Comparison on Zhang Neural Network and Gradient Neural Network for
219506089_基于自组织映射的卷积神经网络架构研究
第10期2023年5月无线互联科技Wireless Internet TechnologyNo.10May,2023作者简介:赵义爱(1989 ),女,河南郑州人,硕士;研究方向:物联网㊂基于自组织映射的卷积神经网络架构研究赵义爱(郑州工业应用技术学院,河南郑州451100)摘要:辅助驾驶和自动驾驶技术将对人类的生活方式带来巨大影响,而交通标志识别技术则是其中至关重要的一环㊂为了进一步完善交通标志识别理论,文章提出了一种融合自组织映射的卷积神经网络架构㊂自组织映射能将图像样本量化至拓扑空间中,从而对微小的变化提供降维和不变性处理㊂该方法与卷积神经网络相结合,能充分利用卷积神经网络对平移㊁旋转㊁缩放和形变的部分不变性能,从而提高该架构的效率和准确度㊂经过初步测试,本系统在200个测试样本中表现出98.5%的准确率,取得了显著的成效㊂关键词:卷积神经网络;交通标志识别;自组织映射;深度学习中图分类号:TP183㊀㊀文献标志码:A 0㊀引言㊀㊀辅助驾驶和自动驾驶技术需要快速准确地从图像中检测交通标志㊂交通标志识别主要依赖于图像视觉信息,如标志的形状㊁大小和颜色等[1]㊂然而,传统的识别算法在实时测试中面临着照明强度㊁摄像头角度㊁障碍物等问题㊂此外,实现多目标检测也是目前技术面临的困难之一[2]㊂虽然深度学习作为一种机器学习方法很早就被提出,但近年来随着计算机硬件和神经网络架构的不断发展,深度学习才开始进入发展黄金时期[3]㊂卷积神经网络(Convolutional Neural Networks,CNN)是一种重要的深度学习架构,可以实现对人脸或其他图像的学习和识别[4],在人脸识别[5]㊁自动驾驶汽车[6]和智能医疗[7]等领域得到广泛应用㊂当采用CNN 模型时,并不需要太多的数据预处理任务,它主要是通过卷积完成图像特征的提取,同时不会丢失重要信息,在降维的同时也保留了与特征相关的信息[8-9]㊂因此,本研究系统性地研究了基于自组织映射(Self -organizing Map,SOM)的CNN 网络架构来实现交通标志识别㊂主要包括3个方面:对交通标志数据集进行分析和预处理㊁介绍CNN 在图像识别中的应用以及提出SOM -CNN 架构并进行数据集地训练和测试㊂实验结果表明,本研究工作具有一定的发展潜力㊂1㊀针对交通标志识别的CNN 架构1.1㊀CNN 的典型结构㊀㊀典型的CNN 由多个层组成,主要包含卷积层和池化层,如图1所示[10]㊂其中,卷积层包含有多个面,每个面都具有固定的特征检测器,与前一层的局部窗口做卷积㊂池化层在卷积层后面,用于进行局部平均和下采样操作,减少数据量,同时保留重要特征㊂在交通标志识别任务中,CNN 已被证明可以有效地识别交通标志的形状㊁颜色㊁符号等㊂该模型的成功应用主要是因为其卷积层可以学习低级特征,例如边缘和角点等,然后在池化层中进一步提取和减少特征,最终在全连接层中组合这些特征,形成对交通标志的分类和识别㊂此外,通过使用反向传播梯度下降法进行训练,可以进一步优化网络中的连接策略,从而减少网络中的权重数量,提高模型的精度和效率㊂1.2㊀SOM -CNN㊀㊀为了进一步提高CNN 架构的效率和精度,本文引入了SOM 来优化整个系统,提出了SOM -CNN 架构,如图2所示㊂该方法能将图像样本投影到量化的低维空间的SOM 上,实现局部图像采样和部分光照不变性技术的使用㊂具体研究工作包括:(1)对于集中训练的图像,在整个图像上设置固定大小的窗口(例如5ˑ5),并在每一步提取局部图像样本,其中每步中窗口移动4个像素点;(2)SOM 的3个维度可以被认为是3个特征,在图1㊀典型的CNN架构前一阶段的向量上进行训练时,SOM将25维输入向量量化为125个拓扑值;(3)在训练集和测试集中的所有图像上都会出现与(1)中相同的窗口㊂局部图像样本在每个步骤都通过SOM,从而在SOM创建的输出空间中创建新㊀㊀的训练和测试集㊂此时,每个输入图像由3个映射表示,每个映射对应于SOM中的维度㊂这些映射的大小等于输入图像的大小除以步长;(4)采用新创建的训练集训练CNN网络㊂图2㊀引入SOM的CNN架构2㊀实验设计和结果2.1㊀实验设计㊀㊀本实验采用了比利时交通标志数据集(BelgiumTraffic Signs Dataset),该数据集包括警示标志㊁优先通行标志㊁禁止通行标志㊁强制通行标志㊁停车路牌㊁指定通行标志等6大类,训练和测试数据文件夹包含62个子文件夹,所有图像的格式均为ppm㊂因此,本实验的任务是将给定图像分类为表示交通标志面板的62个类别之一㊂实验环境搭建基于Python的Tensorflow㊂Python是一种常用的编程语言,在机器学习中广泛使用㊂本实验使用的Python模块包含一个名为scikit-learntool的模块,该模块集成了大量用于监督和非监督问题的机器学习算法㊂Tensorflow则是一个多用途开源库,可以在Python,C++,Java,Scala,R等多种编程语言中使用,并可以在Unix,Windows,iOS和Android等平台上运行㊂Keras是TensorFlow的官方高级API,用于提供开发接口,其模型制作简单,支持卷积神经网络和递归神经网络以及两者的组合,支持任意连接方案(包括多输入和多输出训练)㊂2.2㊀实验结果㊀㊀经过多组实验,本文利用SOM-CNN模型对交通标志进行分类识别㊂每次实验分别具有200张训练图像,200张测试图像,并且训练和测试集之间没有重叠㊂为了比较训练和执行时间,本实验使用了NVIDIA GeForce RTX2060和3080进行对比实验,如表1所示㊂表1㊀SOM-CNN的训练时间和分类时间硬件平台训练时间/min分类时间/ms2060平均14平均0.213080平均29平均0.35实验表明,该模型对交通标志识别效果良好㊂在多次实验中,平均每200张测试图像种有3张被错误分类,其正确率约为98.5%,表现出很好的分类效果㊂3㊀结语㊀㊀交通标志检测通常基于机器学习方法,而深度神经网络的出现进一步提升了其分类精度㊂深度神经网络基于许多简单互连的神经元,可以从大量数据中提取有意义的特征以解决复杂的分类问题㊂为了进一步提高交通标志识别的准确率,文章结合现有理论开发了SOM-CNN架构,并对交通标志数据集进行了分类,取得了良好的效果㊂尽管其准确率与主流方法相比尚有差距,但其高效性使其具有一定的发展潜力㊂未来,研究人员可以通过改进结构来进一步提高SOM-CNN模型的效率和精度,并扩展模型以检测其他对象,如行人㊁动物和其他复杂障碍物,以期在实际应用中取得更好的效果㊂参考文献[1]SAADNA Y,BEHLOUL A.An overview of traffic sign detection and classification methods[J]. International Journal of Multimedia Information Retrieval,2017(6):193-210.