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Multidimensional scaling, Sammon mapping, and Isomap: Tutorial and survey

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arXiv 2020年

Multidimensional Scaling (MDS) is one of the first fundamental manifold learning methods. It can be categorized into several methods, i.e., classical MDS, kernel classical MDS, metric MDS, and non-metric MDS. Sammon mapping and Isomap can be considered as special cases of metric MDS and kernel classical MDS, respectively. In this tutorial and survey paper, we review the theory of MDS, Sammon mapping, and Isomap in detail. We explain all the mentioned categories of MDS. Then, Sammon mapping, Isomap, and kernel Isomap are explained. Out-of-sample embedding for MDS and Isomap using eigenfunctions and kernel mapping are introduced. Then, Nystrom approximation and its use in landmark MDS and landmark Isomap are introduced for big data embedding. We also provide some simulations for illustrating the embedding by these methods. Copyright © 2020, The Authors. All rights reserved.

关键词： Embeddings

Locally linear embedding and its variants: Tutorial and survey

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arXiv 2020年

作者： Ghojogh, Benyamin Ghodsi, Ali Karray, Fakhri Crowley, Mark Department of Electrical and Computer Engineering Machine Learning Laboratory University of Waterloo WaterlooON Canada Department of Statistics and Actuarial Science & David R. Cheriton School of Computer Science Data Analytics Laboratory University of Waterloo WaterlooON Canada Department of Electrical and Computer Engineering Centre for Pattern Analysis and Machine Intelligence University of Waterloo WaterlooON Canada

This is a tutorial and survey paper for Locally Linear Embedding (LLE) and its variants. The idea of LLE is fitting the local structure of manifold in the embedding space. In this paper, we first cover LLE, kernel LLE, inverse LLE, and feature fusion with LLE. Then, we cover out-of-sample embedding using linear reconstruction, eigenfunctions, and kernel mapping. Incremental LLE is explained for embedding streaming data. Landmark LLE methods using the Nystrom approximation and locally linear landmarks are explained for big data embedding. We introduce the methods for parameter selection of number of neighbors using residual variance, Procrustes statistics, preservation neighborhood error, and local neighborhood selection. Afterwards, Supervised LLE (SLLE), enhanced SLLE, SLLE projection, probabilistic SLLE, supervised guided LLE (using Hilbert-Schmidt independence criterion), and semi-supervised LLE are explained for supervised and semi-supervised embedding. Robust LLE methods using least squares problem and penalty functions are also introduced for embedding in the presence of outliers and noise. Then, we introduce fusion of LLE with other manifold learning methods including Isomap (i.e., ISOLLE), principal component analysis, Fisher discriminant analysis, discriminant LLE, and Isotop. Finally, we explain weighted LLE in which the distances, reconstruction weights, or the embeddings are adjusted for better embedding;we cover weighted LLE for deformed distributed data, weighted LLE using probability of occurrence, SLLE by adjusting weights, modified LLE, and iterative LLE. Copyright © 2020, The Authors. All rights reserved.

关键词： Iterative methods

On ADMM in deep learning: convergence and saturation-avoidance

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The Journal of Machine Learning Research

The Journal of machine learning Research 2021年第1期22卷 9024-9090页

作者： Jinshan Zeng Shao-Bo Lin Yuan Yao Ding-Xuan Zhou School of Computer and Information Engineering Jiangxi Normal University Nanchang China and Liu Bie Ju Centre for Mathematical Sciences City University of Hong Kong Hong Kong and Department of Mathematics Hong Kong University of Science and Technology Hong Kong Center of Intelligent Decision-Making and Machine Learning School of Management Xi'an Jiaotong University Xi'an China Department of Mathematics Hong Kong University of Science and Technology Hong Kong School of Data Science and Department of Mathematics City University of Hong Kong Hong Kong

