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Persistent-homology-based machine learning: a survey and a comparative study
A suitable feature representation that can both preserve the data intrinsic information and reduce data complexity and dimensionality is key to the...
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Homology as an Adversarial Attack Indicator
In this paper we show how classical topological information can be automated with machine learning to lessen the threat of an adversarial attack....
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Generating High Dimensional Test Data for Topological Data Analysis
Topological Data Analysis (TDA) characterizes data based on topological invariants present in the data. In general, TDA treats the data as a discrete...
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Revisiting Link Prediction with the Dowker Complex
We propose a novel method to study properties of graph-structured data by means of a geometric construction called Dowker complex. We study this...
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Weighted product of point clouds and simplicial complexes
This paper extends the concept of weighted point clouds and weighted simplicial complexes by introducing product point clouds and product simplicial...
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Effective homological computations on finite topological spaces
The study of topological invariants of finite topological spaces is relevant because they can be used as models of a wide class of topological...
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Persistence homology of networks: methods and applications
Information networks are becoming increasingly popular to capture complex relationships across various disciplines, such as social networks, citation...
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Toward visual quality enhancement of dehazing effect with improved Cycle-GAN
Image dehazing is a fundamental problem in computer vision. However, GT images for supervised dehazing network training are virtually impossible to...
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Constraint-free discretized manifold-based path planner
Autonomous robotic path planning in partially known environments, such as warehouse robotics, deals with static and dynamic constraints. Static...
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Persistent Homology Computation Using Combinatorial Map Simplification
We propose an algorithm for persistence homology computation of orientable 2-dimensional (2D) manifolds with or without boundary (meshes) represented...
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Learning Topology: Bridging Computational Topology and Machine Learning
AbstractTopology is a classical branch of mathematics, born essentially from Euler’s studies in the XVII century, which deals with the abstract...
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Learning Topology: Bridging Computational Topology and Machine Learning
Topology is a classical branch of mathematics, born essentially from Euler’s studies in the XVII century, which deals with the abstract notion of...
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Dynamical Geometry and a Persistence K-Theory in Noisy Point Clouds
The question of whether the underlying geometry of a dynamical point cloud is invariant is considered from the perspective of the algebra of...
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Tracing patterns and shapes in remittance and migration networks via persistent homology
Pattern detection in network models provides insights to both global structure and local node interactions. In particular, studying patterns embedded...
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Temporal network analysis using zigzag persistence
This work presents a framework for studying temporal networks using zigzag persistence, a tool from the field of Topological Data Analysis (TDA). The...
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Topological Analysis of Temporal Hypergraphs
In this work we study the topological properties of temporal hypergraphs. Hypergraphs provide a higher dimensional generalization of a graph that is...
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Structure- and Function-Aware Substitution Matrices via Learnable Graph Matching
Substitution matrices, which are crafted to quantify the functional impact of substitutions or deletions in biomolecules, are central component of...
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Parametrized topological complexity of collision-free motion planning in the plane
Parametrized motion planning algorithms have high degrees of universality and flexibility, as they are designed to work under a variety of external...
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Cellular structure of the Pommaret-Seiler resolution for quasi-stable ideals
We prove that the Pommaret-Seiler resolution for quasi-stable ideals is cellular and give a cellular structure for it. This shows that this...
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Topological Model of Neural Information Networks
This is a brief overview of an ongoing research project, involving topological models of neural information networks and the development of new...