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SI-spreading-based network embedding in static and temporal networks

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arXiv 2020年

作者： Zhan, Xiu-Xiu Li, Ziyu Masuda, Naoki Holme, Petter Wang, Huijuan Faculty of Electrical Engineering Mathematics and Computer Science Delft University of Technology Mekelweg 4 Delft2628 CD Netherlands Department of Mathematics University at Buffalo State University of New York Buffalo New YorkNY14260-2900 United States Computational and Data-Enabled Science and Engineering Program University at Buffalo State University of New York Buffalo New YorkNY14260-2900 United States Institute of Innovative Research Tokyo Institute of Technology Yokohama226-8503 Japan

Link prediction can be used to extract missing information, identify spurious interactions as well as forecast network evolution. Network embedding is a methodology to assign coordinates to nodes in a low-dimensional vector space. By embedding nodes into vectors, the link prediction problem can be converted into a similarity comparison task. Nodes with similar embedding vectors are more likely to be connected. Classic network embedding algorithms are random-walk-based. They sample trajectory paths via random walks and generate node pairs from the trajectory paths. The node pair set is further used as the input for a Skip-Gram model, a representative language model that embeds nodes (which are regarded as words) into vectors. In the present study, we propose to replace random walk processes by a spreading process, namely the susceptible-infected (SI) model, to sample paths. Specifically, we propose two SI-spreading-based algorithms, SINE and TSINE, to embed static and temporal networks, respectively. The performance of our algorithms is evaluated by the missing link prediction task in comparison with state-of-the-art static and temporal network embedding algorithms. Results show that SINE and TSINE outperform the baselines across all six empirical datasets. We further find that the performance of SINE is mostly better than TSINE, suggesting that temporal information does not necessarily improve the embedding for missing link prediction. Moreover, we study the effect of the sampling size, quantified as the total length of the trajectory paths, on the performance of the embedding algorithms. The better performance of SINE and TSINE requires a smaller sampling size in comparison with the baseline algorithms. Hence, SI-spreading-based embedding tends to be more applicable to large-scale networks. Copyright © 2020, The Authors. All rights reserved.

关键词： Network embeddings

OpenMM 8: Molecular Dynamics Simulation with Machine Learning Potentials

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arXiv 2023年

作者： Eastman, Peter Galvelis, Raimondas Peláez, Raúl P. Abreu, Charlles R.A. Farr, Stephen E. Gallicchio, Emilio Gorenko, Anton Henry, Michael M. Hu, Frank Huang, Jing Krämer, Andreas Michel, Julien Mitchell, Joshua A. Pande, Vijay S. Rodrigues, João P.G.L.M. Rodriguez-Guerra, Jaime Simmonett, Andrew C. Singh, Sukrit Swails, Jason Turner, Philip Wang, Yuanqing Zhang, Ivy Chodera, John D. De Fabritiis, Gianni Markland, Thomas E. Department of Chemistry Stanford University StanfordCA94305 United States Acellera Labs C Dr Trueta 183 Barcelona08005 Spain C Dr. Aiguader 88 Barcelona08003 Spain Chemical Engineering Department School of Chemistry Federal University of Rio de Janeiro Rio de Janeiro68542 Brazil Redesign Science Inc. 180 Varick St. New YorkNY10014 United States EaStCHEM School of Chemistry University of Edinburgh EH9 3FJ United Kingdom Department of Chemistry and Biochemistry Brooklyn College The City University of New York NY United States Ph.D. Program in Chemistry Ph.D. Program in Biochemistry The Graduate Center of the City University of New York New YorkNY United States Stream HPC Koningin Wilhelminaplein 1 - 40601 Amsterdam1062 HG Netherlands Computational and Systems Biology Program Sloan Kettering Institute Memorial Sloan Kettering Cancer Center New YorkNY10065 United States Key Laboratory of Structural Biology of Zhejiang Province School of Life Sciences Westlake University 18 Shilongshan Road Zhejiang Hangzhou310024 China Department of Mathematics and Computer Science Freie Universität Berlin Arnimallee 12 Berlin14195 Germany The Open Force Field Initiative Open Molecular Software Foundation DavisCA95616 United States Andreessen Horowitz 2865 Sand Hill Rd Menlo ParkCA94025 United States Department of Structural Biology Stanford University StanfordCA94305 United States Charité Universitätsmedizin Berlin In silico Toxicology and Structural Bioinformatics Virchowweg 6 Berlin10117 Germany Laboratory of Computational Biology National Heart Lung and Blood Institute National Institutes of Health BethesdaMD20892 United States Entos Inc. 9310 Athena Circle La Jolla CA92037 United States College of Engineering Virginia Polytechnic Institute State University BlacksburgVA24061 United States Simons Center for Computational Physical Chemistry Center for Data Science New York University 24 Waverly Place New YorkNY10004 United States T

