Essays about: "Simplicial complex"

Found 5 essays containing the words Simplicial complex.

1. 1. 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. 2. 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. 3. The Weak Lefschetz Property For Artinian Quadratic Monomial Algebras

   University essay from Uppsala universitet/Algebra, logik och representationsteori

   Author : Einar Waara; [2022]
   Keywords : ;

   Abstract : In this thesis we aim to study the Lefschetz properties ofmonomial algebras. First, we present the necessary concepts and resultsfrom commutative algebra, in particular we build up to the Hilbert-Serre theorem regarding the rationality of Hilbert series. READ MORE

5. 4. 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

6. 5. From Relations to Simplicial Complexes: A Toolkit for the Topological Analysis of Networks

   University essay from KTH/Matematik (Avd.)

   Author : Johan Lord; [2021]
   Keywords : applied algebraic topology; complex networks; topological data analysis; brain network analysis;

   Abstract : We present a rigorous yet accessible introduction to structures on finite sets foundational for a formal study of complex networks. This includes a thorough treatment of binary relations, distance spaces, their properties and similarities. READ MORE