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Chung MK, Azizi T, Hanson JL, Alexander AL, Pollak SD, Davidson RJ. Altered topological structure of the brain white matter in maltreated children through topological data analysis. Netw Neurosci 2024; 8:355-376. [PMID: 38711544 PMCID: PMC11073548 DOI: 10.1162/netn_a_00355] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2023] [Accepted: 11/30/2023] [Indexed: 05/08/2024] Open
Abstract
Childhood maltreatment may adversely affect brain development and consequently influence behavioral, emotional, and psychological patterns during adulthood. In this study, we propose an analytical pipeline for modeling the altered topological structure of brain white matter in maltreated and typically developing children. We perform topological data analysis (TDA) to assess the alteration in the global topology of the brain white matter structural covariance network among children. We use persistent homology, an algebraic technique in TDA, to analyze topological features in the brain covariance networks constructed from structural magnetic resonance imaging and diffusion tensor imaging. We develop a novel framework for statistical inference based on the Wasserstein distance to assess the significance of the observed topological differences. Using these methods in comparing maltreated children with a typically developing control group, we find that maltreatment may increase homogeneity in white matter structures and thus induce higher correlations in the structural covariance; this is reflected in the topological profile. Our findings strongly suggest that TDA can be a valuable framework to model altered topological structures of the brain. The MATLAB codes and processed data used in this study can be found at https://github.com/laplcebeltrami/maltreated.
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Affiliation(s)
- Moo K. Chung
- Department of Biostatistics and Medical Informatics, University of Wisconsin–Madison, Madison, WI, USA
| | - Tahmineh Azizi
- Department of Biostatistics and Medical Informatics, University of Wisconsin–Madison, Madison, WI, USA
| | - Jamie L. Hanson
- Department of Psychology, University of Pittsburgh, Pittsburgh, PA, USA
| | - Andrew L. Alexander
- Department of Medical Physics, University of Wisconsin–Madison, Madison, WI, USA
| | - Seth D. Pollak
- Department of Psychology, University of Wisconsin–Madison, Madison, WI, USA
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2
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Ali D, Asaad A, Jimenez MJ, Nanda V, Paluzo-Hidalgo E, Soriano-Trigueros M. A Survey of Vectorization Methods in Topological Data Analysis. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2023; 45:14069-14080. [PMID: 37647183 DOI: 10.1109/tpami.2023.3308391] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
Abstract
Attempts to incorporate topological information in supervised learning tasks have resulted in the creation of several techniques for vectorizing persistent homology barcodes. In this paper, we study thirteen such methods. Besides describing an organizational framework for these methods, we comprehensively benchmark them against three well-known classification tasks. Surprisingly, we discover that the best-performing method is a simple vectorization, which consists only of a few elementary summary statistics. Finally, we provide a convenient web application which has been designed to facilitate exploration and experimentation with various vectorization methods.
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3
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Zabaleta-Ortega A, Masoller C, Guzmán-Vargas L. Topological data analysis of the synchronization of a network of Rössler chaotic electronic oscillators. CHAOS (WOODBURY, N.Y.) 2023; 33:113110. [PMID: 37921586 DOI: 10.1063/5.0167523] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2023] [Accepted: 10/13/2023] [Indexed: 11/04/2023]
Abstract
Synchronization study allows a better understanding of the exchange of information among systems. In this work, we study experimental data recorded from a set of Rössler-like chaotic electronic oscillators arranged in a complex network, where the interactions between the oscillators are given in terms of a connectivity matrix, and their intensity is controlled by a global coupling parameter. We use the zero and one persistent homology groups to characterize the point clouds obtained from the signals recorded in pairs of oscillators. We show that the normalized persistent entropy (NPE) allows us to characterize the effective coupling between pairs of oscillators because it tends to increase with the coupling strength and to decrease with the distance between the oscillators. We also observed that pairs of oscillators that have similar degrees and are nearest neighbors tend to have higher NPE values than pairs with different degrees. However, large variability is found in the NPE values. Comparing the NPE behavior with that of the phase-locking value (PLV, commonly used to evaluate the synchronization of phase oscillators), we find that for large enough coupling, PLV only displays a monotonic increase, while NPE shows a richer behavior that captures variations in the behavior of the oscillators. This is due to the fact that PLV only captures coupling-induced phase changes, while NPE also captures amplitude changes. Moreover, when we consider the same network but with Kuramoto phase oscillators, we also find that NPE captures the transition to synchronization (as it increases with the coupling strength), and it also decreases with the distance between the oscillators. Therefore, we propose NPE as a data analysis technique to try to differentiate pairs of oscillators that have strong effective coupling because they are first or near neighbors, from those that have weaker coupling because they are distant neighbors.
