Introduction to Persistent Homology

10.51939/0002 ◽  
2022 ◽  
Author(s):  
Žiga Virk
Keyword(s):  
Persistent Homology

scholarly journals Exact Topological Inference for Paired Brain Networks via Persistent Homology

2017 ◽  
pp. 299-310 ◽  
Author(s):  
Moo K. Chung ◽  
Victoria Villalta-Gil ◽  
Hyekyoung Lee ◽  
Paul J. Rathouz ◽  
Benjamin B. Lahey ◽  
...  
Keyword(s):  
Persistent Homology ◽  
Brain Networks

scholarly journals Disrupted metabolic connectivity in dopaminergic and cholinergic networks at different stages of dementia from 18F-FDG PET brain persistent homology network

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Tun-Wei Hsu ◽  
Jong-Ling Fuh ◽  
Da-Wei Wang ◽  
Li-Fen Chen ◽  
Chia-Jung Chang ◽  
...  
Keyword(s):  
Algebraic Topology ◽  
Fdg Pet ◽  
Persistent Homology ◽  
Network Connectivity ◽  
Brain Regions ◽  
Imaging Data ◽  
Cholinergic Pathways ◽  
Positron Emission ◽  
Metabolic Connectivity ◽  
Neurochemical Changes

AbstractDementia is related to the cellular accumulation of β-amyloid plaques, tau aggregates, or α-synuclein aggregates, or to neurotransmitter deficiencies in the dopaminergic and cholinergic pathways. Cellular and neurochemical changes are both involved in dementia pathology. However, the role of dopaminergic and cholinergic networks in metabolic connectivity at different stages of dementia remains unclear. The altered network organisation of the human brain characteristic of many neuropsychiatric and neurodegenerative disorders can be detected using persistent homology network (PHN) analysis and algebraic topology. We used 18F-fluorodeoxyglucose positron emission tomography (18F-FDG PET) imaging data to construct dopaminergic and cholinergic metabolism networks, and used PHN analysis to track the evolution of these networks in patients with different stages of dementia. The sums of the network distances revealed significant differences between the network connectivity evident in the Alzheimer’s disease and mild cognitive impairment cohorts. A larger distance between brain regions can indicate poorer efficiency in the integration of information. PHN analysis revealed the structural properties of and changes in the dopaminergic and cholinergic metabolism networks in patients with different stages of dementia at a range of thresholds. This method was thus able to identify dysregulation of dopaminergic and cholinergic networks in the pathology of dementia.

scholarly journals MFCIS: an automatic leaf-based identification pipeline for plant cultivars using deep learning and persistent homology

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Yanping Zhang ◽  
Jing Peng ◽  
Xiaohui Yuan ◽  
Lisi Zhang ◽  
Dongzi Zhu ◽  
...  
Keyword(s):  
Prunus Avium ◽  
Cultivar Identification ◽  
Leaf Shape ◽  
Persistent Homology ◽  
Growth Period ◽  
Image Features ◽  
Crop Species ◽  
Score Level Fusion ◽  
Level Fusion ◽  
Leaf Image

AbstractRecognizing plant cultivars reliably and efficiently can benefit plant breeders in terms of property rights protection and innovation of germplasm resources. Although leaf image-based methods have been widely adopted in plant species identification, they seldom have been applied in cultivar identification due to the high similarity of leaves among cultivars. Here, we propose an automatic leaf image-based cultivar identification pipeline called MFCIS (Multi-feature Combined Cultivar Identification System), which combines multiple leaf morphological features collected by persistent homology and a convolutional neural network (CNN). Persistent homology, a multiscale and robust method, was employed to extract the topological signatures of leaf shape, texture, and venation details. A CNN-based algorithm, the Xception network, was fine-tuned for extracting high-level leaf image features. For fruit species, we benchmarked the MFCIS pipeline on a sweet cherry (Prunus avium L.) leaf dataset with >5000 leaf images from 88 varieties or unreleased selections and achieved a mean accuracy of 83.52%. For annual crop species, we applied the MFCIS pipeline to a soybean (Glycine max L. Merr.) leaf dataset with 5000 leaf images of 100 cultivars or elite breeding lines collected at five growth periods. The identification models for each growth period were trained independently, and their results were combined using a score-level fusion strategy. The classification accuracy after score-level fusion was 91.4%, which is much higher than the accuracy when utilizing each growth period independently or mixing all growth periods. To facilitate the adoption of the proposed pipelines, we constructed a user-friendly web service, which is freely available at http://www.mfcis.online.

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.