[2]HE Z,NAN F,LI X,et al.Traffic sign recognition by combining global and local features based on semi‐supervised classification[J].IET Intelligent Transport Systems,2020(5):323-330.[3]LECUN Y,BENGIO Y,HINTON G.Deep learning [J].Nature,2015(521):436-444.[4]ALZUBAIDI L,ZHANG J,HUMAIDI A J,et al. Review of deep learning:concepts,CNN architectures, challenges,applications,future directions[J].Journal of Big Data,2021(8):71-74.[5]KASAR M M,BHATTACHARYYA D,KIM T H. Face recognition using neural network:a review[J]. International Journal of Security and Its Applications,2016(3):81-100.[6]ALAM A,PRAVEEN S.A review of automatic driving system by recognizing road signs using digital image processing[J].Journal of Informatics Electrical and Electronics Engineering(JIEEE),2021(2):1-9.[7]SINGH S P,WANG L,GUPTA S,et al.3D deep learning on medical images:a review[J].Sensors,2020 (18):5097.[8]LI Z,LIU F,YANG W,et al.A survey of convolutional neural networks:analysis,applications, and prospects[J].IEEE Transactions on Neural Networks and Learning Systems,2021(4):1-21. [9]HINTON G E.To recognize shapes,first learn to generate images[J].Progress in Brain Research,2007 (165):535-547.[10]HAJI S H,ABDULAZEEZ A parison of optimization techniques based on gradient descent algorithm:a review[J].PalArch s Journal of Archaeology of Egypt/Egyptology,2021(4):2715-2743.(编辑㊀王雪芬)Research on convolutional neural network architecture based on self-organizing mapZhao Yi aiZhengzhou University of Industrial Technology Zhengzhou451100 ChinaAbstract Assisted driving and automatic driving technologies are poised to greatly impact human lifestyle with traffic sign recognition technology representing a pivotal aspect thereof.To refine the theoretical underpinnings of traffic sign recognition a convolutional neural network framework combined with self-organizing map algorithm is proposed.And self-organizing map algorithm can quantize image samples into topological space thus providing dimensionality reduction and invariance processing for small changes in image samples.This method combined with the partial invariant performance of convolution neural network for translation rotation scaling and deformation improves the efficiency and accuracy of this architecture.The experimental results show that the accuracy of proposed system is 98.5%in200test samples representing a highly promising outcome.Key words convolution neural network traffic sign recognition self-organizing map deep learning。
图神经网络综述
第47卷第4期Vol.47No.4计算机工程Computer Engineering2021年4月April 2021图神经网络综述王健宗，孔令炜，黄章成，肖京（平安科技（深圳）有限公司联邦学习技术部，广东深圳518063）摘要：随着互联网和计算机信息技术的不断发展，图神经网络已成为人工智能和大数据处理领域的重要研究方向。
图神经网络可对相邻节点间的信息进行有效传播和聚合，并将深度学习理念应用于非欧几里德空间的数据处理中。
简述图计算、图数据库、知识图谱、图神经网络等图结构的相关研究进展，从频域和空间域角度分析与比较基于不同信息聚合方式的图神经网络结构，重点讨论图神经网络与深度学习技术相结合的研究领域，总结归纳图神经网络在动作检测、图系统、文本和图像处理任务中的具体应用，并对图神经网络未来的发展方向进行展望。
