Tutorial 6 pt I: Topological Data Analysis for Biomedical Imaging Data
Lecture 1 and first half of Lectrue 2: Thu, Apr 20, 11:30 – 13:00 SALÓN BARAHONA 2
Tutorial 6 pt II: Topological Data Analysis for Biomedical Imaging Data
The last half of Lecture 2 and Lecture 3: Thu, Apr 20, 16:00 – 17:30 SALÓN BARAHONA 2
Topological data analysis (TDA) is a fast growing field proving many powerful tools for biomedical imaging data. TDA characterizes topological changes of multivariate representations of imaging data in multidimensional scales. In doing so TDA reveals the persistent topological patterns in data only visible on a multiscale level. The overall topological changes hold more significance in TDA features over fleeting structures also makes the approach particularly robust at the presence of imaging noise and artifacts. This is the first TDA tutorial in ISBI. The tutorial is aimed at educating both basics and state of the arts in TDA for students and researchers attending ISBI. The expected audiences are graduate students and researchers trying to learn TDA for the first time. However, existing TDA researchers will also benefit. The knowledge in TDA or topology is not needed.
The tutorial will consist of three major topics covered for one hour each for total three-hour duration. Three professors Moo K. Chung (University of Wisconsin-Madison), Soheil Kolouri (Vanderbilt University) and Hernando Ombao (KAUST) will give one hour lecture each. Chung will give an introductory overview of basic concepts in TDA (filtrations, persistent diagrams, barcodes), Kolouri will explain how to compute the Wasserstein distance between persistent diagrams using existing baseline method and the scalable sliced-Wasserstein distance. Ombao will explain how to transform functional biomedical images such as MEG, EEG, fMRI and fNIR into topological descriptors through time delay embedding and slide window embedding.
The tutorial will consist of a brief theoretical review on the topics with hand-on computer demonstrations. We recommend audience to bring their own laptop to run the provided codes during the tutorial. All the tutorial lecture slides, relevant tutorial paper and computer codes will be provided at https://github.com/laplcebeltrami/ISBI2023TDA. After the tutorial, at minimum, audiences will understand how to extract topological features, compute the topological distances, and convert functional imaging data into topological descriptors. Any administrative issues related to the tutorial should be addressed to mkchung@wisc.edu. The lecture details as follows.
The tutorial will be given by professor Moo K. Chung and of University of Wisconsin-Madison. The tutorial will cover the basics of topological data analysis (TDA) such as Morse filtrations, Rips and graph filtrations, boundary operators and the Hodge Laplacian. Then the concept of persistent diagrams will be introduced. Topological inference and clustering will be explained. The lecture is based on MATLAB TDA toolbox https://github.com/laplcebeltrami/PH-STAT. The detailed manual of the toolbox is given in arXiv:2304.05912. The lecture slides is lecture1.pdf.
The tutorial will be given by professor Hernando Ombao and Anass El Yaagoubi Bourkna of KAUST. The tutorial will explain how to perform varisous topological computations and visualizations using Python. The tutorial will then explain how to transform time series data (functional biomedical images such as MEG, EEG, fMRI and fNIR) into topological descriptors through time delay embedding and slide window embedding. Then simplical complex consist of the scatter points will be used to build persistent diagrams or other topological features. Topological inference procedures for determining statistical singifinace on the extracted topological featrues will be explained. The lecture is based on https://github.com/A-EL-YAAGOUBI/Dynamic-TDA. Simply run the script Dynamic_TDA.ipynb.
The tutorial will be given by professor Soheil Kolouri of Vanderbilt University. The tutorial consists of introduction to Wasserstein distances and its sliced version, which does scalable computation of the Wasserstein distance. Persistent diagrams will be represented as an empirical distributions using the Dirac delta functions. Then the algorithmic detail on the computation of the Wasserstein distance between persistent diagrams will be presented. Its scalable version called the sliced-Wasserstein distance will be also introduced and contrasted against the baseline (Hungarian algorithm). Additional machine learning applications will be presented. Lecture material is based on https://github.com/skolouri/TopoTrans, which can be donwloaded as a zip file TopoTrans-main.zip.
(C) 2022 Anass El Yaagoubi Bourkna, Soheil Kolouri, Hernando Ombao, Moo K. Chung