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Affiliation(s)
- A Zabaleta-Ortega
- Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas, Instituto Politécnico Nacional, 07340 Ciudad de México, Mexico
| | - C Masoller
- Departament de Física, Universitat Politècnica de Catalunya, Rambla St. Nebridi 22, 08222 Terrassa, Spain
| | - L Guzmán-Vargas
- Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas, Instituto Politécnico Nacional, 07340 Ciudad de México, Mexico
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4
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Rouse TC, Ni AM, Huang C, Cohen MR. Topological insights into the neural basis of flexible behavior. Proc Natl Acad Sci U S A 2023; 120:e2219557120. [PMID: 37279273 PMCID: PMC10268229 DOI: 10.1073/pnas.2219557120] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Accepted: 03/28/2023] [Indexed: 06/08/2023] Open
Abstract
It is widely accepted that there is an inextricable link between neural computations, biological mechanisms, and behavior, but it is challenging to simultaneously relate all three. Here, we show that topological data analysis (TDA) provides an important bridge between these approaches to studying how brains mediate behavior. We demonstrate that cognitive processes change the topological description of the shared activity of populations of visual neurons. These topological changes constrain and distinguish between competing mechanistic models, are connected to subjects' performance on a visual change detection task, and, via a link with network control theory, reveal a tradeoff between improving sensitivity to subtle visual stimulus changes and increasing the chance that the subject will stray off task. These connections provide a blueprint for using TDA to uncover the biological and computational mechanisms by which cognition affects behavior in health and disease.
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Affiliation(s)
- Tevin C. Rouse
- Division of Biological Sciences, Department of Neurobiology, University of Chicago, Chicago, IL60637
| | - Amy M. Ni
- Dietrich School of Arts and Sciences, Department of Neuroscience, University of Pittsburgh, Pittsburgh, PA15260
| | - Chengcheng Huang
- Dietrich School of Arts and Sciences, Department of Neuroscience, University of Pittsburgh, Pittsburgh, PA15260
- Department of Mathematics, University of Pittsburgh, Pittsburgh, PA15260
| | - Marlene R. Cohen
- Division of Biological Sciences, Department of Neurobiology, University of Chicago, Chicago, IL60637
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5
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Pritchard Y, Sharma A, Clarkin C, Ogden H, Mahajan S, Sánchez-García RJ. Persistent homology analysis distinguishes pathological bone microstructure in non-linear microscopy images. Sci Rep 2023; 13:2522. [PMID: 36781895 PMCID: PMC9925777 DOI: 10.1038/s41598-023-28985-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2022] [Accepted: 01/27/2023] [Indexed: 02/15/2023] Open
Abstract
We present a topological method for the detection and quantification of bone microstructure from non-linear microscopy images. Specifically, we analyse second harmonic generation (SHG) and two photon excited autofluorescence (TPaF) images of bone tissue which capture the distribution of matrix (fibrillar collagen) structure and autofluorescent molecules, respectively. Using persistent homology statistics with a signed Euclidean distance transform filtration on binary patches of images, we are able to quantify the number, size, distribution, and crowding of holes within and across samples imaged at the microscale. We apply our methodology to a previously characterized murine model of skeletal pathology whereby vascular endothelial growth factor expression was deleted in osteocalcin-expressing cells (OcnVEGFKO) presenting increased cortical porosity, compared to wild type (WT) littermate controls. We show significant differences in topological statistics between the OcnVEGFKO and WT groups and, when classifying the males, or females respectively, into OcnVEGFKO or WT groups, we obtain high prediction accuracies of 98.7% (74.2%) and 77.8% (65.8%) respectively for SHG (TPaF) images. The persistence statistics that we use are fully interpretable, can highlight regions of abnormality within an image and identify features at different spatial scales.