关键词：图神经网络；图结构；图计算；深度学习；频域；空间域开放科学（资源服务）标志码（OSID ）：中文引用格式：王健宗，孔令炜，黄章成，等.图神经网络综述［J ］.计算机工程，2021，47（4）：1-12.英文引用格式：WANG Jianzong ，KONG Lingwei ，HUANG Zhangcheng ，et al.Survey of graph neural network ［J ］.Computer Engineering ，2021，47（4）：1-12.Survey of Graph Neural NetworkWANG Jianzong ，KONG Lingwei ，HUANG Zhangcheng ，XIAO Jing（Federated Learning Technology Department ，Ping An Technology （Shenzhen ）Co.，Ltd.，Shenzhen ，Guangdong 518063，China ）【Abstract 】With the continuous development of the computer and Internet technologies ，graph neural network has become an important research area in artificial intelligence and big data.Graph neural network can effectively transmit and aggregate information between neighboring nodes ，and applies the concept of deep learning to the data processing of non-Euclidean space.This paper briefly introduces the research progress of graph computing ，graph database ，knowledge graph ，graph neural network and other graph-based techniques.It also analyses and compares graph neural network structures based on different information aggregation modes in the spectral and spatial domain.Then the paper discusses research fields that combine graph neural network with deep learning ，and summarizes the specific applications of graph neural networks in action detection ，graph systems ，text and image processing tasks.Finally ，it prospects the future development research directions of graph neural networks.【Key words 】graph neural network ；graph structure ；graph computing ；deep learning ；spectral domain ；spatial domain DOI ：10.19678/j.issn.1000-3428.00583820概述近年来，深度学习技术逐渐成为人工智能领域的研究热点和主流发展方向，主要应用于高维特征规则分布的非欧几里德数据处理中，并且在图像处理、语音识别和语义理解［1］等领域取得了显著成果。
研究生英语论文写作
(2) All the experiments draw on the observations made during the First Global GARP Experiment (FGGE) of 1979, when an intensive international effort acquired as complete a set of global observations as was ever made before or since, in each set of experiments, forecasts were made drawing on all of the observing systems available----satellite temperatures, satellite cloud-track winds, winds and temperatures from commercial aircraft, surface observations (land and ship), and balloon observations. Then new sets of forecasts drew on this maximum system with one or more observing systems deleted from it. -----―Weather Satellites Coming of Age‖, Science, Vol.229. 1. Complexity Written language is relatively more complex than spoken language. Written texts are lexically dense compared to spoken languagethey have proportionately more lexical words than grammatical words. Writ-ten texts are shorter and have longer, more complex words and phrases. They have more noun-based phrases, more nominalizations, and more lexical variation. Written language is grammatically more complex than spoken language. It has more subordinate clauses, more ―that/to‖ complement clauses, more long sequences of prepositional phrases, more attributive adjectives and more passives than spoken language. 1.2.2 Formality Academic writing is relatively formal. Formal writing doesn‘t use contractions, or colloquialisms and slang. In general this means that in an essay you should avoid colloquial words and expressions.
