多傳感器數(shù)據(jù)融合-lecture

第七章特征m個(gè)特征中選擇m1m1m（人為選擇、算法選擇將m個(gè)特征變?yōu)閙2個(gè)新特 ---二次特

m2

mm特征選擇與提取的任務(wù)是找出一組對(duì)分類最好的特征評(píng)價(jià)準(zhǔn)則Jij

Jij

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p(x|1)p(x|2)21112Chernoff12

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p(x|

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（兩類協(xié)方差陣相等8JB

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p(x|1)P(ix與ip(x,i)

p(xp(ip(x)

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gp(x|i

p(x),P(i補(bǔ)充幾種常見的概率距離準(zhǔn)則(J和概率相關(guān)性準(zhǔn)則(IJclnIcln

ps(x|)p1s(x|i ps(x|)p1si JBlnIBln

p(x|1)p(x|2p(x|i)

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p(x)1JK

p(x|1)P1p(x|2)P2

A事件的不確定性大（熵大A事件的觀察所提供的信息量大。把各類i看作一系列事把后驗(yàn)概率P(i|xx上出現(xiàn)ix能確定i，則對(duì)i0——x如從x完全不能確定i，則對(duì)i的觀察信息量大，熵大——x

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XtestD維特征中選取d維（dD

D組合數(shù)CdD

(Dd

D=100,d=2,C=4950D=100,d=3,C=161700D=100,d=10,C=1.73103e+13D=100,d=50,C=1.00891e+29D=1000,d=2,C=499500D=10000,d=2,C=4.9995e+07搜索方 從底向上X0從頂向下X0dDd很小（組合數(shù)較少）

X1X

Xi,

J(X1)

J(X2)

J(XiJ1，J2，J3，J4，J5，JC，JB，JD都滿足這一條按照一定的順序?qū)⑺锌赡艿慕M合排成前提：準(zhǔn)則函數(shù)單調(diào)性（J是估計(jì)值節(jié)約計(jì)算與④dD2時(shí)最經(jīng)搜索到葉結(jié)點(diǎn)后，更新BJ

B如已回溯到頂（根）JBDd412 =4 =12SFS法（SequentialForwardSelection：順序前進(jìn)，前向貫序）SFS法l=d（SBS法（順序后退，后向貫序）SBS法r（6）L-R法（增lr法lr個(gè)特征（lr）rl個(gè)特征（lr）（7）L-R法（(ZlZr法增l分成Zl步進(jìn)行，減r分成Zr----進(jìn)化計(jì)算（Evolutionary“GeneticAlgorithmsaregoodattakinglarge,potentiallyhugesearchspacesandnavigatingthem,lookingforoptimalcombinationsofthings,solutionsyoumightnototherwisefindina ----SalvatoreMangano1960-1970’s,JohnH.Holland,aPh.D.studentinU.JohnHenryHolland,AdaptationinNaturalandArtificialSystems,MITPress,1975用遺傳算法進(jìn)行特征選擇（Dd個(gè)D二值字符串m(01001…0110101)，共CdD適應(yīng)度（fitness）函數(shù)：f(m 選擇概率模型：pfm初始化，t=0，隨機(jī)地產(chǎn)生一個(gè)包含L個(gè)的種群M(0計(jì)算當(dāng)前種群M(t)中每一條的適應(yīng)度f(m按照選擇概率p(f(m))對(duì)種群中的進(jìn)行采樣由采樣出的繁下一代，組成下一代的種群M(t+1重組 突變r(jià)eversion,transposition,Two-StepProcedureTwo-StepProcedureFeatureselection(withsomestand-alonecriteria,likeclass-separationcriteriaorstatisticscriteria)Classification(usingselectedRecursiveProcedure(wrapperClassification(withallFeatureselection(accordingtoclassificationperformance)Classification(usingtheselectedfeatures)例如：R-SVM（SVM）和SVM-RFE（SVM遞歸特征剔除1°2°3°