In this paper, we develop an alternating direction method of multipliers (ADMM) for deep neural networks training with sigmoid-type activation functions (called sigmoid-ADMM pair), mainly motivated by the gradient-free nature of ADMM in avoiding the saturation of sigmoid-type activations and the advantages of deep neural networks with sigmoid-type activations (called deep sigmoid nets) over their rectified linear unit (ReLU) counterparts (called deep ReLU nets) in terms of approximation. In particular, we prove that the approximation capability of deep sigmoid nets is not worse than that of deep ReLU nets by showing that ReLU activation function can be well approximated by deep sigmoid nets with two hidden layers and finitely many free parameters but not vice-verse. We also establish the global convergence of the proposed ADMM for the nonlinearly constrained formulation of the deep sigmoid nets training from arbitrary initial points to a Karush-Kuhn-Tucker (KKT) point at a rate of order O(1/k). Besides sigmoid activation, such a convergence theorem holds for a general class of smooth activations. Compared with the widely used stochastic gradient descent (SGD) algorithm for the deep ReLU nets training (called ReLU-SGD pair), the proposed sigmoid-ADMM pair is practically stable with respect to the algorithmic hyperparameters including the learning rate, initial schemes and the pro-processing of the input data. Moreover, we find that to approximate and learn simple but important functions the proposed sigmoid-ADMM pair numerically outperforms the ReLU-SGD pair.

关键词： deep learning ADMM sigmoid global convergence saturation avoidance

AstroPhot: Fitting Everything Everywhere All at Once in Astronomical Images

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arXiv 2023年

作者： Stone, Connor J. Courteau, Stéphane Cuillandre, Jean-Charles Hezaveh, Yashar Perreault-Levasseur, Laurence Arora, Nikhil Department of Physics Université de Montréal MontréalQC Canada Mila - Québec Artificial Intelligence Institute MontréalQC Canada Ciela - Montréal Institute for Astrophysical Data Analysis and Machine Learning MontréalQC Canada Department of Physics Engineering Physics & Astronomy Queen’s University KingstonON Canada AIM CEA CNRS Université Paris-Saclay Université de Paris Gif-sur-YvetteF-91191 France Center for Computational Astrophysics Flatiron Institute 162 5th Avenue New YorkNY10010 United States New York University Abu Dhabi PO Box 129188 Abu Dhabi United Arab Emirates New York University Abu Dhabi United Arab Emirates

We present ASTROPHOT, a fast, powerful, and user-friendly Python based astronomical image photometry solver. ASTROPHOT incorporates automatic differentiation and GPU (or parallel CPU) acceleration, powered by the machine learning library PYTORCH. Everything: ASTROPHOT can fit models for sky, stars, galaxies, PSFs, and more in a principled X2 forward optimization, recovering Bayesian posterior information and covariance of all parameters. Everywhere: ASTROPHOT can optimize forward models on CPU or GPU;across images that are large, multiband, multi-epoch, rotated, dithered, and more. All at once: The models are optimized together, thus handling overlapping objects and including the covariance between parameters (including PSF and galaxy parameters). A number of optimization algorithms are available including Levenberg-Marquardt, Gradient descent, and No-U-Turn MCMC sampling. With an object-oriented user interface, ASTROPHOT makes it easy to quickly extract detailed information from complex astronomical data for individual images or large survey programs. This paper outlines novel features of the ASTROPHOT code and compares it to other popular astronomical image modeling software. ASTROPHOT is open-source, fully Python based, and freely accessible here: https://***/Autostronomy/AstroPhot © 2023, CC BY.

