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Research on a Fast Image-Matching Algorithm Based on Nonlinear Filtering 基于非线性滤波的快速图像匹配算法研究
Pub Date : 2024-04-19 DOI: 10.3390/a17040165
Chenglong Yin, Fei Zhang, Bin Hao, Zijian Fu, Xiaoyu Pang
Computer vision technology is being applied at an unprecedented speed in various fields such as 3D scene reconstruction, object detection and recognition, video content tracking, pose estimation, and motion estimation. To address the issues of low accuracy and high time complexity in traditional image feature point matching, a fast image-matching algorithm based on nonlinear filtering is proposed. By applying nonlinear diffusion filtering to scene images, details and edge information can be effectively extracted. The feature descriptors of the feature points are transformed into binary form, occupying less storage space and thus reducing matching time. The adaptive RANSAC algorithm is utilized to eliminate mismatched feature points, thereby improving matching accuracy. Our experimental results on the Mikolajcyzk image dataset comparing the SIFT algorithm with SURF-, BRISK-, and ORB-improved algorithms based on the SIFT algorithm conclude that the fast image-matching algorithm based on nonlinear filtering reduces matching time by three-quarters, with an overall average accuracy of over 7% higher than other algorithms. These experiments demonstrate that the fast image-matching algorithm based on nonlinear filtering has better robustness and real-time performance.
计算机视觉技术正以前所未有的速度应用于三维场景重建、物体检测与识别、视频内容跟踪、姿态估计和运动估计等各个领域。针对传统图像特征点匹配精度低、时间复杂度高的问题,提出了一种基于非线性滤波的快速图像匹配算法。通过对场景图像进行非线性扩散滤波,可以有效提取细节和边缘信息。特征点的特征描述符被转换成二进制形式,占用更少的存储空间,从而缩短了匹配时间。利用自适应 RANSAC 算法消除不匹配的特征点,从而提高匹配精度。我们在 Mikolajcyzk 图像数据集上对 SIFT 算法和基于 SIFT 算法的 SURF、BRISK 和 ORB 改进算法进行了比较,实验结果表明,基于非线性过滤的快速图像匹配算法将匹配时间缩短了四分之三,总体平均准确率比其他算法高出 7% 以上。这些实验证明,基于非线性滤波的快速图像匹配算法具有更好的鲁棒性和实时性。
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引用次数: 0
Quantum Recurrent Neural Networks: Predicting the Dynamics of Oscillatory and Chaotic Systems 量子递归神经网络:预测振荡和混沌系统的动力学
Pub Date : 2024-04-19 DOI: 10.3390/a17040163
Yuanbo Chen, Abdul Khaliq
In this study, we investigate Quantum Long Short-Term Memory and Quantum Gated Recurrent Unit integrated with Variational Quantum Circuits in modeling complex dynamical systems, including the Van der Pol oscillator, coupled oscillators, and the Lorenz system. We implement these advanced quantum machine learning techniques and compare their performance with traditional Long Short-Term Memory and Gated Recurrent Unit models. The results of our study reveal that the quantum-based models deliver superior precision and more stable loss metrics throughout 100 epochs for both the Van der Pol oscillator and coupled harmonic oscillators, and 20 epochs for the Lorenz system. The Quantum Gated Recurrent Unit outperforms competing models, showcasing notable performance metrics. For the Van der Pol oscillator, it reports MAE 0.0902 and RMSE 0.1031 for variable x and MAE 0.1500 and RMSE 0.1943 for y; for coupled oscillators, Oscillator 1 shows MAE 0.2411 and RMSE 0.2701 and Oscillator 2 MAE is 0.0482 and RMSE 0.0602; and for the Lorenz system, the results are MAE 0.4864 and RMSE 0.4971 for x, MAE 0.4723 and RMSE 0.4846 for y, and MAE 0.4555 and RMSE 0.4745 for z. These outcomes mark a significant advancement in the field of quantum machine learning.
