A survey of vectorization methods in topological data analysis
Attempts to incorporate topological information in supervised learning tasks have resulted in
the creation of several techniques for vectorizing persistent homology barcodes. In this …
the creation of several techniques for vectorizing persistent homology barcodes. In this …
[HTML][HTML] Advancing precision medicine: algebraic topology and differential geometry in radiology and computational pathology
Precision medicine aims to provide personalized care based on individual patient
characteristics, rather than guideline-directed therapies for groups of diseases or patient …
characteristics, rather than guideline-directed therapies for groups of diseases or patient …
Deciphering the diversity and sequence of extracellular matrix and cellular spatial patterns in lung adenocarcinoma using topological data analysis
Extracellular matrix (ECM) organization influences cancer development and progression. It
modulates the invasion of cancer cells and can hinder the access of immune cells to cancer …
modulates the invasion of cancer cells and can hinder the access of immune cells to cancer …
Persistent Homology-Based Machine Learning Method for Filtering and Classifying Mammographic Microcalcification Images in Early Cancer Detection
Simple Summary The appearance of microcalcifications in mammogram images is an
essential predictor for radiologists to detect early-stage breast cancer. This study aims to …
essential predictor for radiologists to detect early-stage breast cancer. This study aims to …
Signatures, lipschitz-free spaces, and paths of persistence diagrams
Paths of persistence diagrams provide a summary of the dynamic topological structure of a
one-parameter family of metric spaces. These summaries can be used to study and …
one-parameter family of metric spaces. These summaries can be used to study and …
Persistent Homology Identifies Pathways Associated with Hepatocellular Carcinoma from Peripheral Blood Samples
Topological data analysis (TDA) methods have recently emerged as powerful tools for
uncovering intricate patterns and relationships in complex biological data, demonstrating …
uncovering intricate patterns and relationships in complex biological data, demonstrating …
[HTML][HTML] Persistent Homology Analysis of AI-Generated Fractal Patterns: A Mathematical Framework for Evaluating Geometric Authenticity
M Lee, S Lee - Fractal and Fractional, 2024 - mdpi.com
We present a mathematical framework for analyzing fractal patterns in AI-generated images
using persistent homology. Given a text-to-image map** M: T→ I, we demonstrate that the …
using persistent homology. Given a text-to-image map** M: T→ I, we demonstrate that the …
[HTML][HTML] Persistence Symmetric Kernels for Classification: A Comparative Study
C Bandiziol, S De Marchi - Symmetry, 2024 - mdpi.com
The aim of the present work is a comparative study of different persistence kernels applied to
various classification problems. After some necessary preliminaries on homology and …
various classification problems. After some necessary preliminaries on homology and …
Persistence kernels for classification: A comparative study
C Bandiziol, S De Marchi - arxiv preprint arxiv:2408.07090, 2024 - arxiv.org
The aim of the present work is a comparative study of different persistence kernels applied to
various classification problems. After some necessary preliminaries on homology and …
various classification problems. After some necessary preliminaries on homology and …
Improving Classification Performance of Spatial Filters in Mammographic Microcalcifications Images Using Persistent Homology
Noise and artefacts in mammogram images can obscure important indicators of
microcalcifications, complicating accurate diagnosis. While traditional spatial filters can …
microcalcifications, complicating accurate diagnosis. While traditional spatial filters can …