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22nd International Symposium on Experimental Algorithms, SEA 2024

作者： Conrads, Theo Drexler, Lukas Könen, Joshua Schmidt, Daniel R. Schmidt, Melanie Department of Computer Science University of Cologne Germany Faculty of Mathematics and Natural Sciences Department of Computer Science Heinrich Heine University Düsseldorf Germany Institute of Computer Science University of Bonn Germany

ISBN: (纸本)9783959773256

Since its introduction in 1957, Lloyd's algorithm for k-means clustering has been extensively studied and has undergone several improvements. While in its original form it does not guarantee any approximation factor at all, Arthur and Vassilvitskii (SODA 2007) proposed k-means++ which enhances Lloyd's algorithm by a seeding method which guarantees a O(log k)-approximation in expectation. More recently, Lattanzi and Sohler (ICML 2019) proposed LS++ which further improves the solution quality of k-means++ by local search techniques to obtain a O(1)-approximation. On the practical side, the greedy variant of k-means++ is often used although its worst-case behaviour is provably worse than for the standard k-means++ variant. We investigate how to improve LS++ further in practice. We study two options for improving the practical performance: (a) Combining LS++ with greedy k-means++ instead of k-means++, and (b) Improving LS++ by better entangling it with Lloyd's algorithm. Option (a) worsens the theoretical guarantees of k-means++ but improves the practical quality also in combination with LS++ as we confirm in our experiments. Option (b) is our new algorithm, Foresight LS++. We experimentally show that FLS++ improves upon the solution quality of LS++. It retains its asymptotic runtime and its worst-case approximation bounds. © Theo Conrads, Lukas Drexler.

关键词： Local search (optimization)

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Geometric Progressions in the Sets of Values of Reducible Cubic Forms 20th

Geometric Progressions in the Sets of Values of Reducible Cu...

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20th Combinatorial and Additive Number Theory, New York Number Theory Seminar, CANT 2022 and 21st Combinatorial and Additive Number Theory, New York Number Theory Seminar, CANT 2023

作者： Glowacki, Bartosz Ulas, Maciej Faculty of Mathematics and Computer Science Institute of Mathematics Jagiellonian University Lojasiewicza 6 Kraków30-348 Poland

ISBN: (纸本)9783031650635

Let a, (Formula Presented) be given and consider the set G (Formula Presented) of terms of geometric progression with 0th term equal to a and the quotient Q. Let (Formula Presented) and (Formula Presented) be the set of finite values of f. It is known that for any quadratic form f, there are infinitely many pairs a, Q such that (Formula Presented). In this note we prove that the same statement is true for reducible cubic forms. The main tool in the proof is the density of rational points on the quartic surface (Formula Presented), where (Formula Presented). © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

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GRA: Graph Representation Alignment for Semi-Supervised Action Recognition

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IEEE Transactions on Neural Networks and Learning Systems 2024年第9期35卷 11896-11905页

作者： Huang, Kuan-Hung Huang, Yao-Bang Lin, Yong-Xiang Hua, Kai-Lung Tanveer, M. Lu, Xuequan Razzak, Imran National Taiwan University of Science and Technology Department of Computer Science and Information Engineering Taipei10607 Taiwan Indian Institute of Technology Indore Department of Mathematics Indore Simrol453552 India La Trobe University Department of Computer Science and IT MelbourneVIC3086 Australia University of New South Wales School of Computer Science and Engineering SydneyNSW2052 Australia

Graph convolutional networks (GCNs) have emerged as a powerful tool for action recognition, leveraging skeletal graphs to encapsulate human motion. Despite their efficacy, a significant challenge remains the dependency on huge labeled datasets. Acquiring such datasets is often prohibitive, and the frequent occurrence of incomplete skeleton data, typified by absent joints and frames, complicates the testing phase. To tackle these issues, we present graph representation alignment (GRA), a novel approach with two main contributions: 1) a self-training (ST) paradigm that substantially reduces the need for labeled data by generating high-quality pseudo-labels, ensuring model stability even with minimal labeled inputs and 2) a representation alignment (RA) technique that utilizes consistency regularization to effectively reduce the impact of missing data components. Our extensive evaluations on the NTU RGB+D and Northwestern-UCLA (N-UCLA) benchmarks demonstrate that GRA not only improves GCN performance in data-constrained environments but also retains impressive performance in the face of data incompleteness. © 2012 IEEE.