在本研究中,我们研究了量子长短期记忆和量子门控递归单元与变分量子电路在复杂动态系统建模中的集成,包括范德波尔振荡器、耦合振荡器和洛伦兹系统。我们实现了这些先进的量子机器学习技术,并将其性能与传统的长短期记忆和门控递归单元模型进行了比较。研究结果表明,基于量子的模型在范德尔波尔振荡器和耦合谐波振荡器的 100 个历时周期以及洛伦兹系统的 20 个历时周期内都能提供更高的精度和更稳定的损耗指标。量子门控循环单元的性能优于同类竞争模型,展示了显著的性能指标。对于范德尔波尔振荡器,它报告的变量 x MAE 为 0.0902,RMSE 为 0.1031,变量 y MAE 为 0.1500,RMSE 为 0.1943;对于耦合振荡器,振荡器 1 显示 MAE 为 0.2411,RMSE 为 0.2701,振荡器 2 MAE 为 0.0482,RMSE 为 0.0602。这些结果标志着量子机器学习领域的重大进展。
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引用次数: 0
Advancing Pulmonary Nodule Diagnosis by Integrating Engineered and Deep Features Extracted from CT Scans 通过整合从 CT 扫描中提取的工程特征和深度特征推进肺结节诊断
Pub Date : 2024-04-18 DOI: 10.3390/a17040161
Wiem Safta, A. Shaffie
Enhancing lung cancer diagnosis requires precise early detection methods. This study introduces an automated diagnostic system leveraging computed tomography (CT) scans for early lung cancer identification. The main approach is the integration of three distinct feature analyses: the novel 3D-Local Octal Pattern (LOP) descriptor for texture analysis, the 3D-Convolutional Neural Network (CNN) for extracting deep features, and geometric feature analysis to characterize pulmonary nodules. The 3D-LOP method innovatively captures nodule texture by analyzing the orientation and magnitude of voxel relationships, enabling the distinction of discriminative features. Simultaneously, the 3D-CNN extracts deep features from raw CT scans, providing comprehensive insights into nodule characteristics. Geometric features and assessing nodule shape further augment this analysis, offering a holistic view of potential malignancies. By amalgamating these analyses, our system employs a probability-based linear classifier to deliver a final diagnostic output. Validated on 822 Lung Image Database Consortium (LIDC) cases, the system’s performance was exceptional, with measures of 97.84%, 98.11%, 94.73%, and 0.9912 for accuracy, sensitivity, specificity, and Area Under the ROC Curve (AUC), respectively. These results highlight the system’s potential as a significant advancement in clinical diagnostics, offering a reliable, non-invasive tool for lung cancer detection that promises to improve patient outcomes through early diagnosis.
加强肺癌诊断需要精确的早期检测方法。本研究介绍了一种利用计算机断层扫描(CT)进行早期肺癌识别的自动诊断系统。主要方法是整合三种不同的特征分析方法:用于纹理分析的新型三维局部八进制模式(LOP)描述符、用于提取深度特征的三维卷积神经网络(CNN)以及用于描述肺结节特征的几何特征分析。3D-LOP 方法通过分析体素关系的方向和大小,创新性地捕捉到了结节纹理,从而区分了鉴别特征。同时,3D-CNN 从原始 CT 扫描中提取深层特征,提供有关结节特征的全面见解。几何特征和结节形状评估进一步增强了这一分析,提供了潜在恶性肿瘤的整体视图。通过综合这些分析,我们的系统采用了基于概率的线性分类器来提供最终诊断结果。经过对 822 个肺图像数据库联盟(LIDC)病例的验证,该系统的表现非常出色,准确率、灵敏度、特异性和 ROC 曲线下面积(AUC)分别为 97.84%、98.11%、94.73% 和 0.9912。这些结果凸显了该系统在临床诊断方面的巨大进步潜力,它为肺癌检测提供了一种可靠的无创工具,有望通过早期诊断改善患者的预后。
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引用次数: 0
Efficient Algorithm for Proportional Lumpability and Its Application to Selfish Mining in Public Blockchains 比例结块性的高效算法及其在公共区块链中自私挖矿的应用
Pub Date : 2024-04-15 DOI: 10.3390/a17040159
Carla Piazza, Sabina Rossi, Daria Smuseva
This paper explores the concept of proportional lumpability as an extension of the original definition of lumpability, addressing the challenges posed by the state space explosion problem in computing performance indices for large stochastic models. Lumpability traditionally relies on state aggregation techniques and is applicable to Markov chains demonstrating structural regularity. Proportional lumpability extends this idea, proposing that the transition rates of a Markov chain can be modified by certain factors, resulting in a lumpable new Markov chain. This concept facilitates the derivation of precise performance indices for the original process. This paper establishes the well-defined nature of the problem of computing the coarsest proportional lumpability that refines a given initial partition, ensuring a unique solution exists. Additionally, a polynomial time algorithm is introduced to solve this problem, offering valuable insights into both the concept of proportional lumpability and the broader realm of partition refinement techniques. The effectiveness of proportional lumpability is demonstrated through a case study that consists of designing a model to investigate selfish mining behaviors on public blockchains. This research contributes to a better understanding of efficient approaches for handling large stochastic models and highlights the practical applicability of proportional lumpability in deriving exact performance indices.
