8_08_feature_extraction

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1、NeuralnetworksSparsecoding-featureextraction1X⇣11Universit1⌘⇣1edeSherbrooke´1XX1t⌘>TU=⇤U2U⇤=>(xU2(t⇤U)>2Uµb>)U⇤2(Ux((tx>)((tx)µb(t)()x(µbt)µb)()µxb)(t)UX2⇤µb111>XT1hugo.larochelle@usherbrooke.caT1=U=⇤12U>U⇤>21U⌃bU((ttT1=tU⇤2U(xFEATURE

2、EXTRACTION1>⌃bU⇤1t>T1T1>1t=U⇤2U2U!>=U⇤2UtU⇤1111X2>1⌃b>U⇤>2>11>2>⌃>bU⌃b⇤U⇤12>>1>=1U⇤=U(⇤Ut)2November1,2012UU(⇤t)U=U=U⇤UU⇤2U⇤2UU1>2UU=U⇤2U(xµb)(xµb)=IU⇤12U111>>>>Topics:featurelearningT1=I>>==UU⇤⇤2U2U>UU⇤U⇤UUU⇤⇤=U⇤t2UU⇤UU⇤2U•Aspars

3、ecodingmodelcanbeusedtoextractfeatures1>⌃bU⇤1>=I=I=U⇤2U=I2UAbstract1>>1(t)>(t)‣givenalabeledtrainingset=•U{(⇤x(t),y2(Ut))}U⇤UU•⇤{(x2U,y)}Mathformyslides“Sparsecoding”.=I(t)••{({x(x(t()t,y)(,yt()t)(t))})}‣trainsparsecodingdictionaryonlyontraininginp

4、uts•{x}•{x}-thisyieldsadictionaryfromwhichtoinfersparsecodes•x(t()t)h((tt))D(t)(t)••{x{x(t()t})}h(x((tt)))(t)•{(x,y)}•{(h(x),y)}x•{(h(x),y)}xXT‣trainfavoriteclassifierontransformedtrainingset••{({h(h(x(x(1t)(t)),y),y(t)()t)})}xx1(t)(t)2•{(x(t),y(t))}(t)

5、(t)argminTargmin2

6、

7、xDh

8、

9、2+

10、

11、h•{x}h(x)Dh(t)t=1•{x(t)}h(x(t))•Whenclassifyingtestinput,mustinferitssparse••{(h(x(t)),y(t))}x1•{(hrepresentationfirst,thenfeedittotheclassifier(x(t)),y(t))}xh(x)h(x(t))=argmin

12、

13、x(t)Dh(t)

14、

15、2+

16、

17、h(t)2h(t)23333313FEATUREEXTRA

18、CTIONTopics:featurelearningSelf-taughtLearning•Whentrainedonhandwrittendigits:Table4.AccuracyTrainingsetsize10010005000Table5.Textbasesdocuments.Top:Figure5.Left:ExampleimagesfromthehandwrittendigittiveonaverageSelf-taughtLearning:TransferLearningfromU

19、nlabeledDatadataset(top),thehandwrittencharacterRaina,Battle,Lee,PackerandNg.dataset(middle)left.Foreachbasisandthefontcharacterdataset(bottom).Right:Examplelargestmagnitudesparsecodingbaseslearnedonhandwrittendigits.rowrepresentstheTable3.Top:Classific

20、ationaccuracyon26-wayhandwrit-tudeelementfortenEnglishcharacterclassification,usingbasestrainedonspondingtootherhandwrittendigits.Bottom:ClassificationaccuracyonDesigndesign,26-wayEnglishfontcharacterclassification,usingbasesBusinesscar,tr