模拟ai英文面试题目及答案
模拟ai英文面试题目及答案模拟AI英文面试题目及答案1. 题目: What is the difference between a neural network anda deep learning model?答案: A neural network is a set of algorithms modeled loosely after the human brain that are designed to recognize patterns. A deep learning model is a neural network with multiple layers, allowing it to learn more complex patterns and features from data.2. 题目: Explain the concept of 'overfitting' in machine learning.答案: Overfitting occurs when a machine learning model learns the training data too well, including its noise and outliers, resulting in poor generalization to new, unseen data.3. 题目: What is the role of a 'bias' in an AI model?答案: Bias in an AI model refers to the systematic errors introduced by the model during the learning process. It can be due to the choice of model, the training data, or the algorithm's assumptions, and it can lead to unfair or inaccurate predictions.4. 题目: Describe the importance of data preprocessing in AI.答案: Data preprocessing is crucial in AI as it involves cleaning, transforming, and reducing the data to a suitableformat for the model to learn effectively. Proper preprocessing can significantly improve the performance of AI models by ensuring that the input data is relevant, accurate, and free from noise.5. 题目: How does reinforcement learning differ from supervised learning?答案: Reinforcement learning is a type of machine learning where an agent learns to make decisions by performing actions in an environment to maximize a reward signal. It differs from supervised learning, where the model learns from labeled data to predict outcomes based on input features.6. 题目: What is the purpose of a 'convolutional neural network' (CNN)?答案: A convolutional neural network (CNN) is a type of deep learning model that is particularly effective for processing data with a grid-like topology, such as images. CNNs use convolutional layers to automatically and adaptively learn spatial hierarchies of features from input images.7. 题目: Explain the concept of 'feature extraction' in AI.答案: Feature extraction in AI is the process of identifying and extracting relevant pieces of information from the raw data. It is a crucial step in many machine learning algorithms, as it helps to reduce the dimensionality of the data and to focus on the most informative aspects that can be used to make predictions or classifications.8. 题目: What is the significance of 'gradient descent' in training AI models?答案: Gradient descent is an optimization algorithm used to minimize a function by iteratively moving in the direction of steepest descent as defined by the negative of the gradient. In the context of AI, it is used to minimize the loss function of a model, thus refining the model's parameters to improve its accuracy.9. 题目: How does 'transfer learning' work in AI?答案: Transfer learning is a technique where a pre-trained model is used as the starting point for learning a new task. It leverages the knowledge gained from one problem to improve performance on a different but related problem, reducing the need for large amounts of labeled data and computational resources.10. 题目: What is the role of 'regularization' in preventing overfitting?答案: Regularization is a technique used to prevent overfitting by adding a penalty term to the loss function, which discourages overly complex models. It helps to control the model's capacity, forcing it to generalize better to new data by not fitting too closely to the training data.。
联合训练生成对抗网络的半监督分类方法
光学 精密工程Optics and Precision Engineering第 29 卷 第 5 期2021年5月Vol. 29 No. 5May 2021文章编号 1004-924X( 2021)05-1127-09联合训练生成对抗网络的半监督分类方法徐哲，耿杰*，蒋雯，张卓，曾庆捷(西北工业大学电子信息学院，西安710072)摘要：深度神经网络需要大量数据进行监督训练学习，而实际应用中往往难以获取大量标签数据°半监督学习可以减小深度网络对标签数据的依赖，基于半监督学习的生成对抗网络可以提升分类效果,旦仍存在训练不稳定的问题°为进一步提高网络的分类精度并解决网络训练不稳定的问题，本文提出一种基于联合训练生成对抗网络的半监督分类方法，通 过两个判别器的联合训练来消除单个判别器的分布误差，同时选取无标签数据中置信度高的样本来扩充标签数据集，提高半监督分类精度并提升网络模型的泛化能力°在CIFAR -10和SVHN 数据集上的实验结果表明，本文方法在不同数量的标签数据下都获得更好的分类精度°当标签数量为2 000时，在CIFAR -10数据集上分类精度可达80.36% ;当标签 数量为10时，相比于现有的半监督方法，分类精度提升了约5%°在一定程度上解决了 GAN 网络在小样本条件下的过拟合问题°关键词：生成对抗网络；半监督学习；图像分类；深度学习中图分类号:TP391文献标识码：Adoi ：10. 