adaboost算法

基于AdaBoost的脑电信号分类算法目录脑电信号的分类问题1AdaBoost算法简介AdaBoost算法基本原理仿真试验及结论234什么是脑电信号？脑电信号是由脑神经活动产生并且始终存在于中枢神经系统的自发性电位活动，是一种重要的生物电信号。脑电信号非常微弱。主要有以下几个特点：1）随机性及非平稳性相当强。2）脑电信号具有非线性。3）采集到的脑电信号背景噪声比较复杂，有50Hz的工频干扰，电极与皮肤的接触噪声以及电极与地之间的共模信号的干扰等等。关于脑电信号分类在数据处理中，EEG信号的模式分类是BCI系统能否翻译出大脑信息的关键。目前常用方法有很多:(1)BP神经网络(2)线性判别式分类器（LDA）(3)SVM…AdaBoost算法简介Adaboost是一种迭代算法，其核心思想是针对同一个训练集训练不同的分类器(弱分类器)，然后把这些弱分类器集合起来，构成一个更强的最终分类器(强分类器)。其算法本身是通过改变数据分布来实现的，它根据每次训练集之中每个样本的分类是否正确，以及上次的总体分类的准确率，来确定每个样本的权值。将修改过权值的新数据集送给下层分类器进行训练，最后将每次训练得到的分类器最后融合起来，作为最后的决策分类器。使用AdaBoost分类器可以排除一些不必要的训练数据特征，并放在关键的训练数据上面。Given:11(,),,(,)where,{1,1}mmiixyxyxXyInitialization:11(),1,,mDiimFor:1,,tT•FindclassifierwhichminimizeserrorwrtDt,i.e.,:{1,1}thX1argminwhere()[()]jmtjjtijiihhDiyhx:probabilitydistributionof'sattime()tiDixt•Weightclassifier:11ln2ttt•Updatedistribution:1()exp[()](),isfornormalizationttititttDiyhxDiZZminimizeweightederrorforminimizeexponentiallossGiveerrorclassifiedpatternsmorechanceforlearning.TheAdaBoostAlgorithmTheAdaBoostAlgorithmGiven:11(,),,(,)where,{1,1}mmiixyxyxXyInitialization:11(),1,,mDiimFor:1,,tT•FindclassifierwhichminimizeserrorwrtDt,i.e.,:{1,1}thX1argminwhere()[()]jmtjjtijiihhDiyhx•Weightclassifier:11ln2ttt•Updatedistribution:1()exp[()](),isfornormalizationttititttDiyhxDiZZOutputfinalclassifier:1()()TtttsignHxhxWeakClassifier1BoostingillustrationWeakClassifier2BoostingillustrationWeightsIncreasedBoostingillustrationWeakClassifier3BoostingillustrationFinalclassifierisacombinationofweakclassifiersBoostingillustrationGoal:MinimizeexponentiallossFinalclassifier:1()()TtttsignHxhx()exp,()yHxxylossHxEeGoal:MinimizeexponentiallossFinalclassifier:1()()TtttsignHxhx()exp,()yHxxylossHxEe()yHxMaximizethemarginyH(x)Goal:Finalclassifier:1()()TtttsignHxhx()exp,()yHxxylossHxEeMinimize()(),|ttyHxyHxxyxyEeEEexDefine1()()()ttttHxHxhxwith0()0HxThen,()()THxHx1[()()]|tttyHxhxxyEEex1()()|tttyHxyhxxyEEeex1()(())(())tttyHxxttEeePyhxePyhx()(),|ttyHxyHxxyxyEeEEexFinalclassifier:1()()TtttsignHxhx()exp,()yHxxylossHxEeMinimizeDefine1()()()ttttHxHxhxwith0()0HxThen,()()THxHx1()(())(())tttyHxxttEeePyhxePyhx(),0tyHxxytEeSet1()(())(())0tttyHxxttEeePyhxePyhx0?tFinalclassifier:1()()TtttsignHxhxMinimizeDefine1()()()ttttHxHxhxwith0()0HxThen,()()THxHx1()(())(())0tttyHxxttEeePyhxePyhx0(())1ln2(())tttPyhxPyhx11ln2ttt(error)tP?t()exp,()yHxxylossHxEe(,)()iitPxyDi1()[()]mtijiiDiyhx()exp,()yHxxylossHxEewithFinalclassifier:1()()TtttsignHxhxMinimizeDefine1()()()ttttHxHxhx0()0HxThen,()()THxHx1()(())(())0tttyHxxttEeePyhxePyhx0(())1ln2(())tttPyhxPyhx11ln2ttt?tGiven:11where(,),,(,),{1,1}mmiixyxyxXyInitialization:11(),1,,mDiimFor:1,,tT•FindclassifierwhichminimizeserrorwrtDt,i.e.,:{1,1}thX1whereargmin()[()]jmtjjtijiihhDiyhx•Weightclassifier:11ln2ttt•Updatedistribution:1()exp[()],isfornormalizati()onttititttDiyhxDiZZOutputfinalclassifier:1()()TtttsignHxhx(error)tP(,)()iitPxyDi1()[()]mtijiiDiyhx()exp,()yHxxylossHxEewithFinalclassifier:1()()TtttsignHxhxMinimizeDefine1()()()ttttHxHxhx0()0HxThen,()()THxHx1()(())(())0tttyHxxttEeePyhxePyhx0(())1ln2(())tttPyhxPyhx11ln2tttGiven:11where(,),,(,),{1,1}mmiixyxyxXyInitialization:11(),1,,mDiimFor:1,,tT•FindclassifierwhichminimizeserrorwrtDt,i.e.,:{1,1}thX1whereargmin()[()]jmtjjtijiihhDiyhx•Weightclassifier:11ln2ttt•Updatedistribution:1()exp[()],isfornormalizati()onttititttDiyhxDiZZOutputfinalclassifier:1()()TtttsignHxhx(error)tP(,)()iitPxyDi1()[()]mtijiiDiyhx1?tDwithFinalclassifier:1()()TtttsignHxhx()exp~,()yHxxDylossHxEeMinimizeDefine0()0HxThen,1?tD1,,ttttyHyHyhxyxyEeEee1222,112tyHxyttttEeyhyh1222,1argmin12tyHtxytthhEeyhyh221yh12,1argmin12tyHtxytthhEeyh121argmin1|2tyHtxytthhEEeyhx1()()()ttttHxHxhx()()THxHxwithFinalclassifier:()exp~,()yHxxDylossHxEeMinimizeDefineThen,1argmin|tyHtxythhEEeyhx1argmax|tyHtxyhhEEeyhx11()()argmax1()(1|)(1)()(1|)ttHxHxtxhhEhxePyxhxePyx1()()TtttsignHxhx1?tD0()0Hx1()()()ttttHxHxhx()()THxHx121argmin1|2tyHtxytthhEEeyhxwithFinalclassifier:MinimizeDefineThen,()1,~(|)argmax()yHxttxyePyxhhEyhxmaximizedwhen()yhxx()()11,~(|),~(|)()(1|)(1|)yHxyHxtttxyePyxxyePyxhxsignPyxPyx()1,~(|)()|yHxttxyePyxhxsignEyx11()()argmax1()(1|)(1)()(1|)ttHxHxtxhhEhxePyxhxePyxwith()exp~,()yHxxDylossHxEe1()()TtttsignHxhx1?tD1()()()ttttHxHxhx()()THxHx0()0H