Machine learning plays an important and growing role in molecular simulation. The newest version of the OpenMM molecular dynamics toolkit introduces new features to support the use of machine learning potentials. Arbitrary PyTorch models can be added to a simulation and used to compute forces and energy. A higher-level interface allows users to easily model their molecules of interest with general purpose, pretrained potential functions. A collection of optimized CUDA kernels and custom PyTorch operations greatly improves the speed of simulations. We demonstrate these features on simulations of cyclin-dependent kinase 8 (CDK8) and the green fluorescent protein (GFP) chromophore in water. Taken together, these features make it practical to use machine learning to improve the accuracy of simulations at only a modest increase in cost. Copyright © 2023, The Authors. All rights reserved.

关键词： Machine learning

Bioinformatics Pathway Analysis Pipeline for NGS Transcriptome Profile data on Nasopharyngeal Carcinoma

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IOP Conference Series: Earth and Environmental science 2021年第1期794卷

作者： Digdo Sudigyo Gisti Rahmawati Dicka W. Setiasari Risky H. Poluan Tjeng Wawan Cenggoro Arif Budiarto Alam Ahmad Hidayat Sri R. Indrasari Afiahayati Sofia M. Haryana Bens Pardamean Bioinformatics & Data Science Research Center Bina Nusantara University Jakarta Indonesia 11480 Study Program of Biotechnology Gadjah Mada University Yogyakarta Indonesia 55281 Computer Science Department School of Computer Science Bina Nusantara University Jakarta Indonesia 11480 Faculty of Medicine Public Health and Nursing Gadjah Mada University Yogyakarta Indonesia 55281 Department of Computer Science and Electronics Faculty of Mathematics and Natural Science Gadjah Mada University Yogyakarta Indonesia 55281 Computer Science Department BINUS Graduate Program - Master of Computer Science Program Bina Nusantara University Jakarta Indonesia 11480

Next-Generation Sequencing (NGS)-based genomics data have a huge potential to be used in transcriptomic profiling of Nasopharyngeal Carcinoma (NPC) to study the biosynthesis mechanism behind it. The high dimensionality of NGS data is the main challenge in performing the data analysis to extract useful information. In this workflow pipeline, memory-efficient Linux-based software such as HISAT2 and HTSeq are utilized to process the raw NGS data. Furthermore, Differential Expression Gene (DEG) list can be obtained by performing advanced analysis to the aligned Ribonucleic Acid (RNA) sequence using the edgeR protocol. This DEG list is one of the main inputs of biological pathway analysis that can be done in DAVID and PANTHER web-based software. Both tools generate a different pathway result related to inflammation.

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Deep learning inference with the Event Horizon Telescope I. Calibration improvements and a comprehensive synthetic data library

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Astronomy and Astrophysics 2025年第1期698卷

作者： Janssen, M. Chan, C.K. Davelaar, J. Natarajan, I. Olivares, H. Ripperda, B. Röder, J. Rynge, M. Wielgus, M. Department of Astrophysics Institute for Mathematics Astrophysics and Particle Physics (IMAPP) Radboud University PO Box 9010 Nijmegen 6500 GL Netherlands Max-Planck-Institut für Radioastronomie Auf dem Hügel 69 Bonn 53121 Germany Steward Observatory Department of Astronomy University of Arizona 933 N. Cherry Ave. Tucson 85721 AZ United States Data Science Institute University of Arizona 1230 N. Cherry Ave. Tucson 85721 AZ United States Program in Applied Mathematics University of Arizona 617 N. Santa Rita Ave. Tucson 85721 AZ United States Department of Astrophysical Sciences Peyton Hall Princeton University Princeton 08544 NJ United States Center for Astrophysics Harvard & Smithsonian 60 Garden Street Cambridge 02138 MA United States Black Hole Initiative Harvard University 20 Garden Street Cambridge 02138 MA United States Canadian Institute for Theoretical Astrophysics University of Toronto Toronto M5S 3H8 ON Canada Department of Astronomy University of Toronto 50 St. George Street Toronto M5S 3H4 ON Canada Department of Physics University of Toronto 60 St. George Street Toronto M5S 1A7 ON Canada Perimeter Institute for Theoretical Physics Waterloo N2L 2Y5 ON Canada University of Southern California – Information Sciences Institute 4676 Admiralty Way Suite 1001 Marina del Rey 90292 CA United States Instituto de Astrofísica de Andalucía-CSIC Glorieta de la Astronomía s/n Granada 18008 Spain Departamento de Matemática da Universidade de Aveiro Centre for Research and Development in Mathematics and Applications (CIDMA) Campus de Santiago Aveiro 3810-193 Portugal