37188/OPE. 20212905.1127Co -training generative adversarial networks forsemi -supervised classification methodXU Zhe , GENG Jie * , JIANG Wen , ZHANG Zhuo , ZENG Qing -jie(School of E lectronics and Information , Northwestern Polytechnical University , Xian 710072, China )* Corresponding author , E -mail ： gengjie@nwpu. edu. cnAbstract ： Deep neural networks require a large amount of data for supervised learning ； however , it is dif ficult to obtain enough labeled data in practical applications. Semi -supervised learning can train deep neuralnetworks with limited samples. Semi -supervised generative adversarial networks can yield superior classifi cation performance ； however ， they are unstable during training in classical networks. To further improve the classification accuracy and solve the problem of training instability for networks ， we propose a semi -su pervised classification model called co -training generative adversarial networks ( CT -GAN ) for image clas sification. In the proposed model ， co -training of two discriminators is applied to eliminate the distribution error of a single discriminator and unlabeled samples with higher confidence are selected to expand thetraining set , which can be utilized for semi -supervised classification and enhance the generalization of deep networks. Experimental results on the CIFAR -10 dataset and the SVHN dataset showed that the pro posed method achieved better classification accuracies with different numbers of labeled data. The classifi cation accuracy was 80. 36% with 2000 labeled data on the CIFAR -10 dataset , whereas it improved by收稿日期：2020-11-04；修订日期:2021-01-04.基金项目:装备预研领域基金资助项目(No. 61400010304);国家自然科学基金资助项目(No. 61901376)1128光学精密工程第29卷about5%compared with the existing semi-supervised method with10labeled data.To a certain extent, the problem of GAN overfitting under a few sample conditions is solved.Key words：generative adversarial networks；semi-supervised learning；image classification；deep learning1引言图像分类作为计算机视觉领域最基础的任务之一，主要通过提取原始图像的特征并根据特征学习进行分类［11o传统的特征提取方法主要是对图像的颜色、纹理、局部特征等图像表层特征进行处理实现的，例如尺度不变特征变换法［21,方向梯度法［31以及局部二值法［41等。
aigc检测相似度的原理
aigc检测相似度的原理AIGC, or Artificial Intelligence Graphic Comparison, is a technology that is used to detect and measure the similarity between two or more images. The principle behind AIGC is based on the use of advanced algorithms and machine learning techniques to analyze and compare the visual features of images. This technology has variousapplications in different fields, including image recognition, content-based image retrieval, and copyright protection.One of the key principles behind AIGC is the use of deep learning algorithms, such as convolutional neural networks (CNNs), to extract and analyze the visual features of images. CNNs are a type of artificial neural networkthat is particularly well-suited for image recognition tasks, as they are able to automatically learn and extract hierarchical features from raw pixel data. By using CNNs, AIGC is able to effectively capture and analyze the visual content of images, allowing for accurate and reliablesimilarity measurements.Another important principle behind AIGC is the use of similarity metrics, such as cosine similarity or Euclidean distance, to quantitatively measure the similarity between images. These metrics allow AIGC to compare the visual features of images and determine how similar or dissimilar they are. By using these metrics, AIGC is able to provide a numerical measure of similarity, which can be used for various applications, such as image retrieval or copyright infringement detection.In addition to deep learning algorithms and similarity metrics, AIGC also relies on large-scale image datasets for training and evaluation. By using these datasets, AIGC is able to learn and extract a wide range of visual features, allowing for robust and accurate similarity measurements. Furthermore, the use of large-scale datasets also enables AIGC to generalize well to new and unseen images, making it a powerful tool for various real-world applications.From a practical perspective, AIGC works by firstextracting visual features from the input images using deep learning algorithms. These features are then compared using similarity metrics to determine the degree of similarity between the images. The result is a quantitative measure of similarity, which can be used for various purposes, such as image search, content-based recommendation systems, or copyright protection.Overall, the principle behind AIGC is based on the use of advanced algorithms, machine learning techniques, and large-scale image datasets to analyze and compare thevisual features of images. By leveraging these principles, AIGC is able to provide accurate and reliable similarity measurements, making it a valuable tool for various applications in different fields.。
