第2章 神经网络(2)VIP免费

第2章神经网络（2）内容：感知器、多层前馈型神经、反向传播算法（BP算法）、神经网络应用。重点、难点：感知器、反向传播算法（BP算法）。1．引例引例1981年生物学家格若根（W.Grogan）和维什（W．Wirth）发现了两类蚊子(或飞蠓midges)．他们测量了这两类蚊子每个个体的翼长和触角长，数据如下：问：如果抓到三只新的蚊子，它们的触角长和翼长分别为(l.24,1.80);(l.28，1.84)；（1.40，2.04）．问它们应分别属于哪一个种类？解法：•把翼长作纵坐标，触角长作横坐标；那么每个蚊子的翼长和触角决定了坐标平面的一个点.其中6个蚊子属于APf类；用黑点“·”表示；9个蚊子属Af类；用小圆圈翼长触角长类别1.781.14Apf1.961.18Apf1.861.20Apf1.721.24Af2.001.26Apf2.001.28Apf1.961.30Apf1.741.36Af•翼长触角长类别•1.641.38Af•1.821.38Af•1.901.38Af•1.701.40Af•1.821.48Af•1.821.54Af•2.081.56Af“。”表示．•得到的结果见图1思路：作一直线将两类飞蠓分开•例如；取A＝（1.44，2.10）和B＝(1.10，1.16)，过AB两点作一条直线：•y＝1.47x-0.017•其中X表示触角长；y表示翼长．•分类规则：设一个蚊子的数据为（x,y）•如果y≥1.47x-0.017，则判断蚊子属Apf类；•如果y＜1.47x-0.017；则判断蚊子属Af类．•分类结果：(1.24，1.80)，(1.28，1.84)属于Af类；(1.40，2.04）属于Apf类．分类直线图如下的情形已经不能用分类直线的办法：新思路：将问题看作一个系统，飞蠓的数据作为输入，飞蠓的类型作为输出，研究输入与输出的关系。2．PerceptronModelModelisanassemblyofinter-connectednodesandweightedlinksOutputnodesumsupeachofitsinputvalueaccordingtotheweightsofitslinksCompareoutputnodeagainstsomethresholdtFirstneuralnetworkwiththeabilitytolearnMadeupofonlyinputneuronsandoutputneuronsInputneuronstypicallyhavetwostates:ONandOFFOutputneuronsuseasimplethresholdactivationfunctionInbasicform,canonlysolvelinearproblems(limitedapplications)（Canonlyexpresslineardecisionsurfaces）HowDoPerceptronsLearn?UsesSupervisedtraining(trainingmeanslearningtheweightsoftheneurons)Iftheoutputisnotcorrect,theweightsareadjustedaccordingtotheformula:3．BackPropagationNetworksThefollowingdiagramshowsaBackPropagationNN:ThisNNconsistsofthreelayers:1.Inputlayerwiththreeneurons.2.Hiddenlayerwithtwoneurons.3.Outputlayerwithtwoneurons.Generally,BackPropagationNNMostcommonneuralnetworkAnextensionoftheperceptron(1)MultiplelayersTheadditionofoneormore“hidden”layersinbetweentheinputandoutputlayers(2)ActivationfunctionisnotsimplyathresholdUsuallyasigmoidfunction(3)AgeneralfunctionapproximatorNotlimitedtolinearproblemsForexample,atypicalmultilayernetworkanddecisionsurfaceisdepictedinFigure:Informationflowsinonedirection(1)TheoutputsofonelayeractasinputstothelayerNotethat:1.Theoutputofaneuroninalayergoestoallneuronsinthefollowinglayer.2.Eachneuronhasitsowninputweights.3.Theweightsfortheinputlayerareassumedtobe1foreachinput.Inotherwords,inputvaluesarenotchanged.4.TheoutputoftheNNisreachedbyapplyinginputvaluestotheinputlayer,passingtheoutputofeachneurontothefollowinglayerasinput.5.TheBackPropagationNNmusthaveatleastaninputlayerandanoutputlayer.Itcouldhavezeroormorehiddenlayers.Thenumberofneuronsintheinputlayerdependsonthenumberofpossibleinputswehave,whilethenumberofneuronsintheoutputlayerdependsonthenumberofdesiredoutputs.Thenumberofhiddenlayersandhowmanyneuronsineachhiddenlayercannotbewelldefinedinadvance,andcouldchangepernetworkconfigurationandtypeofdata.Ingeneraltheadditionofahiddenlayercouldallowthenetworktolearnmorecomplexpatterns,butatthesametimedecreasesitsperformance.Youcouldstartanetworkconfigurationusinga...