关键词： Alignment

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Quadratic and Lagrange interpolation-based butterfly optimization algorithm for numerical optimization and engineering design problem

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Soft Computing 2025年第1期29卷 157-194页

作者： Sharma, Sushmita Saha, Apu Kumar Chakraborty, Sanjoy Deb, Suman Sahoo, Saroj Kumar Department of Computer Science and Engineering Indian Institute of Information Technology Tripura Agartala India Department of Computer Science and Engineering National Institute of Technology Tripura Agartala India Department of Mathematics National Institute of Technology Agartala Tripura Agartala India Department of Information Technology Bir Bikram Memorial College Tripura Agartala India

This work proposes a novel and improved Butterfly Optimization Algorithm (BOA), known as LQBOA, to solve BOA’s inherent limitations. The LQBOA uses Lagrange interpolation and simple quadratic interpolation techniques with adapted parameter settings to enhance the search strategy of BOA and to achieve a better balance of diversification and intensification. LQBOA’s performance was examined on 45 traditional benchmark issues as well as the IEEE CEC 2017 benchmark suites with 10, 30 and 50 dimensions, and the results were compared against popular state-of-the-art and modified algorithms. It was discovered that in more than 85% of cases, the proposed LQBOA outperformed the compared algorithms. The Friedman rank test and Wilcoxon rank test were used to validate the suggested LQBOA’s rank and significance. Additionally, convergence and diversity analyses were performed to investigate its convergence speed and searching behavior, respectively. Furthermore, LQBOA has been successfully deployed to solve twelve real-world issues including several engineering design problems and two multiple gravity assist spacecraft trajectory problems. The results of these problems were compared to those of a wide range of algorithms, demonstrating the superior performance of the proposed LQBOA. In conclusion, LQBOA makes a significant addition to the optimization area, and its application could greatly improve the performance of numerous optimization jobs. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.

关键词： Lagrange multipliers

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Hebbian Continual Representation Learning 56

Hebbian Continual Representation Learning

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56th Annual Hawaii International Conference on System sciences, HICSS 2023

作者： Morawiecki, Pawel Wolczyk, Maciej Krutsylo, Andrii Śmieja, Marek Polish Academy of Sciences Institute of Computer Science Poland Faculty of Mathematics and Computer Science Jagiellonian University Poland

ISBN: (纸本)9780998133164

Continual Learning aims to bring machine learning into a more realistic scenario, where tasks are learned sequentially and the independent and identically distributed assumption is not preserved. Although this setting is natural for biological systems, it proves very difficult for machine learning models such as artificial neural networks. To reduce this performance gap, we investigate whether biologically inspired Hebbian learning is useful for tackling continual challenges. In particular, we highlight a realistic and often overlooked unsupervised setting where the learner has to build representations without any supervision. By combining sparse neural networks with the Hebbian learning principle, we build a simple yet effective alternative (HebbCL) to typical neural network models trained via gradient descent. Due to Hebbian learning, the network have easily interpretable weights, which might be essential in critical application such as security or healthcare. We demonstrate the efficacy of HebbCL in an unsupervised learning setting applied to the MNIST and Omniglot datasets. We also adapt the algorithm to the supervised scenario and obtain promising results in the class-incremental learning. © 2023 IEEE computer Society. All rights reserved.

关键词： Unsupervised learning

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MATHEMATICAL MODELLING OF CHEMICAL REACTION WITH PROPANE 23

MATHEMATICAL MODELLING OF CHEMICAL REACTION WITH PROPANE

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23rd International Scientific Conference Engineering for Rural Development, ERDev 2024

作者： Kalis, Harijs Kangro, Ilmars Institute of Mathematics and Computer Science University of Latvia Latvia Rezekne Academy of Technologies Latvia

The main goal of the present study is to promote a more effective use of agricultural residues as an alternative renewable fuel for cleaner energy production with reduced greenhouse gas emissions. The complex experimental study and mathematical modelling of the processes developing during the co-firing of biomass pellets with gaseous fuel were carried out. The experimental study of the effect of co-firing on the main gasification and combustion characteristics was carried out by varying the propane supply and additional heat input into the pilot device with an estimation of the effect of co-firing on the thermal decomposition of pallets. The mathematical model is developed using the environment of MATLAB (2-D modelling) and MATLAB package "pdepe" (1-D modelling) with account variations of supplying the heat energy and combustible volatiles into the bottom of the combustor. The dominant exothermal chemical reactions were used to evaluate the effect of co-firing on the main combustion characteristics and composition of products CO2 and H2O. The results prove that the additional heat from the propane flame allows control of the thermal decomposition, the formation of volatiles, and the development of combustion dynamics, thus completing the combustion of biomass and leading to cleaner heat energy production. © 2024 Latvia University of Life sciences and Technologies. All rights reserved.

关键词： Propane

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Towards a representer theorem for identification of passive systems 63

Towards a representer theorem for identification of passive ...