本文探讨了比例可凑合性的概念,将其作为可凑合性原始定义的扩展,以解决在计算大型随机模型性能指标时状态空间爆炸问题带来的挑战。可凑合性传统上依赖于状态聚合技术,适用于表现出结构规律性的马尔可夫链。比例可凑合性扩展了这一理念,提出马尔可夫链的过渡率可以通过某些因素进行修改,从而产生可凑合的新马尔可夫链。这一概念有助于推导出原始流程的精确性能指标。本文确定了计算最粗比例可叠加性问题的定义明确的性质,以完善给定的初始分区,确保存在唯一的解决方案。此外,本文还介绍了一种多项式时间算法来解决这一问题,为比例可包性概念和更广泛的分区细化技术领域提供了宝贵的见解。比例可凑合性的有效性通过一个案例研究得到了证明,该案例研究包括设计一个模型来调查公共区块链上的自私挖矿行为。这项研究有助于人们更好地理解处理大型随机模型的有效方法,并突出了比例可凑合性在推导精确性能指标方面的实际应用性。
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引用次数: 0
Point-Sim: A Lightweight Network for 3D Point Cloud Classification Point-Sim:用于 3D 点云分类的轻量级网络
Pub Date : 2024-04-15 DOI: 10.3390/a17040158
Jiachen Guo, Wenjie Luo
Analyzing point clouds with neural networks is a current research hotspot. In order to analyze the 3D geometric features of point clouds, most neural networks improve the network performance by adding local geometric operators and trainable parameters. However, deep learning usually requires a large amount of computational resources for training and inference, which poses challenges to hardware devices and energy consumption. Therefore, some researches have started to try to use a nonparametric approach to extract features. Point-NN combines nonparametric modules to build a nonparametric network for 3D point cloud analysis, and the nonparametric components include operations such as trigonometric embedding, farthest point sampling (FPS), k-nearest neighbor (k-NN), and pooling. However, Point-NN has some blindness in feature embedding using the trigonometric function during feature extraction. To eliminate this blindness as much as possible, we utilize a nonparametric energy function-based attention mechanism (ResSimAM). The embedded features are enhanced by calculating the energy of the features by the energy function, and then the ResSimAM is used to enhance the weights of the embedded features by the energy to enhance the features without adding any parameters to the original network; Point-NN needs to compute the similarity between each feature at the naive feature similarity matching stage; however, the magnitude difference of the features in vector space during the feature extraction stage may affect the final matching result. We use the Squash operation to squeeze the features. This nonlinear operation can make the features squeeze to a certain range without changing the original direction in the vector space, thus eliminating the effect of feature magnitude, and we can ultimately better complete the naive feature matching in the vector space. We inserted these modules into the network and build a nonparametric network, Point-Sim, which performs well in 3D classification tasks. Based on this, we extend the lightweight neural network Point-SimP by adding some trainable parameters for the point cloud classification task, which requires only 0.8 M parameters for high performance analysis. Experimental results demonstrate the effectiveness of our proposed algorithm in the point cloud shape classification task. The corresponding results on ModelNet40 and ScanObjectNN are 83.9% and 66.3% for 0 M parameters—without any training—and 93.3% and 86.6% for 0.8 M parameters. The Point-SimP reaches a test speed of 962 samples per second on the ModelNet40 dataset. The experimental results show that our proposed method effectively improves the performance on point cloud classification networks.