An introduction to persistent homology for time series

2021 ◽  
Vol 13 (3) ◽  
Author(s):  
Nalini Ravishanker ◽  
Renjie Chen
Keyword(s):  
Time Series ◽  
Persistent Homology

scholarly journals Machine learning with persistent homology and chemical word embeddings improves prediction accuracy and interpretability in metal-organic frameworks

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Aditi S. Krishnapriyan ◽  
Joseph Montoya ◽  
Maciej Haranczyk ◽  
Jens Hummelshøj ◽  
Dmitriy Morozov
Keyword(s):  
Machine Learning ◽  
Language Processing ◽  
Metal Organic Framework ◽  
Persistent Homology ◽  
Level Structure ◽  
Chemical Information ◽  
Material System ◽  
Word Embeddings ◽  
Structure Property ◽  
Metal Organic

AbstractMachine learning has emerged as a powerful approach in materials discovery. Its major challenge is selecting features that create interpretable representations of materials, useful across multiple prediction tasks. We introduce an end-to-end machine learning model that automatically generates descriptors that capture a complex representation of a material’s structure and chemistry. This approach builds on computational topology techniques (namely, persistent homology) and word embeddings from natural language processing. It automatically encapsulates geometric and chemical information directly from the material system. We demonstrate our approach on multiple nanoporous metal–organic framework datasets by predicting methane and carbon dioxide adsorption across different conditions. Our results show considerable improvement in both accuracy and transferability across targets compared to models constructed from the commonly-used, manually-curated features, consistently achieving an average 25–30% decrease in root-mean-squared-deviation and an average increase of 40–50% in R2 scores. A key advantage of our approach is interpretability: Our model identifies the pores that correlate best to adsorption at different pressures, which contributes to understanding atomic-level structure–property relationships for materials design.

scholarly journals Effect of APOE ε4 on multimodal brain connectomic traits: a persistent homology study

2020 ◽  
Vol 21 (S21) ◽  
Author(s):  
Jin Li ◽  
◽  
Chenyuan Bian ◽  
Dandan Chen ◽  
Xianglian Meng ◽  
...  
Keyword(s):  
Magnetic Resonance Imaging ◽  
Magnetic Resonance ◽  
Genetic Risk ◽  
Brain Connectivity ◽  
Persistent Homology ◽  
Brain Network ◽  
Resonance Imaging ◽  
Modeling Framework ◽  
Apoe Ε4 ◽  
Topological Features

Abstract Background Although genetic risk factors and network-level neuroimaging abnormalities have shown effects on cognitive performance and brain atrophy in Alzheimer’s disease (AD), little is understood about how apolipoprotein E (APOE) ε4 allele, the best-known genetic risk for AD, affect brain connectivity before the onset of symptomatic AD. This study aims to investigate APOE ε4 effects on brain connectivity from the perspective of multimodal connectome. Results Here, we propose a novel multimodal brain network modeling framework and a network quantification method based on persistent homology for identifying APOE ε4-related network differences. Specifically, we employ sparse representation to integrate multimodal brain network information derived from both the resting state functional magnetic resonance imaging (rs-fMRI) data and the diffusion-weighted magnetic resonance imaging (dw-MRI) data. Moreover, persistent homology is proposed to avoid the ad hoc selection of a specific regularization parameter and to capture valuable brain connectivity patterns from the topological perspective. The experimental results demonstrate that our method outperforms the competing methods, and reasonably yields connectomic patterns specific to APOE ε4 carriers and non-carriers. Conclusions We have proposed a multimodal framework that integrates structural and functional connectivity information for constructing a fused brain network with greater discriminative power. Using persistent homology to extract topological features from the fused brain network, our method can effectively identify APOE ε4-related brain connectomic biomarkers.

scholarly journals Medium-range order in amorphous ices revealed by persistent homology

2019 ◽  
Vol 31 (45) ◽  
pp. 455403 ◽  
Author(s):  
Sungyeon Hong ◽  
Donghun Kim
Keyword(s):  
Persistent Homology ◽  
Range Order ◽  
Medium Range Order ◽  
Medium Range ◽  
Amorphous Ices

scholarly journals Statistical Inference Over Persistent Homology Predicts Fluid Flow in Porous Media

2019 ◽  
Vol 55 (11) ◽  
pp. 9592-9603
Author(s):  
Chul Moon ◽  
Scott A. Mitchell ◽  
Jason E. Heath ◽  
Matthew Andrew
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Statistical Inference ◽  
Persistent Homology ◽  
Flow In Porous Media
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