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Affiliation(s)
- Ysanne Pritchard
- School of Mathematical Sciences, University of Southampton, Southampton, SO17 1BJ, UK.
| | - Aikta Sharma
- School of Biological Sciences, University of Southampton, Southampton, SO17 1BJ, UK
- Mechanical Engineering, University College London, London, WC1E 7JE, UK
| | - Claire Clarkin
- School of Biological Sciences, University of Southampton, Southampton, SO17 1BJ, UK
| | - Helen Ogden
- School of Mathematical Sciences, University of Southampton, Southampton, SO17 1BJ, UK
- Institute for Life Sciences, University of Southampton, Southampton, SO17 1BJ, UK
- The Alan Turing Institute, London, NW1 2DB, UK
| | - Sumeet Mahajan
- School of Chemistry, University of Southampton, Southampton, SO17 1BJ, UK
- Institute for Life Sciences, University of Southampton, Southampton, SO17 1BJ, UK
| | - Rubén J Sánchez-García
- School of Mathematical Sciences, University of Southampton, Southampton, SO17 1BJ, UK
- Institute for Life Sciences, University of Southampton, Southampton, SO17 1BJ, UK
- The Alan Turing Institute, London, NW1 2DB, UK
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6
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Xia K, Liu X, Wee J. Persistent Homology for RNA Data Analysis. Methods Mol Biol 2023; 2627:211-229. [PMID: 36959450 DOI: 10.1007/978-1-0716-2974-1_12] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/25/2023]
Abstract
Molecular representations are of great importance for machine learning models in RNA data analysis. Essentially, efficient molecular descriptors or fingerprints that characterize the intrinsic structural and interactional information of RNAs can significantly boost the performance of all learning modeling. In this paper, we introduce two persistent models, including persistent homology and persistent spectral, for RNA structure and interaction representations and their applications in RNA data analysis. Different from traditional geometric and graph representations, persistent homology is built on simplicial complex, which is a generalization of graph models to higher-dimensional situations. Hypergraph is a further generalization of simplicial complexes and hypergraph-based embedded persistent homology has been proposed recently. Moreover, persistent spectral models, which combine filtration process with spectral models, including spectral graph, spectral simplicial complex, and spectral hypergraph, are proposed for molecular representation. The persistent attributes for RNAs can be obtained from these two persistent models and further combined with machine learning models for RNA structure, flexibility, dynamics, and function analysis.
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Affiliation(s)
- Kelin Xia
- Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore.
| | - Xiang Liu
- Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore
- Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, China
| | - JunJie Wee
- Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore
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Leykam D, Rondón I, Angelakis DG. Dark soliton detection using persistent homology. CHAOS (WOODBURY, N.Y.) 2022; 32:073133. [PMID: 35907713 DOI: 10.1063/5.0097053] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2022] [Accepted: 07/01/2022] [Indexed: 06/15/2023]
Abstract
Classifying images often requires manual identification of qualitative features. Machine learning approaches including convolutional neural networks can achieve accuracy comparable to human classifiers but require extensive data and computational resources to train. We show how a topological data analysis technique, persistent homology, can be used to rapidly and reliably identify qualitative features in experimental image data. The identified features can be used as inputs to simple supervised machine learning models, such as logistic regression models, which are easier to train. As an example, we consider the identification of dark solitons using a dataset of 6257 labeled atomic Bose-Einstein condensate density images.