用神经网络分析点云是当前的研究热点。为了分析点云的三维几何特征,大多数神经网络通过添加局部几何算子和可训练参数来提高网络性能。然而,深度学习通常需要大量的计算资源来进行训练和推理,这对硬件设备和能耗提出了挑战。因此,一些研究开始尝试使用非参数方法来提取特征。Point-NN 结合了非参数模块,为三维点云分析构建了一个非参数网络,非参数组件包括三角嵌入、最远点采样(FPS)、k-近邻(k-NN)和池化等操作。然而,Point-NN 在特征提取过程中使用三角函数进行特征嵌入时存在一定的盲区。为了尽可能消除这种盲目性,我们采用了一种基于非参数能量函数的关注机制(ResSimAM)。通过能量函数计算特征的能量来增强嵌入特征,然后利用 ResSimAM 以能量来增强嵌入特征的权重,从而在不增加原始网络任何参数的情况下增强特征;Point-NN 需要在天真特征相似性匹配阶段计算每个特征之间的相似性,但特征提取阶段特征在向量空间中的大小差异可能会影响最终的匹配结果。我们使用挤压操作来挤压特征。这种非线性操作可以在不改变向量空间中原有方向的情况下,将特征挤压到一定范围,从而消除了特征大小的影响,最终可以更好地完成向量空间中的天真特征匹配。我们将这些模块植入网络,构建了一个非参数网络 Point-Sim,它在三维分类任务中表现出色。在此基础上,我们扩展了轻量级神经网络 Point-SimP,为点云分类任务添加了一些可训练参数,只需要 0.8 M 个参数就能实现高性能分析。实验结果证明了我们提出的算法在点云形状分类任务中的有效性。在 ModelNet40 和 ScanObjectNN 上的相应结果是:在 0 M 个参数(未进行任何训练)的情况下,分别为 83.9% 和 66.3%;在 0.8 M 个参数的情况下,分别为 93.3% 和 86.6%。在 ModelNet40 数据集上,Point-SimP 的测试速度达到了每秒 962 个样本。实验结果表明,我们提出的方法有效提高了点云分类网络的性能。
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引用次数: 0
A Communication-Efficient Federated Learning Framework for Sustainable Development Using Lemurs Optimizer 利用 Lemurs Optimizer 建立通信效率高的可持续发展联合学习框架
Pub Date : 2024-04-15 DOI: 10.3390/a17040160
M. Al-Betar, A. Abasi, Zaid Abdi Alkareem Alyasseri, Salam Fraihat, Raghad Falih Mohammed
The pressing need for sustainable development solutions necessitates innovative data-driven tools. Machine learning (ML) offers significant potential, but faces challenges in centralized approaches, particularly concerning data privacy and resource constraints in geographically dispersed settings. Federated learning (FL) emerges as a transformative paradigm for sustainable development by decentralizing ML training to edge devices. However, communication bottlenecks hinder its scalability and sustainability. This paper introduces an innovative FL framework that enhances communication efficiency. The proposed framework addresses the communication bottleneck by harnessing the power of the Lemurs optimizer (LO), a nature-inspired metaheuristic algorithm. Inspired by the cooperative foraging behavior of lemurs, the LO strategically selects the most relevant model updates for communication, significantly reducing communication overhead. The framework was rigorously evaluated on CIFAR-10, MNIST, rice leaf disease, and waste recycling plant datasets representing various areas of sustainable development. Experimental results demonstrate that the proposed framework reduces communication overhead by over 15% on average compared to baseline FL approaches, while maintaining high model accuracy. This breakthrough extends the applicability of FL to resource-constrained environments, paving the way for more scalable and sustainable solutions for real-world initiatives.