Context. In a series of publications, we describe a comprehensive comparison of Event Horizon Telescope (EHT) data with theoretical models of the observed Sagittarius A* (Sgr A^∗) and Messier 87* (M87^∗) horizon-scale sources. Aims. In this article, we report on improvements made to our observational data reduction pipeline and present the generation of observables derived from the EHT models. We make use of ray-traced general relativistic magnetohydrodynamic simulations that are based on different black hole spacetime metrics and accretion physics parameters. These broad classes of models provide a good representation of the primary targets observed by the EHT. Methods. We describe how we combined multiple frequency bands and polarization channels of the observational data to improve our fringe-finding sensitivity and stabilization of atmospheric phase fluctuations. To generate realistic synthetic data from our models, we took the signal path as well as the calibration process, and thereby the aforementioned improvements, into account. We could thus produce synthetic visibilities akin to calibrated EHT data and identify salient features for the discrimination of model parameters. Results. We have produced a library consisting of an unparalleled 962 000 synthetic Sgr A^∗ and M87^∗ datasets. In terms of baseline coverage and noise properties, the library encompasses 2017 EHT measurements as well as future observations with an extended telescope array. Conclusions. We differentiate between robust visibility data products related to model features and data products that are strongly affected by data corruption effects. Parameter inference is mostly limited by intrinsic model variability, which highlights the importance of long-term monitoring observations with the EHT. In later papers in this series, we will show how a Bayesian neural network trained on our synthetic data is capable of dealing with the model variability and extra

关键词： accretion, accretion disks black hole physics galaxies: active techniques: high angular resolution techniques: interferometric

DeePMD-kit v2: A software package for Deep Potential models

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arXiv 2023年

作者： Zeng, Jinzhe Zhang, Duo Lu, Denghui Mo, Pinghui Li, Zeyu Chen, Yixiao Rynik, Marián Huang, Li'ang Li, Ziyao Shi, Shaochen Wang, Yingze Ye, Haotian Tuo, Ping Yang, Jiabin Ding, Ye Li, Yifan Tisi, Davide Zeng, Qiyu Bao, Han Xia, Yu Huang, Jiameng Muraoka, Koki Wang, Yibo Chang, Junhan Yuan, Fengbo Bore, Sigbjørn Løland Cai, Chun Lin, Yinnian Wang, Bo Xu, Jiayan Zhu, Jia-Xin Luo, Chenxing Zhang, Yuzhi Goodall, Rhys E.A. Liang, Wenshuo Singh, Anurag Kumar Yao, Sikai Zhang, Jingchao Wentzcovitch, Renata Han, Jiequn Liu, Jie Jia, Weile York, Darrin M. Weinan, E. Car, Roberto Zhang, Linfeng Wang, Han Laboratory for Biomolecular Simulation Research Institute for Quantitative Biomedicine Department of Chemistry and Chemical Biology Rutgers University PiscatawayNJ08854 United States AI for Science Institute Beijing100080 China DP Technology Beijing100080 China Academy for Advanced Interdisciplinary Studies Peking University Beijing100871 China HEDPS CAPT College of Engineering Peking University Beijing100871 China College of Electrical and Information Engineering Hunan University Changsha China Yuanpei College Peking University Beijing100871 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States Department of Experimental Physics Comenius University Mlynská Dolina F2 Bratislava842 48 Slovakia Center for Quantum Information Institute for Interdisciplinary Information Sciences Tsinghua University Beijing100084 China Center for Data Science Peking University Beijing100871 China ByteDance Research Zhonghang Plaza No. 43 North 3rd Ring West Road Haidian District Beijing China College of Chemistry and Molecular Engineering Peking University Beijing100871 China Baidu Inc. Beijing China Key Laboratory of Structural Biology of Zhejiang Province School of Life Sciences Westlake University Zhejiang Hangzhou China Westlake AI Therapeutics Lab Westlake Laboratory of Life Sciences and Biomedicine Zhejiang Hangzhou China Department of Chemistry Princeton University PrincetonNJ08544 United States SISSA Scuola Internazionale Superiore di Studi Avanzati Trieste34136 Italy Laboratory of Computational Science and Modeling Institute of Materials École Polytechnique Fédérale de Lausanne Lausanne1015 Switzerland Department of Physics National University of Defense Technology Hunan Changsha410073 China State Key Lab of Processors Institute of Computing Technology Chinese Academy of Sciences Beijing China University of Chinese Academy of Sciences Beijing China School of Electronics Engineerin

DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials (MLP) known as Deep Potential (DP) models. This package, which was released in 2017, has been widely used in the fields of physics, chemistry, biology, and material science for studying atomistic systems. The current version of DeePMD-kit offers numerous advanced features such as DeepPot-SE, attention-based and hybrid descriptors, the ability to fit tensile properties, type embedding, model deviation, Deep Potential - Range Correction (DPRc), Deep Potential Long Range (DPLR), GPU support for customized operators, model compression, non-von Neumann molecular dynamics (NVNMD), and improved usability, including documentation, compiled binary packages, graphical user interfaces (GUI), and application programming interfaces (API). This article presents an overview of the current major version of the DeePMD-kit package, highlighting its features and technical details. Additionally, the article benchmarks the accuracy and efficiency of different models and discusses ongoing developments. © 2023, CC BY-NC-ND.

关键词： Molecular dynamics

APPROXIMATE BAYESIAN INFERENCE OF DIRECTED ACYCLIC GRAPHS IN BIOLOGY WITH FLEXIBLE PRIORS ON EDGE STATES

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arXiv 2019年

作者： Martin, Evan A. Fu, Audrey Qiuyan The Bioinformatics and Computational Biology Program University of Idaho United States The Bioinformatics and Computational Biology Program Department of Mathematics and Statistical Science Institute for Modeling Collaboration and Innovation Institute for Interdisciplinary Data Sciences University of Idaho United States

Graphical models or networks describe the statistical dependence among multiple variables and are widely used in biology (e.g., gene regulatory networks). Under appropriate assumptions, directed edges may represent causal relationships. A key feature of a biological network is sparsity, defined by how likely an edge is present, of which we often have some knowledge. However, most existing Bayesian methods use priors for the entire graph, making it difficult to specify the level of sparsity. The few methods that use priors on edges estimate the two directions independently;the sum of the two probabilities can exceed 1. Here, we present baycn (BAYesian Causal Network), a novel approximate Bayesian method that represents a graph in terms of three states of edges: the two directions and edge absence, and specifies priors on these edge states. We design a pseudo Bayesian sampling algorithm for efficient inference. We apply baycn to two genomic problems: i) distinguishing direct and indirect target genes of genetic variants, using these variants as instrumental variables, and ii) inferring combinatorial binding of highly-correlated transcription factors in Drosophila. In both cases and in extensive simulations, our method demonstrates much improved accuracy over existing methods for the whole graph and for individual edges. Copyright © 2019, The Authors. All rights reserved.

关键词： Inference engines

FUTURE-AI: International consensus guideline for trustworthy and deployable artificial intelligence in healthcare