基于多尺度各向异性高斯核主方向角度变化的角点检测
2021年第05期(总第221期）《蓿窟画蓿基于多尺度各向异性高斯核主方向角度变化的角点检测王天赋，任劫,章为川，晁凯(西安工程大学大学电子信息学院，陕西西安710048)摘要：角点检测在图像分析和计算机视觉领域有着及其重要的作用。
各向异性高斯方向导数(AG D Ds)可以很好的提取 不同方向的图像局部灰度变化信息，并且具有很强的噪声鲁棒性,在对不同尺度下的轮康信息和各向异性高斯方向导数 进行研究后，将两者相结合提出了一种基于多尺度各向异性高斯核主方向角度变化的角点检测算法。
该算法可以有效 的降低角点检测的误检率。
实验采用了两幅标注了真实角点测试图，在无噪声和加入不同等级噪声的情况下，对该算法 和其它三种经典的角点检测算法从角点检测的能力和角点定位的精度进行对比。
实验表明，研究所得的算法对于角点 的检测具有更好的噪声稳健性和更低的误检率。
关键词：角点检测；图像轮摩;各向异性高斯核；多尺度;鲁棒性中图分类号:TP391.41 文献标识码:B文章编号=2096-9759(2021)05-0032-04A muHkeale coma-detection v ia ai^ledifi»iHice ofpnnc^le directions of a nis»tropk Gaussian daivativesW ang T ianfu,Ren Jie9Zhang W eichuan,Chao kai(School o f Electronics and Inform ation,X i;an Polytechnic University,X i^an710048, China)A bstract:Comer detection plays an important role in image analysis and computer vision.Anisotropic Gaussian directionalderivatives(AGDDs)can extract the local gray change inform ation o f images in different directions,and has strong noise ro-bustness.A fter studying the contour inform ation and anisotropic Gaussian directional derivatives in different scales，a comer detection a lg o ritto based on multi-scale anisottopic Gaussian kernel principal direction angle change is proposed.The algor-ithm can effectively reduce the false detection rate o f comer detection.Two real comer test images are used in the experiment.In the case o f no noise and adding different levels o f noise,the comer detection ability and comer positioning accuracy o f the algorithm are compared w ith other three classical comer detection algorithms.Experimental results show that the proposed al圓gorithm has better noise robustness and lower false detection rate for comer detection.Key words:comer detection;image contours;anisotropic Gaussian kernel;m ulti-scale;robustness〇引言角点中包含了图像中重要的结构信息，是图像的基本特 征。
东北大学本科毕业设计论文《基于支持向量机算法的电网故障诊断方法研究》
ABSTRACT
With electricity demand growth and technology progress, power grid has become larger and more complex. Due to the formation of large power grids, the quality of electricity supply and electric security improves, also, resources complementary has been strengthened. Once fault occurs, however, it will spread to a wider area with a faster speed. For these merits, this study focuses on the fault diagnosis for power network based on support vector machine. By analyzing relative literatures and building a simulation model, this thesis finishes the analyzing of fault waveforms and harmonic distribution, and studies fault characteristics from the perspective of signal synthesis. To extract fault features submerged in original fault data, this thesis deeply studies the fuzzy processing method, the value detection of instantaneous current and the common fault feature extraction method based on wavelet singular entropy. For the error-prone of instantaneous current detection, fuzzing set ideas is drew to optimize the training samples and by modifying diagnostic strategies, the shortcoming is overcame. To reduce the elapsed time of the common fault feature extraction method based on wavelet singular entropy, a new fault feature combination is proposed by comparing the method with instantaneous current detection. This new combination can inspect faults rapidly when current has a sharp rise such as no- load line closing serious short circuit and improve the diagnostic accuracy when fault current rise is more gentle by taking advantage of wavelet transform which has a wealth of information. Under the condition that the fault features are extracted entirely, artifirt vector machine are used to diagnose power network faults. On one hand, a comparison of the two methods and a study on kernels, multi-class classification methods and SVM training algorithms are carried out. On the other hand, for a figurative expression of the diagnostic results, two dimensions are constructed from the training samples and a twodimensional optimal hyperplane is established by analyzing simulation system structure and data characteristics. Finally, by analyzing the spatial distribution of sample points, the three-dimensional optimal hyperplane is explored. －III－