可持续发展解决方案的迫切需求需要创新的数据驱动工具。机器学习(ML)具有巨大的潜力,但在集中式方法中面临着挑战,特别是在地理位置分散的环境中,数据隐私和资源限制方面。联邦学习(FL)通过将 ML 训练分散到边缘设备,成为可持续发展的变革范例。然而,通信瓶颈阻碍了其可扩展性和可持续性。本文介绍了一种能提高通信效率的创新型分布式学习框架。所提出的框架通过利用 Lemurs 优化器(LO)的力量来解决通信瓶颈问题,LO 是一种受大自然启发的元启发算法。受狐猴合作觅食行为的启发,LO 会战略性地选择最相关的模型更新进行通信,从而显著降低通信开销。该框架在代表可持续发展各领域的 CIFAR-10、MNIST、水稻叶病和废物回收植物数据集上进行了严格评估。实验结果表明,与基线 FL 方法相比,所提出的框架平均减少了 15% 以上的通信开销,同时保持了较高的模型准确性。这一突破将 FL 的适用性扩展到了资源受限的环境中,为现实世界中更多可扩展、可持续的解决方案铺平了道路。
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引用次数: 0
Prime Number Sieving—A Systematic Review with Performance Analysis 质数筛分--系统回顾与性能分析
Pub Date : 2024-04-14 DOI: 10.3390/a17040157
Mircea Ghidarcea, Decebal Popescu
The systematic generation of prime numbers has been almost ignored since the 1990s, when most of the IT research resources related to prime numbers migrated to studies on the use of very large primes for cryptography, and little effort was made to further the knowledge regarding techniques like sieving. At present, sieving techniques are mostly used for didactic purposes, and no real advances seem to be made in this domain. This systematic review analyzes the theoretical advances in sieving that have occurred up to the present. The research followed the PRISMA 2020 guidelines and was conducted using three established databases: Web of Science, IEEE Xplore and Scopus. Our methodical review aims to provide an extensive overview of the progress in prime sieving—unfortunately, no significant advancements in this field were identified in the last 20 years.
自 20 世纪 90 年代以来,质数的系统生成几乎被忽视了,当时与质数有关的大部分信息技术研究资源都转移到了对超大质数在密码学中的应用的研究上,而对筛分等技术的进一步了解却少之又少。目前,筛分技术主要用于教学目的,在这一领域似乎没有取得真正的进展。本系统综述分析了筛分技术迄今为止取得的理论进展。研究遵循 PRISMA 2020 指南,并使用三个成熟的数据库进行:Web of Science、IEEE Xplore 和 Scopus。我们有条不紊的综述旨在对筛分技术的进展提供一个广泛的概述--遗憾的是,在过去的 20 年中,该领域没有取得任何重大进展。
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引用次数: 0
Spike-Weighted Spiking Neural Network with Spiking Long Short-Term Memory: A Biomimetic Approach to Decoding Brain Signals 具有尖峰长短期记忆的尖峰加权神经网络:解码大脑信号的仿生方法
Pub Date : 2024-04-12 DOI: 10.3390/a17040156
Kyle McMillan, R. So, Camilo Libedinsky, Kai Keng Ang, Brian Premchand
Background. Brain–machine interfaces (BMIs) offer users the ability to directly communicate with digital devices through neural signals decoded with machine learning (ML)-based algorithms. Spiking Neural Networks (SNNs) are a type of Artificial Neural Network (ANN) that operate on neural spikes instead of continuous scalar outputs. Compared to traditional ANNs, SNNs perform fewer computations, use less memory, and mimic biological neurons better. However, SNNs only retain information for short durations, limiting their ability to capture long-term dependencies in time-variant data. Here, we propose a novel spike-weighted SNN with spiking long short-term memory (swSNN-SLSTM) for a regression problem. Spike-weighting captures neuronal firing rate instead of membrane potential, and the SLSTM layer captures long-term dependencies. Methods. We compared the performance of various ML algorithms during decoding directional movements, using a dataset of microelectrode recordings from a macaque during a directional joystick task, and also an open-source dataset. We thus quantified how swSNN-SLSTM performed compared to existing ML models: an unscented Kalman filter, LSTM-based ANN, and membrane-based SNN techniques. Result. The proposed swSNN-SLSTM outperforms both the unscented Kalman filter, the LSTM-based ANN, and the membrane based SNN technique. This shows that incorporating SLSTM can better capture long-term dependencies within neural data. Also, our proposed swSNN-SLSTM algorithm shows promise in reducing power consumption and lowering heat dissipation in implanted BMIs.