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arXiv 2023年

作者： Lekadir, Karim Feragen, Aasa Fofanah, Abdul Joseph Frangi, Alejandro F. Buyx, Alena Emelie, Anais Lara, Andrea Porras, Antonio R. Chan, An-Wen Navarro, Arcadi Glocker, Ben Botwe, Benard O. Khanal, Bishesh Beger, Brigit Wu, Carol C. Cintas, Celia Langlotz, Curtis P. Rueckert, Daniel Mzurikwao, Deogratias Fotiadis, Dimitrios I. Zhussupov, Doszhan Ferrante, Enzo Meijering, Erik Weicken, Eva González, Fabio A. Asselbergs, Folkert W. Prior, Fred Krestin, Gabriel P. Collins, Gary S. Tegenaw, Geletaw S. Kaissis, Georgios Misuraca, Gianluca Tsakou, Gianna Dwivedi, Girish Kondylakis, Haridimos Jayakody, Harsha Woodruf, Henry C. Mayer, Horst Joachim Aerts, Hugo JWL Walsh, Ian Chouvarda, Ioanna Buvat, Irène Tributsch, Isabell Rekik, Islem Duncan, James Kalpathy-Cramer, Jayashree Zahir, Jihad Park, Jinah Mongan, John Gichoya, Judy W. Schnabel, Julia A. Kushibar, Kaisar Riklund, Katrine Mori, Kensaku Marias, Kostas Amugongo, Lameck M. Fromont, Lauren A. Maier-Hein, Lena Alberich, Leonor Cerdá Rittner, Leticia Phiri, Lighton Marrakchi-Kacem, Linda Donoso-Bach, Lluís Martí-Bonmatí, Luis Cardoso, M. Jorge Bobowicz, Maciej Shabani, Mahsa Tsiknakis, Manolis Zuluaga, Maria A. Bielikova, Maria Fritzsche, Marie-Christine Camacho, Marina Linguraru, Marius George Wenzel, Markus De Bruijne, Marleen Tolsgaard, Martin G. Ghassemi, Marzyeh Ashrafuzzaman, Md Goisauf, Melanie Yaqub, Mohammad Abadía, Mónica Cano Mahmoud, Mukhtar M.E. Elattar, Mustafa Rieke, Nicola Papanikolaou, Nikolaos Lazrak, Noussair Díaz, Oliver Salvado, Olivier Pujol, Oriol Sall, Ousmane Guevara, Pamela Gordebeke, Peter Lambin, Philippe Brown, Pieta Abolmaesumi, Purang Dou, Qi Lu, Qinghua Osuala, Richard Nakasi, Rose Zhou, S. Kevin Napel, Sandy Colantonio, Sara Albarqouni, Shadi Joshi, Smriti Carter, Stacy Klein, Stefan Petersen, Steffen E. Aussó, Susanna Awate, Suyash Raviv, Tammy Riklin Cook, Tessa Mutsvangwa, Tinashe E.M. Rogers, Wendy A. Niessen, Wiro J. Puig-Bosch, Xènia Zeng, Yi Mohammed, Yunusa G. Aquino, Yves Saint James Salahuddin, Zohaib Starmans, Martijn P.A. Department de Matemàtiques i Informàtica Universitat de Barcelona Barcelona Spain Barcelona Spain DTU Compute Technical University of Denmark Kgs Lyngby Denmark Department of Mathematics and Computer Science Faculty of Science and Technology Milton Margai Technical University Freetown Sierra Leone Center for Computational Imaging & Simulation Technologies in Biomedicine Schools of Computing and Medicine University of Leeds Leeds United Kingdom Cardiovascular Science and Electronic Engineering Departments KU Leuven Leuven Belgium Institute of History and Ethics in Medicine Technical University of Munich Munich Germany Faculty of Engineering of Systems Informatics and Sciences of Computing Galileo University Guatemala City Guatemala Department of Biostatistics and Informatics Colorado School of Public Health University of Colorado Anschutz Medical Campus AuroraCO United States Department of Medicine Women’s College Research Institute University of Toronto Toronto Canada Universitat Pompeu Fabra BarcelonaBeta Brain Research Center Barcelona Spain Department of Computing Imperial College London London United Kingdom School of Biomedical & Allied Health Sciences University of Ghana Accra Ghana Department of Midwifery & Radiography School of Health & Psychological Sciences City University of London United Kingdom Kathmandu Nepal European Heart Network Brussels Belgium Department of Thoracic Imaging University of Texas MD Anderson Cancer Center Houston United States IBM Research Africa Nairobi Kenya Departments of Radiology Medicine and Biomedical Data Science Stanford University School of Medicine Stanford United States Institute for AI and Informatics in Medicine Klinikum rechts der Isar Technical University Munich Munich Germany Department of Computing Imperial College London London United Kingdom Muhimbili University of Health and Allied Sciences Dar es Salaam Tanzania United Republic of Ioannina Greece Almaty AI Lab Almaty Kazakhstan