关键词： Python

machine learning Approaches in Polymer Science:Progress and Fundamental for a New

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SmartMat 2025年第1期6卷 102-142页

作者： 482.T.-S.Lin C.W.ColeyH.Mochigaseet al.“Bigsmiles:A Structurally-Based Line Notation for Describing Macromolecules"ACs Central Science 5no.9(2019):1523-1531.483.J.Wu and M.Gu“Perfecting Liquid-State Theories With Machine Intelligence"Journal of Physical Chemistry Letters 14no.47(2023):10545-10552.484.M.Rubinstein and R.H.ColbyPolymer Physics(Oxford University Press2003).485.M.E.DeagenB.Dalle-CortN.J.RebelloT.S.LinD.J.Walshand B.D.Olsen“Machine Translation Between BigSMILES Line Notation and Chemical Structure Diagrams"Macromolecules 57no.1(2023):42-53.486.S.M.McDonaldE.K.AugustineQ.LannersC.RudinL.Catherine Brinsonand M.L.Becker“Applied Machine Learning as a Driver for Polymeric Biomaterials Design"Nature Communications 14no.1(2023):4838.487.B.HuA.Linand L.C.Brinson“Tackling Structured Knowledge Extraction From Polymer Nanocomposite Literature as an NER/RE Task With seq2seq"Integrating Materials and Manufacturing Innovation 13no.3(2024):656-668.488.P.V.CoveneyE.R.Doughertyand R.R.Highfield“Big Data Need Big Theory Too"Philosophical Transactions of the Royal Society A:MathematicalPhysical and Engineering Sciences 374no.2080(2016):201601 489.M.Tang R.ZhangS.Liet al.“Towards a Supertough Thermo-plastic Polyisoprene Elastomer Based on a Biomimic Strategy"Angewandte Chemie International Edition557no.48(2018):15836-15840.490.M.Z.Naser“An Engineer's Guide to Explainable Artificial Intel-ligence and Interpretable Machine Learning:Navigating CausalityForced Goodnessand the False Perception of Inference"Automation in Construction 129(2021):103821 .491.T.K.Patra V.MeenakshisundaramJ.H.Hungand D.S.Simmons“Neural-Network-Biased Genetic Algorithms for Materials Design:Evolutionary Algorithms That LearnACS Combinatorial Science 19no.2(2017):96-107.

machine learning(ML),material genome,and big data approaches are highly overlapped in their strategies,algorithms,and *** can target various definitions,distributions,and correlations of concerned physical parameters in given polymer systems,and have expanding applications as a new paradigm indispensable to conventional *** inherent advantages in building quantitative multivariate correlations have largely enhanced the capability of scientific understanding and discoveries,thus facilitating mechanism exploration,target prediction,high-throughput screening,optimization,and rational and inverse *** article summarizes representative progress in the recent two decades focusing on the design,preparation,application,and sustainable development of polymer materials based on the exploration of key physical parameters in the composition-process-structure-property-performance *** integration of both data-driven and physical insights through ML approaches to deepen fundamental understanding and discover novel polymer materials is categorically *** the construction and application of robust ML models,strategies and algorithms to deal with variant tasks in polymer science are still in rapid *** challenges and prospects are then *** believe that the innovation in polymer materials will thrive along the development of ML approaches,from efficient design to sustainable applications.

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Conformational and state-specific effects in reactions of 2,3-dibromobutadiene with Coulomb-crystallized calcium ions

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arXiv 2023年

作者： Kilaj, Ardita Käser, Silvan Wang, Jia Straňák, Patrik Schwilk, Max Xu, Lei von Lilienfeld, O. Anatole Küpper, Jochen Meuwly, Markus Willitsch, Stefan Department of Chemistry University of Basel Klingelbergstrasse 80 Basel4056 Switzerland Center for Free-Electron Laser Science CFEL Deutsches Elektronen-Synchrotron DESY Notkestr. 85 Hamburg22607 Germany Vector Institute for Artificial Intelligence TorontoONM5S 1M1 Canada Departments of Chemistry Materials Science and Engineering and Physics University of Toronto St. George Campus TorontoONM5S 3H6 Canada Machine Learning Group Technische Universität Berlin Berlin10587 Germany Berlin Institute for the Foundations of Learning and Data BIFOLD Germany Department of Physics Universität Hamburg Luruper Chaussee 149 Hamburg22761 Germany Department of Chemistry Universität Hamburg Martin-Luther-King-Platz 6 Hamburg20146 Germany Center for Ultrafast Imaging Universität Hamburg Luruper Chaussee 149 Hamburg22761 Germany Department of Chemistry Brown University ProvidenceRI02912 United States