背景。脑机接口(BMI)通过基于机器学习(ML)算法解码的神经信号,为用户提供与数字设备直接通信的能力。尖峰神经网络(SNN)是人工神经网络(ANN)的一种,它通过神经尖峰而非连续标量输出来运行。与传统的人工神经网络相比,SNN 的计算量更少,使用的内存更少,而且能更好地模拟生物神经元。然而,SNN 只在短时间内保留信息,限制了其捕捉时变数据中长期依赖关系的能力。在这里,我们针对回归问题提出了一种具有尖峰长短期记忆的新型尖峰加权 SNN(swSNN-SLSTM)。尖峰加权捕捉神经元发射率而不是膜电位,SLSTM 层捕捉长期依赖性。方法我们使用猕猴在定向操纵杆任务中的微电极记录数据集和一个开源数据集,比较了各种 ML 算法在解码定向运动时的性能。因此,我们量化了 swSNN-SLSTM 与现有 ML 模型(无香味卡尔曼滤波器、基于 LSTM 的 ANN 和基于膜的 SNN 技术)相比的表现。结果所提出的 swSNN-SLSTM 优于无香味卡尔曼滤波器、基于 LSTM 的 ANN 和基于膜的 SNN 技术。这表明,SLSTM 可以更好地捕捉神经数据中的长期依赖关系。此外,我们提出的 swSNN-SLSTM 算法有望降低植入式 BMI 的功耗和散热。
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引用次数: 0
Impacting Robustness in Deep Learning-Based NIDS through Poisoning Attacks 通过中毒攻击影响基于深度学习的 NIDS 的鲁棒性
Pub Date : 2024-04-11 DOI: 10.3390/a17040155
Shahad Alahmed, Qutaiba Alasad, J. Yuan, Mohammed Alawad
The rapid expansion and pervasive reach of the internet in recent years have raised concerns about evolving and adaptable online threats, particularly with the extensive integration of Machine Learning (ML) systems into our daily routines. These systems are increasingly becoming targets of malicious attacks that seek to distort their functionality through the concept of poisoning. Such attacks aim to warp the intended operations of these services, deviating them from their true purpose. Poisoning renders systems susceptible to unauthorized access, enabling illicit users to masquerade as legitimate ones, compromising the integrity of smart technology-based systems like Network Intrusion Detection Systems (NIDSs). Therefore, it is necessary to continue working on studying the resilience of deep learning network systems while there are poisoning attacks, specifically interfering with the integrity of data conveyed over networks. This paper explores the resilience of deep learning (DL)—based NIDSs against untethered white-box attacks. More specifically, it introduces a designed poisoning attack technique geared especially for deep learning by adding various amounts of altered instances into training datasets at diverse rates and then investigating the attack’s influence on model performance. We observe that increasing injection rates (from 1% to 50%) and random amplified distribution have slightly affected the overall performance of the system, which is represented by accuracy (0.93) at the end of the experiments. However, the rest of the results related to the other measures, such as PPV (0.082), FPR (0.29), and MSE (0.67), indicate that the data manipulation poisoning attacks impact the deep learning model. These findings shed light on the vulnerability of DL-based NIDS under poisoning attacks, emphasizing the significance of securing such systems against these sophisticated threats, for which defense techniques should be considered. Our analysis, supported by experimental results, shows that the generated poisoned data have significantly impacted the model performance and are hard to be detected.