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Affiliation(s)
- Daniel Leykam
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543
| | - Irving Rondón
- School of Computational Sciences, Korea Institute for Advanced Study, 85 Hoegi-ro, Seoul 02455, Republic of Korea
| | - Dimitris G Angelakis
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543
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8
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Pun CS, Lee SX, Xia K. Persistent-homology-based machine learning: a survey and a comparative study. Artif Intell Rev 2022. [DOI: 10.1007/s10462-022-10146-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Liu C, Yu D, Ma X, Xie S, Zhang H. Neural evidence for image quality perception based on algebraic topology. PLoS One 2021; 16:e0261223. [PMID: 34914746 PMCID: PMC8675722 DOI: 10.1371/journal.pone.0261223] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2021] [Accepted: 11/27/2021] [Indexed: 11/18/2022] Open
Abstract
In this paper, the algebraic topological characteristics of brain networks composed of electroencephalogram(EEG) signals induced by different quality images were studied, and on that basis, a neurophysiological image quality assessment approach was proposed. Our approach acquired quality perception-related neural information via integrating the EEG collection with conventional image assessment procedures, and the physiologically meaningful brain responses to different distortion-level images were obtained by topological data analysis. According to the validation experiment results, statistically significant discrepancies of the algebraic topological characteristics of EEG data evoked by a clear image compared to that of an unclear image are observed in several frequency bands, especially in the beta band. Furthermore, the phase transition difference of brain network caused by JPEG compression is more significant, indicating that humans are more sensitive to JPEG compression other than Gaussian blur. In general, the algebraic topological characteristics of EEG signals evoked by distorted images were investigated in this paper, which contributes to the study of neurophysiological assessment of image quality.
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Affiliation(s)
- Chang Liu
- Institute of Intelligent Media Technology, Communication University of Zhejiang, Hangzhou, Zhejiang, China
| | - Dingguo Yu
- Institute of Intelligent Media Technology, Communication University of Zhejiang, Hangzhou, Zhejiang, China
- College of Media Engineering, Communication University of Zhejiang, Hangzhou, Zhejiang, China
| | - Xiaoyu Ma
- Institute of Intelligent Media Technology, Communication University of Zhejiang, Hangzhou, Zhejiang, China
| | - Songyun Xie
- College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, Zhejiang, China
| | - Honggang Zhang
- School of Electronics and Information, Northwestern Polytechnical University, Xi’an, Shaanxi, China
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10
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Weighted persistent homology for osmolyte molecular aggregation and hydrogen-bonding network analysis. Sci Rep 2020; 10:9685. [PMID: 32546801 PMCID: PMC7297731 DOI: 10.1038/s41598-020-66710-6] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2019] [Accepted: 05/20/2020] [Indexed: 12/24/2022] Open
Abstract
It has long been observed that trimethylamine N-oxide (TMAO) and urea demonstrate dramatically different properties in a protein folding process. Even with the enormous theoretical and experimental research work on these two osmolytes, various aspects of their underlying mechanisms still remain largely elusive. In this paper, we propose to use the weighted persistent homology to systematically study the osmolytes molecular aggregation and their hydrogen-bonding network from a local topological perspective. We consider two weighted models, i.e., localized persistent homology (LPH) and interactive persistent homology (IPH). Boltzmann persistent entropy (BPE) is proposed to quantitatively characterize the topological features from LPH and IPH, together with persistent Betti number (PBN). More specifically, from the localized persistent homology models, we have found that TMAO and urea have very different local topology. TMAO is found to exhibit a local network structure. With the concentration increase, the circle elements in these networks show a clear increase in their total numbers and a decrease in their relative sizes. In contrast, urea shows two types of local topological patterns, i.e., local clusters around 6 Å and a few global circle elements at around 12 Å. From the interactive persistent homology models, it has been found that our persistent radial distribution function (PRDF) from the global-scale IPH has same physical properties as the traditional radial distribution function. Moreover, PRDFs from the local-scale IPH can also be generated and used to characterize the local interaction information. Other than the clear difference of the first peak value of PRDFs at filtration size 4 Å, TMAO and urea also shows very different behaviors at the second peak region from filtration size 5 Å to 10 Å. These differences are also reflected in the PBNs and BPEs of the local-scale IPH. These localized topological information has never been revealed before. Since graphs can be transferred into simplicial complexes by the clique complex, our weighted persistent homology models can be used in the analysis of various networks and graphs from any molecular structures and aggregation systems.