Recent advances in experimental methodology enabled studies of the quantum-state- and conformational dependence of chemical reactions under precisely controlled conditions in the gas phase. Here, we generated samples of selected gauche and s-trans 2,3-dibromobutadiene (DBB) by electrostatic deflection in a molecular beam and studied their reaction with Coulomb crystals of laser-cooled Ca+ ions in an ion trap. The rate coefficients for the total reaction were found to strongly depend on both the conformation of DBB and the electronic state of Ca+. In the (4p) 2P1/2 and (3d) 2D3/2 excited states of Ca+, the reaction is capture-limited and faster for the gauche conformer due to long-range ion-dipole interactions. In the (4s) 2S1/2 ground state of Ca+, the reaction rate for s-trans DBB still conforms with the capture limit, while that for gauche DBB is strongly suppressed. The experimental observations were analysed with the help of adiabatic capture theory, ab-initio calculations and reactive molecular dynamics simulations on a machine-learned full-dimensional potential energy surface of the system. The theory yields near-quantitative agreement for s-trans-DBB, but overestimates the reactivity of the gauche- conformer compared to the experiment. The present study points to the important role of molecular geometry even in strongly reactive exothermic systems and illustrates striking differences in the reactivity of individual conformers in gas-phase ion-molecule reactions. © 2023, CC BY-SA.

关键词： Electronic states

Antisymmetry rules of response properties in certain chemical spaces

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arXiv 2025年

作者： Shiraogawa, Takafumi Krug, Simon León Ehara, Masahiro von Lilienfeld, O. Anatole Institute for Molecular Science National Institutes of Natural Sciences 38 Nishigonaka Myodaiji Okazaki444-8585 Japan Research Center for Computational Science National Institutes of Natural Sciences 38 Nishigonaka Myodaiji Okazaki444-8585 Japan The Graduate University for Advanced Studies 38 Nishigonaka Myodaiji Okazaki444-8585 Japan Machine Learning Group Technische Universität Berlin Berlin10587 Germany Chemical Physics Theory Group Department of Chemistry University of Toronto St. George Campus TorontoM5S3H6 Ontario Canada Department of Materials Science and Engineering University of Toronto St. George Campus TorontoM5S 3E4 Ontario Canada Vector Institute for Artificial Intelligence TorontoM5S 1M1 Ontario Canada Berlin Institute for the Foundations of Learning and Data Berlin10587 Germany Department of Physics University of Toronto St. George Campus TorontoM5S 1A7 Ontario Canada Acceleration Consortium University of Toronto TorontoM5R 0A3 Ontario Canada

Understanding chemical compound space (CCS), a set of molecules and materials, is crucial for the rational discovery of molecules and materials. Concepts of symmetry have recently been introduced into CCS to account for near degeneracies and differences in electronic energies between iso-electronic materials. In this work, we present approximate relationships of response properties based on a first-principles view of CCS. They have been derived from perturbation theory and antisymmetry considerations involving nuclear charges. These rules allow approximate predictions of relative response properties of pairs of distinct compounds with opposite nuclear charge variations from a highly symmetric reference material, without the need for experiments or quantum chemical calculations of each compound. We numerically and statistically verified these rules for electric and magnetic response properties (electric dipole moment, polarizabilities, hyperpolarizabilities, and magnetizabilities) among charge-neutral and iso-electronic BN-doped polycyclic aromatic hydrocarbon derivatives of naphthalene, anthracene, and pyrene. Our analysis indicates that, despite their simplicity, antisymmetry rule-based predictions are remarkably accurate, enabling dimensionality reduction of CCS. Response properties in alchemical perturbation density functional theory were investigated to clarify the origin of this predictive power. © 2025, CC BY.

