Develop a closed form solution for learning the parameters { µ , Φ , σ 2 } of a subspace identity model where the noise is spherical: P r ( x ij ) = Norm x ij [ µ , ΦΦ T + σ 2 I ] . Hint : Assume you...

1. 
   

   
   Develop a closed form solution for learning the parameters
   
   {
   
   
   
   µ
   
   
   
   ,
   
   
   
   
   Φ
   
   
   ,
   
   
   
   
   σ
   
   
   ²
   
   
   }
   
   
   
   of a subspace identity model where the noise is spherical:
   

   
   

<sup>P




r



(



x</sup>



ij




<sup>)




=




Norm</sup>


x



_ij







<sup>[




µ





,








ΦΦ</sup>

T

+

σ


²


I

]

.

Hint

: Assume you have exactly

J

= 2 examples of each of the

I

training images and base your solution on probabilistic PCA.