A Machine Learning Exploration of Topological Data Analysis Applied to Low and High Dimensional fMRI Data

2019 ◽  
Author(s):  
Maria E. Gommel
Keyword(s):  
Machine Learning ◽  
Data Analysis ◽  
Topological Data Analysis ◽  
Fmri Data ◽  
High Dimensional ◽  
Topological Data

scholarly journals Classification of apatite structures via topological data analysis: a framework for a ‘Materials Barcode’ representation of structure maps

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Scott Broderick ◽  
Ruhil Dongol ◽  
Tianmu Zhang ◽  
Krishna Rajan
Keyword(s):  
Machine Learning ◽  
Data Analysis ◽  
Crystal Chemistry ◽  
Persistent Homology ◽  
Hierarchical Classification ◽  
Topological Data Analysis ◽  
Learning Tool ◽  
Coordination Polyhedra ◽  
Machine Learning Tool ◽  
Topological Data

AbstractThis paper introduces the use of topological data analysis (TDA) as an unsupervised machine learning tool to uncover classification criteria in complex inorganic crystal chemistries. Using the apatite chemistry as a template, we track through the use of persistent homology the topological connectivity of input crystal chemistry descriptors on defining similarity between different stoichiometries of apatites. It is shown that TDA automatically identifies a hierarchical classification scheme within apatites based on the commonality of the number of discrete coordination polyhedra that constitute the structural building units common among the compounds. This information is presented in the form of a visualization scheme of a barcode of homology classifications, where the persistence of similarity between compounds is tracked. Unlike traditional perspectives of structure maps, this new “Materials Barcode” schema serves as an automated exploratory machine learning tool that can uncover structural associations from crystal chemistry databases, as well as to achieve a more nuanced insight into what defines similarity among homologous compounds.

scholarly journals Towards Personalized Diagnosis of Glioblastoma in Fluid-Attenuated Inversion Recovery (FLAIR) by Topological Interpretable Machine Learning

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 770
Author(s):  
Matteo Rucco ◽  
Giovanna Viticchi ◽  
Lorenzo Falsetti
Keyword(s):  
Machine Learning ◽  
Data Analysis ◽  
Tumor Growth ◽  
Topological Data Analysis ◽  
Textural Features ◽  
The Third ◽  
Interpretable Machine Learning ◽  
Fluid Attenuated Inversion Recovery ◽  
Topological Data

Glioblastoma multiforme (GBM) is a fast-growing and highly invasive brain tumor, which tends to occur in adults between the ages of 45 and 70 and it accounts for 52 percent of all primary brain tumors. Usually, GBMs are detected by magnetic resonance images (MRI). Among MRI, a fluid-attenuated inversion recovery (FLAIR) sequence produces high quality digital tumor representation. Fast computer-aided detection and segmentation techniques are needed for overcoming subjective medical doctors (MDs) judgment. This study has three main novelties for demonstrating the role of topological features as new set of radiomics features which can be used as pillars of a personalized diagnostic systems of GBM analysis from FLAIR. For the first time topological data analysis is used for analyzing GBM from three complementary perspectives—tumor growth at cell level, temporal evolution of GBM in follow-up period and eventually GBM detection. The second novelty is represented by the definition of a new Shannon-like topological entropy, the so-called Generator Entropy. The third novelty is the combination of topological and textural features for training automatic interpretable machine learning. These novelties are demonstrated by three numerical experiments. Topological Data Analysis of a simplified 2D tumor growth mathematical model had allowed to understand the bio-chemical conditions that facilitate tumor growth—the higher the concentration of chemical nutrients the more virulent the process. Topological data analysis was used for evaluating GBM temporal progression on FLAIR recorded within 90 days following treatment completion and at progression. The experiment had confirmed that persistent entropy is a viable statistics for monitoring GBM evolution during the follow-up period. In the third experiment we developed a novel methodology based on topological and textural features and automatic interpretable machine learning for automatic GBM classification on FLAIR. The algorithm reached a classification accuracy up to 97%.

scholarly journals Correction: Designing machine learning workflows with an application to topological data analysis

PLoS ONE ◽  
2020 ◽  
Vol 15 (2) ◽  
pp. e0229821
Author(s):  
Eric Cawi ◽  
Patricio S La Rosa ◽  
Arye Nehorai
Keyword(s):  
Machine Learning ◽  
Data Analysis ◽  
Topological Data Analysis ◽  
Topological Data

scholarly journals Chatter Classification in Turning using Machine Learning and Topological Data Analysis

2018 ◽  
Vol 51 (14) ◽  
pp. 195-200 ◽  
Author(s):  
Firas A. Khasawneh ◽  
Elizabeth Munch ◽  
Jose A. Perea
Keyword(s):  
Machine Learning ◽  
Data Analysis ◽  
Topological Data Analysis ◽  
Topological Data

scholarly journals Feasibility of topological data analysis for event-related fMRI

2019 ◽  
Vol 3 (3) ◽  
pp. 695-706 ◽  
Author(s):  
Cameron T. Ellis ◽  
Michael Lesnick ◽  
Gregory Henselman-Petrusek ◽  
Bryn Keller ◽  
Jonathan D. Cohen
Keyword(s):  
Data Analysis ◽  
Persistent Homology ◽  
Time Frame ◽  
Topological Data Analysis ◽  
Fmri Data ◽  
Cognitive Representations ◽  
New Approach ◽  
Neural Data ◽  
Topological Features ◽  
Topological Data

Recent fMRI research shows that perceptual and cognitive representations are instantiated in high-dimensional multivoxel patterns in the brain. However, the methods for detecting these representations are limited. Topological data analysis (TDA) is a new approach, based on the mathematical field of topology, that can detect unique types of geometric features in patterns of data. Several recent studies have successfully applied TDA to study various forms of neural data; however, to our knowledge, TDA has not been successfully applied to data from event-related fMRI designs. Event-related fMRI is very common but limited in terms of the number of events that can be run within a practical time frame and the effect size that can be expected. Here, we investigate whether persistent homology—a popular TDA tool that identifies topological features in data and quantifies their robustness—can identify known signals given these constraints. We use fmrisim, a Python-based simulator of realistic fMRI data, to assess the plausibility of recovering a simple topological representation under a variety of conditions. Our results suggest that persistent homology can be used under certain circumstances to recover topological structure embedded in realistic fMRI data simulations.

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