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I. I NTRODUCTION The problem of linear matrix equations solving (including matrix-inverse problems as a sub-topic) is considered to be a very fundamental problem widely encountered in science and engineering. It could usually be an essential part of many solutions; e.g., in control system design [1][2] and image-processing [3]. In view of these, we consider in this paper the following general problem formulation of linear matrix equation: AXB = C , where coefficient matrices A ∈ Rm×m , B ∈ Rn×n and C ∈ Rm×n , while X ∈ Rm×n is the unknown matrix to be found. Evidently, when B = C = I and m = n, the problem reduces to the matrix-inversion problem. There are two general types of solutions to the problem of linear matrix equations. One is the numerical algorithms per-
formed on digital computers (i.e., on our today’s computers). Usually, such numerical algorithms are of serial-processing nature and may not be efficient enough for large-scale online or real-time applications. Being the second general type of solution, many parallel-processing computational methods have been developed, analyzed, and implemented on specific architectures [3]-[13]. The dynamic-system approach is one of such important parallel-processing methods for solving linear matrix equations. Recently, because of the in-depth research in neural networks, numerous dynamic and analog solvers based on recurrent neural networks (RNN) have been developed and investigated [3][6][10]-[13]. The neural dynamic approach is thus now regarded as a powerful alternative to online computation of matrix problems because of its parallel distributed nature and convenience of hardware implementation [10][14]. Different from gradient neural networks for constant problems solving [2][3][6][10][15]-[17], a special kind of recurrent neural networks has recently been proposed by Zhang et al [10]-[12] for real-time solution of time-varying problems solving. In other words, in our context of AXB = C , coefficient matrices A, B and C could be A(t), B (t) and C (t), time-varying ones. The design method of Zhang neural network is completely different from that of gradient neural networks. In this paper, we generalize such a design method to solving online the time-varying linear matrix equation, A(t)X (t)B (t) = C (t) over time t ∈ [0, +∞). Theoretical and simulation results both demonstrate the efficacy of the proposed ZNN neural approach. To the best of our knowledge, there is little work dealing with such a timevarying problem in the literature at present stage, except some preliminary results presented in [11]-[13]. The main contributions of the paper are thus as follows. 1) In our paper, we propose a special kind of recurrent neural network to solve the time-varying linear matrix equation in real-time. As far as we know (with 10year research experience on neural networks), there are almost no other papers working on these time-varying
1
Yunongct— For solving online the linear matrix equation AXB = C with time-varying coefficients, this paper presents a special kind of recurrent neural networks by using a design method recently proposed by Zhang et al. Compared with gradient neural networks (abbreviated as GNN, or termed as gradient-based neural networks), the resultant Zhang neural network (termed as such and abbreviated as ZNN hereafter for presentation convenience) is designed based on a matrixvalued error function, instead of a scalar-valued error function. Zhang neural network is deliberately developed in the way that its trajectory could be guaranteed to globally exponentially converge to the time-varying theoretical solution of given linear matrix equation. In addition, Zhang neural network is described by an implicit dynamics, instead of an explicit dynamics usually describing recurrent neural networks. Convergence results of Zhang neural network are presented to show the neuralnetwork performance. In comparison, we develop and simulate the gradient neural network as well, which is exploited to solve online the time-varying linear matrix equation. Computersimulation results substantiate the theoretical efficacy and superior performance of Zhang neural network for the online solution of time-varying linear matrix equation, especially when using a power-sigmoid activation function. Index Terms— Recurrent neural network; Gradient neural network; Time-varying linear matrix equation; Matrix-valued error function; Implicit dynamics.