关键词： Naphthalene

Evaluating deep transfer learning for whole-brain cognitive decoding

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arXiv 2021年

作者： Thomas, Armin W. Lindenberger, Ulman Samek, Wojciech Müller, Klaus-Robert Machine Learning Group Dept. of Computer Science and Electrical Engineering Technische Universität Berlin Berlin Germany Center for Lifespan Psychology Max Planck Institute for Human Development Berlin Germany Stanford Data Science Stanford University StanfordCA United States Dept. of Psychology Stanford University StanfordCA United States Max Planck UCL Centre for Computational Psychiatry and Ageing Research Berlin Germany Dept. of Artificial Intelligence Fraunhofer Heinrich Hertz Institute Berlin Germany BIFOLD – Berlin Institute for the Foundations of Learning and Data Berlin Germany Dept. of Artificial Intelligence Korea University Seoul Korea Republic of Max Planck Institute for Informatics Saarbrücken Germany

Research in many fields has shown that transfer learning (TL) is well-suited to improve the performance of deep learning (DL) models in datasets with small numbers of samples. This empirical success has triggered interest in the application of TL to cognitive decoding analyses with functional neuroimaging data. Here, we systematically evaluate TL for the application of DL models to the decoding of cognitive states (e.g., viewing images of faces or houses) from whole-brain functional Magnetic Resonance Imaging (fMRI) data. We first pre-train two DL architectures on a large, public fMRI dataset and subsequently evaluate their performance in an independent experimental task and a fully independent dataset. The pre-trained models consistently achieve higher decoding accuracies and generally require less training time and data than model variants that were not pre-trained, clearly underlining the benefits of pre-training. We demonstrate that these benefits arise from the ability of the pre-trained models to reuse many of their learned features when training with new data, providing deeper insights into the mechanisms giving rise to the benefits of pre-training. Yet, we also surface nuanced challenges for whole-brain cognitive decoding with DL models when interpreting the decoding decisions of the pre-trained models, as these have learned to utilize the fMRI data in unforeseen and counterintuitive ways to identify individual cognitive states. © 2021, CC BY.

关键词： Decoding

Drone flight data reveal energy and greenhouse gas emissions savings for small package delivery

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arXiv 2021年

作者： Rodrigues, Thiago A. Patrikar, Jay Oliveira, Natalia L. Scott Matthews, H. Scherer, Sebastian Samaras, Constantine Department of Civil and Environmental Engineering Carnegie Mellon University 5000 Forbes Avenue PittsburghPA15213 United States Robotics Institute Carnegie Mellon University 5000 Forbes Avenue Pittsburgh15213 United States Department of Statistics and Data Science Carnegie Mellon University 5000 Forbes Avenue Pittsburgh15213 United States Machine Learning Department Carnegie Mellon University 5000 Forbes Avenue Pittsburgh15213 United States

The adoption of Uncrewed Aerial Vehicles (UAVs) for last-mile deliveries will affect the energy productivity of package delivery and require new methods to understand the associated energy consumption and greenhouse gas (GHG) emissions. Here we combine empirical testing of 187 quadcopter flights with first principles analysis to develop a usable energy model for drone package delivery. We develop a machine learning algorithm to assess energy use across three different flight regimes: takeoff, cruise, and landing. Our model shows that, in the US, a small electric quadcopter drone with a payload of 1 kg would consume approximately 0.05 MJ/km and result in 41 g of CO2e per package. The energy per package delivered by drones (0.19 MJ/package) can be up to 96% lower than conventional transportation modes. Our open model and generalizable coefficients can assist stakeholders in understanding and improving the energy use of drone package delivery. © 2021, CC BY-NC-SA.

关键词： Energy utilization