近年来,互联网的快速扩张和无处不在的覆盖范围引发了人们对不断发展和适应性强的在线威胁的担忧,特别是随着机器学习(ML)系统广泛融入我们的日常生活。这些系统正日益成为恶意攻击的目标,这些攻击试图通过 "中毒 "概念来扭曲系统的功能。此类攻击旨在扭曲这些服务的预期运行,使其偏离真正的目的。中毒会使系统容易受到未经授权的访问,使非法用户伪装成合法用户,损害网络入侵检测系统(NIDS)等基于智能技术的系统的完整性。因此,有必要继续研究深度学习网络系统在受到中毒攻击时的恢复能力,特别是干扰网络数据传输完整性的攻击。本文探讨了基于深度学习(DL)的 NIDS 对非绑定白盒攻击的恢复能力。更具体地说,本文介绍了一种专为深度学习设计的中毒攻击技术,方法是在训练数据集中以不同的速率添加各种数量的篡改实例,然后研究攻击对模型性能的影响。我们发现,增加注入率(从 1%到 50%)和随机放大分布略微影响了系统的整体性能,这在实验结束时的准确率(0.93)中有所体现。然而,与其他指标相关的其他结果,如 PPV(0.082)、FPR(0.29)和 MSE(0.67),表明数据操纵中毒攻击影响了深度学习模型。这些发现揭示了基于 DL 的 NIDS 在中毒攻击下的脆弱性,强调了确保此类系统免受这些复杂威胁的重要性,并应考虑采用防御技术。在实验结果的支持下,我们的分析表明,生成的中毒数据严重影响了模型的性能,而且很难被检测到。
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引用次数: 0
Hybrid Newton-like Inverse Free Algorithms for Solving Nonlinear Equations 求解非线性方程的混合牛顿式自由逆算法
Pub Date : 2024-04-10 DOI: 10.3390/a17040154
Ioannis K. Argyros, S. George, Samundra Regmi, Christopher I. Argyros
Iterative algorithms requiring the computationally expensive in general inversion of linear operators are difficult to implement. This is the reason why hybrid Newton-like algorithms without inverses are developed in this paper to solve Banach space-valued nonlinear equations. The inverses of the linear operator are exchanged by a finite sum of fixed linear operators. Two types of convergence analysis are presented for these algorithms: the semilocal and the local. The Fréchet derivative of the operator on the equation is controlled by a majorant function. The semi-local analysis also relies on majorizing sequences. The celebrated contraction mapping principle is utilized to study the convergence of the Krasnoselskij-like algorithm. The numerical experimentation demonstrates that the new algorithms are essentially as effective but less expensive to implement. Although the new approach is demonstrated for Newton-like algorithms, it can be applied to other single-step, multistep, or multipoint algorithms using inverses of linear operators along the same lines.
迭代算法需要对线性算子进行计算昂贵的一般反演,很难实现。因此,本文开发了无反演的混合牛顿算法,用于求解巴拿赫空间值非线性方程。线性算子的倒数由固定线性算子的有限和交换。本文针对这些算法提出了两种收敛分析方法:半局部收敛分析和局部收敛分析。方程上算子的弗雷谢特导数由主要函数控制。半局部分析也依赖于大化序列。著名的收缩映射原理被用来研究类似 Krasnoselskij 算法的收敛性。数值实验证明,新算法本质上同样有效,但实施成本更低。虽然新方法是针对类似牛顿的算法进行演示的,但它也可以按照同样的思路应用于使用线性算子逆的其他单步、多步或多点算法。
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引用次数: 0
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Algorithms
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