Sökning: "topologisk data analys"

Visar resultat 1 - 5 av 11 uppsatser innehållade orden topologisk data analys.

1. 1. Unauthorised Session Detection with RNN-LSTM Models and Topological Data Analysis

   Master-uppsats, KTH/Matematik (Avd.)

   Författare :Nazar Maksymchuk Netterström; [2023]
   Nyckelord :Recurrent Neural Network; Long-Short-Term-Memory; Topological Data Analysis; Session based data; Anomaly detection; Time-series analysis; Imbalanced data; Master thesis; Neurala nätverk; Topologisk data analys; Detektion av avvikelse; Sessionsbaserad data; Tidserieanalys; Inbalancerad data; Masteruppsats;

   Sammanfattning : This thesis explores the possibility of using session-based customers data from Svenska Handelsbanken AB to detect fraudulent sessions. Tools within Topological Data Analysis are employed to analyse customers behavior and examine topological properties such as homology and stable rank at the individual level. LÄS MER

3. 2. Exploring persistent homology as a method for capturing functional connectivity differences in Parkinson’s Disease.

   Master-uppsats, KTH/Matematik (Avd.)

   Författare :Naomi Hulst; [2022]
   Nyckelord :persistent homology; topological data analysis; computational topology; parkinson s disease; parkinson; functional connectivity; stable rank; ihållande homologi; topologisk data analys; beräknings topologi; Parkinsons sjukdom; parkinson; funktionell konnektivitet; stable ranks;

   Sammanfattning : Parkinson’s Disease (PD) is the fastest growing neurodegenerative disease, currently affecting two to three percent of the population over 65. Studying functional connectivity (FC) in PD patients may provide new insights into how the disease alters brain organization in different subjects. LÄS MER

4. 3. Towards topology-aware Variational Auto-Encoders : from InvMap-VAE to Witness Simplicial VAE

   Master-uppsats, KTH/Skolan för elektroteknik och datavetenskap (EECS)

   Författare :Aniss Aiman Medbouhi; [2022]
   Nyckelord :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.;

   Sammanfattning : 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. LÄS MER

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

   Master-uppsats, KTH/Matematisk statistik

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

   Sammanfattning : 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. LÄS MER

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

   Master-uppsats, KTH/Matematik (Avd.)

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

   Sammanfattning : 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. LÄS MER