Background: Despite major advances in artificial intelligence (AI) research for healthcare, the deployment and adoption of AI technologies remain limited in clinical practice. In recent years, concerns have been raised about the clinical, technical, ethical and legal risks associated with healthcare AI. To increase adoption in the real world, it is essential that AI technologies are trusted and accepted by patients, clinicians, health organisations and authorities. This paper describes the FUTURE-AI framework as the first international consensus guideline for trustworthy AI in healthcare. Methods: The FUTURE-AI consortium was founded in 2021 and now comprises 117 interdisciplinary experts from 50 countries representing all continents, including AI scientists, clinical researchers, biomedical ethicists, and social scientists. Over a two-year period, the consortium established guiding principles and best practices for trustworthy and deployable AI through an iterative process comprising an in-depth literature review, a modified Delphi survey, and online consensus meetings. Findings: The FUTURE-AI framework was established based on six guiding principles for trustworthy AI in healthcare, i.e. Fairness, Universality, Traceability, Usability, Robustness and Explainability. Through consensus, a set of 30 best practices were defined, addressing technical, clinical, socio-ethical and legal dimensions of trustworthy AI. The recommendations cover the entire lifecycle of healthcare AI, from design, development and validation to regulation, deployment, and monitoring. Interpretation: FUTURE-AI is a structured, risk-informed framework which provides guidance for constructing healthcare AI tools that will be trusted, deployed and adopted in real-world clinical practice. Researchers are encouraged to take the recommendations into account in proof-of-concept stages to facilitate future translation towards clinical practice of healthcare AI. Copyright © 2023, The Authors. All rights

关键词： Clinical research

Cost-sensitive selection of variables by ensemble of model sequences

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arXiv 2019年

作者： Yan, Donghui Qin, Zhiwei Gu, Songxiang Xu, Haiping Shao, Ming Department of Mathematics and Program in Data Science DiDi Research America Mountain ViewCA United States JD Digital Mountain ViewCA United States Department of Computer and Information Science University of Massachusetts Dartmouth MA United States

Many applications require the collection of data on different variables or measurements over many system performance metrics. We term those broadly as measures or variables. Often data collection along each measure incurs a cost, thus it is desirable to consider the cost of measures in modeling. This is a fairly new class of problems in the area of cost-sensitive learning. A few attempts have been made to incorporate costs in combining and selecting measures. However, existing studies either do not strictly enforce a budget constraint, or are not the 'most' cost effective. With a focus on classification problems, we propose a computationally efficient approach that could find a near optimal model under a given budget by exploring the most 'promising' part of the solution space. Instead of outputting a single model, we produce a model schedule-a list of models, sorted by model costs and expected predictive accuracy. This could be used to choose the model with the best predictive accuracy under a given budget, or to trade off between the budget and the predictive accuracy. Experiments on some benchmark datasets show that our approach compares favorably to competing methods. © 2019, CC BY-NC-ND.

关键词： data acquisition

Bounded Manifold Completion

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arXiv 2019年

作者： Gajamannage, Kelum Paffenroth, Randy Department of Mathematics and Statistics Texas A&M University–Corpus Christi Corpus ChristiTX78412 United States Department of Mathematical Sciences Department of Computer Science and Data Science Program Worcester Polytechnic Institute WorcesterMA01609 United States

Nonlinear dimensionality reduction or, equivalently, the approximation of high-dimensional data using a low-dimensional nonlinear manifold is an active area of research. In this paper, we will present a thematically different approach to detect the existence of a low-dimensional manifold of a given dimension that lies within a set of bounds derived from a given point cloud. A matrix representing the appropriately defined distances on a low-dimensional manifold is low-rank, and our method is based on current techniques for recovering a partially observed matrix from a small set of fully observed entries that can be implemented as a low-rank Matrix Completion (MC) problem. MC methods are currently used to solve challenging real-world problems, such as image inpainting and recommender systems, and we leverage extent efficient optimization techniques that use a nuclear norm convex relaxation as a surrogate for non-convex and discontinuous rank minimization. Our proposed method provides several advantages over current nonlinear dimensionality reduction techniques, with the two most important being theoretical guarantees on the detection of low-dimensional embeddings and robustness to non-uniformity in the sampling of the manifold. We validate the performance of this approach using both a theoretical analysis as well as synthetic and real-world benchmark *** Codes 68T05 Copyright © 2019, The Authors. All rights reserved.

关键词： Relaxation processes