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Area Digital technology – Fundamental concepts / Information theory

IEV ref171-07-22

Symbol
H(X,Y)

en
joint entropy
mean value of the joint information content of the events in a finite set of mutually exclusive and jointly exhaustive events

H(X,Y)= i=1 n j=1 m p( x i , y j )I( x i , y j ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGibGaaiikaiaadIfacaGGSaGaamywaiaacMcacqGH9aqpdaae WbqaamaaqahabaGaamiCaiaacIcacaWG4bWaaSbaaSqaaiaadMgaae qaaOGaaiilaiaadMhadaWgaaWcbaGaamOAaaqabaGccaGGPaGaeyyX ICTaamysaiaacIcacaWG4bWaaSbaaSqaaiaadMgaaeqaaOGaaiilai aadMhadaWgaaWcbaGaamOAaaqabaGccaGGPaaaleaacaWGQbGaeyyp a0tcLboacaaIXaaaleaacaWGTbaaniabggHiLdaaleaacaWGPbGaey ypa0tcLboacaaIXaaaleaacaWGUbaaniabggHiLdaaaa@61BF@

where X={ x 1 ,, x n } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGybGaeyypa0ZaaiWaaeaacaWG4bWaaSbaaSqaaKqzGdGaaGym aaWcbeaakiaacYcacaGGUaGaaiOlaiaac6cacaWG4bWaaSbaaSqaai aad6gaaeqaaaGccaGL7bGaayzFaaaaaa@494E@ is the set of events x i ( i=1,,n ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWG4bWaaSbaaSqaaiaadMgaaeqaaOWaaeWaaeaacaWGPbGaeyyp a0tcLbuacaaIXaGccaGGSaGaaiOlaiaac6cacaGGUaGaamOBaaGaay jkaiaawMcaaaaa@47D2@ , Y={ y 1 ,, y m } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGzbGaeyypa0ZaaiWaaeaacaWG5bWaaSbaaSqaaKqzGdGaaGym aaWcbeaakiaacYcacaGGUaGaaiOlaiaac6cacaWG5bWaaSbaaSqaai aad2gaaeqaaaGccaGL7bGaayzFaaaaaa@4950@ is the set of events y j ( j=1,,m ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWG5bWaaSbaaSqaaiaadQgaaeqaaOWaaeWaaeaacaWGQbGaeyyp a0tcLbuacaaIXaGaaiilaOGaaiOlaiaac6cacaGGUaGaamyBaaGaay jkaiaawMcaaaaa@47D4@ , I( x i , y j ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGjbWaaeWaaeaacaWG4bWaaSbaaSqaaiaadMgaaeqaaOGaaiil aiaadMhadaWgaaWcbaGaamOAaaqabaaakiaawIcacaGLPaaaaaa@4452@ is the joint information content of x i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWG4bWaaSbaaSqaaiaadMgaaeqaaaaa@3F1E@ and y j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWG5bWaaSbaaSqaaiaadQgaaeqaaaaa@3F20@ , and p( x i , y j ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGWbWaaeWaaeaacaWG4bWaaSbaaSqaaiaadMgaaeqaaOGaaiil aiaadMhadaWgaaWcbaGaamOAaaqabaaakiaawIcacaGLPaaaaaa@4479@ the joint probability that both events occur


fr
entropie conjointe, f
espérance mathématique de la quantité d'information conjointe des événements d'un ensemble exhaustif d'événements s'excluant mutuellement

H(X,Y)= i=1 n j=1 m p( x i , y j )I( x i , y j ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGibGaaiikaiaadIfacaGGSaGaamywaiaacMcacqGH9aqpdaae WbqaamaaqahabaGaamiCaiaacIcacaWG4bWaaSbaaSqaaiaadMgaae qaaOGaaiilaiaadMhadaWgaaWcbaGaamOAaaqabaGccaGGPaGaeyyX ICTaamysaiaacIcacaWG4bWaaSbaaSqaaiaadMgaaeqaaOGaaiilai aadMhadaWgaaWcbaGaamOAaaqabaGccaGGPaaaleaacaWGQbGaeyyp a0tcLboacaaIXaaaleaacaWGTbaaniabggHiLdaaleaacaWGPbGaey ypa0tcLboacaaIXaaaleaacaWGUbaaniabggHiLdaaaa@61BF@

X={ x 1 ,, x n } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGybGaeyypa0ZaaiWaaeaacaWG4bWaaSbaaSqaaKqzGdGaaGym aaWcbeaakiaacYcacaGGUaGaaiOlaiaac6cacaWG4bWaaSbaaSqaai aad6gaaeqaaaGccaGL7bGaayzFaaaaaa@494E@ est l'ensemble d'événements x i ( i=1,,n ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWG4bWaaSbaaSqaaiaadMgaaeqaaOWaaeWaaeaacaWGPbGaeyyp a0tcLbuacaaIXaGccaGGSaGaaiOlaiaac6cacaGGUaGaamOBaaGaay jkaiaawMcaaaaa@47D2@ , Y={ y 1 ,, y m } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGzbGaeyypa0ZaaiWaaeaacaWG5bWaaSbaaSqaaKqzGdGaaGym aaWcbeaakiaacYcacaGGUaGaaiOlaiaac6cacaWG5bWaaSbaaSqaai aad2gaaeqaaaGccaGL7bGaayzFaaaaaa@4950@ est l'ensemble d'événements y j ( j=1,,m ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWG5bWaaSbaaSqaaiaadQgaaeqaaOWaaeWaaeaacaWGQbGaeyyp a0tcLbuacaaIXaGaaiilaOGaaiOlaiaac6cacaGGUaGaamyBaaGaay jkaiaawMcaaaaa@47D4@ , I( x i , y j ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGjbWaaeWaaeaacaWG4bWaaSbaaSqaaiaadMgaaeqaaOGaaiil aiaadMhadaWgaaWcbaGaamOAaaqabaaakiaawIcacaGLPaaaaaa@4452@ est la quantité d'information conjointe de x i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWG4bWaaSbaaSqaaiaadMgaaeqaaaaa@3F1E@ et y j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWG5bWaaSbaaSqaaiaadQgaaeqaaaaa@3F20@ , and p( x i , y j ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGWbWaaeWaaeaacaWG4bWaaSbaaSqaaiaadMgaaeqaaOGaaiil aiaadMhadaWgaaWcbaGaamOAaaqabaaakiaawIcacaGLPaaaaaa@4479@ est la probabilité de réalisation simultanée des deux événements


ar
الانتروبيا المشتركة
القيمة المتوسطة المشتركة لمحتوى المعلومات

de
verbundene Entropie, f

fi
yhteisentropia

ja
結合エントロピー

pl
entropia łączna, f

pt
entropia conjunta

zh
联合熵

Publication date: 2019-03-29
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