable and unobtrusive monitoring and prediction of epileptic seizures has the potential to significantly increase the life quality of patients, but is still an unreached goal due to challenges of real-time detection and wearable devices…

This paper focuses on developing an efficient algorithm for analyzing a directed network (graph) from a topological viewpoint. A prevalent technique for such topological analysis involves computation of homology groups and their…

Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often…

Inspired by the recently remarkable successes of Sparse Representation (SR), Collaborative Representation (CR) and sparse graph, we present a novel hypergraph model named Regression-based Hypergraph (RH) which utilizes the regression models…

Hierarchical reinforcement learning (HRL) enables agents to solve complex, long-horizon tasks by decomposing them into manageable sub-tasks. However, HRL methods face two fundamental challenges: (i) non-stationarity caused by the evolving…

We study the use of local heuristics to determine spanning subgraphs for use in the dissemination of information in complex networks. We introduce two different heuristics and analyze their behavior in giving rise to spanning subgraphs that…

Similarity graphs are an active research direction for the nearest neighbor search (NNS) problem. New algorithms for similarity graph construction are continuously being proposed and analyzed by both theoreticians and practitioners.…

The limited penetrable horizontal visibility graph algorithm was recently introduced to map time series in complex networks. We extend this visibility graph and create a directed limited penetrable horizontal visibility graph and an image…

Persistent homology (PH) characterizes the shape of brain networks through persistence features. Group comparison of persistence features from brain networks can be challenging as they are inherently heterogeneous. A recent scale-space…