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Matrix Derivative of Fisher Discriminant Analysis

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0

$begingroup$

Let $Z_c in mathbbR^Dtimes N_c$ is column matrix which includes mapped data of class C, and $alpha_c = frac1N_c$ where $D:$ dimension, $N_c:$ data number of class C. $mathbfi:$ One vector as $[1,1,1,...]^T$.

I tried to define Fisher discriminant over $Z_c$ as (I hope, I wasn't wrong ?!):

s = $fracsum_c left(alpha_cZ_cmathbfi - sum_c alpha_c Z_c textbfi right)^Tleft(alpha_cZ_cmathbfi - sum_c alpha_c Z_c textbfi right)
sum_c trleftleft(Z_c - alpha_c Z_c textbfitextbfi^Tright)^Tleft(Z_c - alpha_c Z_c textbfitextbfi^Tright)right$

Problem is : $fracpartial spartial Z_c $

Many thanks to everyone interested...

partial-derivative matrix-equations fisher-information

share|cite|improve this question

edited Mar 16 at 20:19

ncalik

asked Mar 16 at 20:02

ncalikncalik

85

$endgroup$

add a comment | 

0

$begingroup$

Let $Z_c in mathbbR^Dtimes N_c$ is column matrix which includes mapped data of class C, and $alpha_c = frac1N_c$ where $D:$ dimension, $N_c:$ data number of class C. $mathbfi:$ One vector as $[1,1,1,...]^T$.

I tried to define Fisher discriminant over $Z_c$ as (I hope, I wasn't wrong ?!):

s = $fracsum_c left(alpha_cZ_cmathbfi - sum_c alpha_c Z_c textbfi right)^Tleft(alpha_cZ_cmathbfi - sum_c alpha_c Z_c textbfi right)
sum_c trleftleft(Z_c - alpha_c Z_c textbfitextbfi^Tright)^Tleft(Z_c - alpha_c Z_c textbfitextbfi^Tright)right$

Problem is : $fracpartial spartial Z_c $

Many thanks to everyone interested...

partial-derivative matrix-equations fisher-information

share|cite|improve this question

edited Mar 16 at 20:19

ncalik

asked Mar 16 at 20:02

ncalikncalik

85

$endgroup$

add a comment | 

$begingroup$

Let $Z_c in mathbbR^Dtimes N_c$ is column matrix which includes mapped data of class C, and $alpha_c = frac1N_c$ where $D:$ dimension, $N_c:$ data number of class C. $mathbfi:$ One vector as $[1,1,1,...]^T$.

I tried to define Fisher discriminant over $Z_c$ as (I hope, I wasn't wrong ?!):

s = $fracsum_c left(alpha_cZ_cmathbfi - sum_c alpha_c Z_c textbfi right)^Tleft(alpha_cZ_cmathbfi - sum_c alpha_c Z_c textbfi right)
sum_c trleftleft(Z_c - alpha_c Z_c textbfitextbfi^Tright)^Tleft(Z_c - alpha_c Z_c textbfitextbfi^Tright)right$

Problem is : $fracpartial spartial Z_c $

Many thanks to everyone interested...

partial-derivative matrix-equations fisher-information

share|cite|improve this question

edited Mar 16 at 20:19

ncalik

asked Mar 16 at 20:02

ncalikncalik

85

$endgroup$

share|cite|improve this question

edited Mar 16 at 20:19

ncalik

asked Mar 16 at 20:02

ncalikncalik

85

share|cite|improve this question

edited Mar 16 at 20:19

ncalik

asked Mar 16 at 20:02

ncalikncalik

85

asked Mar 16 at 20:02

ncalikncalik

85

asked Mar 16 at 20:02

ncalikncalik

85