Essays about: "Topological Data Analysis"

Showing result 6 - 10 of 37 essays containing the words Topological Data Analysis.

1. 6. Towards topology-aware Variational Auto-Encoders : from InvMap-VAE to Witness Simplicial VAE

   University essay from KTH/Skolan för elektroteknik och datavetenskap (EECS)

   Author : Aniss Aiman Medbouhi; [2022]
   Keywords : Variational Auto-Encoder; Nonlinear dimensionality reduction; Generative model; Inverse projection; Computational topology; Algorithmic topology; Topological Data Analysis; Data visualisation; Unsupervised representation learning; Topological machine learning; Betti number; Simplicial complex; Witness complex; Simplicial map; Simplicial regularization.; Variations autokodare; Ickelinjär dimensionalitetsreducering; Generativ modell; Invers projektion; Beräkningstopologi; Algoritmisk topologi; Topologisk Data Analys; Datavisualisering; Oövervakat representationsinlärning; Topologisk maskininlärning; Betti-nummer; Simplicielt komplex; Vittneskomplex; Simpliciel avbildning; Simpliciel regularisering.;

   Abstract : Variational Auto-Encoders (VAEs) are one of the most famous deep generative models. After showing that standard VAEs may not preserve the topology, that is the shape of the data, between the input and the latent space, we tried to modify them so that the topology is preserved. READ MORE

3. 7. Comparison in Barcode and Computing Time for Persistent Homology Applied to a Subset of a Point Cloud

   University essay from

   Author : André Lasses Armatowski; [2022]
   Keywords : ;

   Abstract : At the intersection of topology and computer science lies the field of topological data analysis(TDA). TDA uses the concept of persistence to identify low dimensional topological features of data embedded in high dimensions. READ MORE

4. 8. Properties of Discrete Laplacians With Application on Brain Networks

   University essay from KTH/Matematisk statistik

   Author : David Thinsz; [2022]
   Keywords : Graph Laplacian; Combinatorial Laplacian; Persistent Laplacian; Topological data analysis; Spectral theory; Homology; Clustering.; Graf-Laplacian; Kombinatorisk Laplacian; Beständig Laplacian; Topologisk dataanalys; Spektralteori; Homologi; Klustring.;

   Abstract : This thesis investigates three discrete Laplace operators: the graph Laplacian, combinatorial Laplacian, and the more recently introduced persistent Laplacian. We discuss how these operators relate to each other and study their spectral properties. The graph Laplacian is a well-studied operator that plays a central role in spectral graph theory. READ MORE

5. 9. Metrics for Multidimensional Persistence

   University essay from KTH/Matematik (Avd.)

   Author : Daniel Lundin; [2022]
   Keywords : topological data analysis; multidimensional persistence; persistence modules; metrics; noise systems; topologisk dataanalys; multidimensionell persistens; persistensmoduler; metriker; noise system;

   Abstract : A fundamental mathematical object in topological data analysis today is the persistence module. This thesis explores different metrics on multidimensional persistence modules, where spaces are parametrized along multiple dimensions. The focus is especially on metrics constructed by the use of so called noise systems, introduced by Scolamiero et al. READ MORE

6. 10. Traffic Prediction From Temporal Graphs Using Representation Learning

   University essay from KTH/Matematisk statistik

   Author : Andreas Movin; [2021]
   Keywords : Dynamic time warping DTW ; embedding; graph convolutional networks GCN ; graph neural networks GNN ; persistent homology; spectral graph theory; temporal graphs; topological data analysis TDA ; Dynamisk time warping DTW ; inbäddning; convolutional grafnätverk GCN ; neurala grafnätverk GNN ; persistent homologi; spektral graf teori; dynamisk graf; topologisk dataanalys TDA ;

   Abstract : With the arrival of 5G networks, telecommunication systems are becoming more intelligent, integrated, and broadly used. This thesis focuses on predicting the upcoming traffic to efficiently promote resource allocation, guarantee stability and reliability of the network. READ MORE