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63rd IEEE Conference on Decision and Control, CDC 2024

作者： Shali, Brayan M. Van Waarde, Henk J. Bernoulli Institute for Mathematics Computer Science and Artificial Intelligence University of Groningen Groningen Netherlands

ISBN: (纸本)9798350316339

A major problem in system identification is the incorporation of prior knowledge about the physical properties of the given system, such as stability, positivity and passivity. In this paper, we present first steps towards tackling this problem for passive systems. In particular, using ideas from the theory of reproducing kernel Hilbert spaces, we solve the problem of identifying a nonnegative input-output operator from data consisting of input-output trajectories of the system. We prove a representer theorem for this problem in the case where the input space is finite-dimensional. This provides a computationally tractable solution, which we show can be obtained by solving an associated semidefinite program. © 2024 IEEE.

关键词： Vector spaces

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Particle-based Data-driven Nonlinear State Estimation of Model-free Process from Nonlinear Measurements

Particle-based Data-driven Nonlinear State Estimation of Mod...

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2025 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2025

作者： Ghosh, Anubhab Eldar, Yonina C. Chatterjee, Saikat Digital Futures Centre School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Sweden Faculty of Mathematics and Computer Science The Weizmann Institute of Science Israel

ISBN: (纸本)9798350368741

We consider the problem of causal filtering of a model-free process from (noisy) nonlinear measurements. The 'model-free process' means that we do not have a state-space model (SSM) of the process dynamics, limiting the use of traditional model-driven filters, such as unscented Kalman filter (UKF) and particle filter (PF). To address the problem we propose a particle-based data-driven nonlinear state estimation (pDANSE) method. In pDANSE, a recurrent neural network (RNN) provides the statistical parameters of a Gaussian prior of the underlying state, and particles are then drawn from the prior to compute the posterior moments. pDANSE is typically trained in a semi-supervised fashion. For our experiments we study the use of half-wave rectification as a nonlinear transformation of measurements. We first show that an unsupervised learning-based method under-performs, and subsequently the semi-supervised learning-based pDANSE performs satisfactorily. Using Lorenz-63 system as benchmark, pDANSE is found to be competitive against a model-driven PF that knows the exact SSM. © 2025 IEEE.

关键词： deep neural network Kalman filter particle filter semi-supervised learning State estimation

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Interpretable Deep Learning For Automated Retinal Damage Detection in Optical Coherence Tomography

Interpretable Deep Learning For Automated Retinal Damage Det...

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2024 IEEE International Conference on Big Data, BigData 2024

作者： Suganya, R. Sharma, Abhiram Srivats, R. Kalyanasundaram, V. Shanmugam, Selvanayaki Kolandapalayam Vellore Institute of Technology School of Computer Science and Engineering Chennai India Ashland University Department of the Mathematics and Computer Science AshlandOH United States

ISBN: (纸本)9798350362480

This work portrays developing and evaluating deep learning models for automatically identifying retinal injuries using Optical Coherence Tomography (OCT) images. In particular, this study optimizes three pre-trained Convolutional Neural Networks (CNNs), VGG16, EfficientNetB3, and ResNet50, using transfer learning to classify retinal images into four categories, Drusen, Normal, Diabetic Macular Edema (DME), and Choroidal Neovascularization (CNV). In addition to high-performance classification, the study integrates Explainable Artificial Intelligence (XAI) methods, utilizing Gradient-weighted Class Activation Mapping (Grad-CAM) to highlight the retinal regions influencing the model's predictions visually. This offers critical interpretability for clinical settings. The Key performance metrics indicators include accuracy, precision, and F1-score and help to evaluate the models. With the available selected models, EfficientNetB3 achieved the highest performance with an accuracy of 93%, outperforming VGG16 and ResNet50. The application of Grad-CAM highlights the increase in transparency and prediction trust of this model's decision-making process. This study demonstrated the profound learning model efficacy, particularly EfficientNetB3, for accurate retinal injury detection and provides valuable insights into model interpretability for clinical use. © 2024 IEEE.

关键词： Convolutional neural networks

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Intuitionistic Propositional Logic in Lean 8

Intuitionistic Propositional Logic in Lean

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8th Symposium on Working Formal Methods, FROM 2024

作者： Trufas, Dafina LOS Faculty of Mathematics and Computer Science University of Bucharest Institute for Logic and Data Science Bucharest Romania

In this paper we present a formalization of Intuitionistic Propositional Logic in the Lean proof assistant. Our approach focuses on verifying two completeness proofs for the studied logical system, as well as exploring the relation between the two analyzed semantical paradigms - Kripke and algebraic. In addition, we prove a large number of theorems and derived deduction rules. © Dafina Trufas.

关键词： computer circuits

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