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Dugast M, Bouleux G, Mory O, Marcon E. Improving Health Care Management Through Persistent Homology of Time-Varying Variability of Emergency Department Patient Flow. IEEE J Biomed Health Inform 2019; 23:2174-2181. [DOI: 10.1109/jbhi.2018.2882748] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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12
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Piangerelli M, Rucco M, Tesei L, Merelli E. Topolnogical classifier for detecting the emergence of epileptic seizures. BMC Res Notes 2018; 11:392. [PMID: 29903043 PMCID: PMC6003048 DOI: 10.1186/s13104-018-3482-7] [Citation(s) in RCA: 33] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2018] [Accepted: 06/05/2018] [Indexed: 01/19/2023] Open
Abstract
OBJECTIVE An innovative method based on topological data analysis is introduced for classifying EEG recordings of patients affected by epilepsy. We construct a topological space from a collection of EEGs signals using Persistent Homology; then, we analyse the space by Persistent entropy, a global topological feature, in order to classify healthy and epileptic signals. RESULTS The performance of the resulting one-feature-based linear topological classifier is tested by analysing the Physionet dataset. The quality of classification is evaluated in terms of the Area Under Curve (AUC) of the receiver operating characteristic curve. It is shown that the linear topological classifier has an AUC equal to [Formula: see text] while the performance of a classifier based on Sample Entropy has an AUC equal to 62.0%.
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Affiliation(s)
- Marco Piangerelli
- Computer Science Division, School of Science and Technology, University of Camerino, Via Madonna delle Carceri, 9, 62032 Camerino, IT Italy
| | - Matteo Rucco
- ALES S.r.l.-United Technologies Research Center, Via Praga, 5, 38121 Trento, IT Italy
| | - Luca Tesei
- Computer Science Division, School of Science and Technology, University of Camerino, Via Madonna delle Carceri, 9, 62032 Camerino, IT Italy
| | - Emanuela Merelli
- Computer Science Division, School of Science and Technology, University of Camerino, Via Madonna delle Carceri, 9, 62032 Camerino, IT Italy
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Multiscale Persistent Functions for Biomolecular Structure Characterization. Bull Math Biol 2017; 80:1-31. [PMID: 29098540 DOI: 10.1007/s11538-017-0362-6] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2016] [Accepted: 10/19/2017] [Indexed: 10/18/2022]
Abstract
In this paper, we introduce multiscale persistent functions for biomolecular structure characterization. The essential idea is to combine our multiscale rigidity functions (MRFs) with persistent homology analysis, so as to construct a series of multiscale persistent functions, particularly multiscale persistent entropies, for structure characterization. To clarify the fundamental idea of our method, the multiscale persistent entropy (MPE) model is discussed in great detail. Mathematically, unlike the previous persistent entropy (Chintakunta et al. in Pattern Recognit 48(2):391-401, 2015; Merelli et al. in Entropy 17(10):6872-6892, 2015; Rucco et al. in: Proceedings of ECCS 2014, Springer, pp 117-128, 2016), a special resolution parameter is incorporated into our model. Various scales can be achieved by tuning its value. Physically, our MPE can be used in conformational entropy evaluation. More specifically, it is found that our method incorporates in it a natural classification scheme. This is achieved through a density filtration of an MRF built from angular distributions. To further validate our model, a systematical comparison with the traditional entropy evaluation model is done. It is found that our model is able to preserve the intrinsic topological features of biomolecular data much better than traditional approaches, particularly for resolutions in the intermediate range. Moreover, by comparing with traditional entropies from various grid sizes, bond angle-based methods and a persistent homology-based support vector machine method (Cang et al. in Mol Based Math Biol 3:140-162, 2015), we find that our MPE method gives the best results in terms of average true positive rate in a classic protein structure classification test. More interestingly, all-alpha and all-beta protein classes can be clearly separated from each other with zero error only in our model. Finally, a special protein structure index (PSI) is proposed, for the first time, to describe the "regularity" of protein structures. Basically, a protein structure is deemed as regular if it has a consistent and orderly configuration. Our PSI model is tested on a database of 110 proteins; we find that structures with larger portions of loops and intrinsically disorder regions are always associated with larger PSI, meaning an irregular configuration, while proteins with larger portions of secondary structures, i.e., alpha-helix or beta-sheet, have smaller PSI. Essentially, PSI can be used to describe the "regularity" information in any systems.
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