This problem considers the process of whitening a data set with two sources. Let 1 , 2 , ··· , n be the source data vectors, with i = ( i 1 , i 2 ) T . (a) Suppose it’s possible to find an invertible...

This problem considers the process of whitening a data set with two sources. Let

₁,

₂, ··· ,


_n

be the source data vectors, with


_i

= (

_i1,


_i2)
^T

.

(a) Suppose it’s possible to find an invertible 2×2 matrix Z with the property that

Setting

^∗

_i

=
Z
⁻¹


_i
, show that the

^∗

_i

’s satisfy (9.30). This shows that any matrix
Z
with the above property can be used to whiten the data set.

(b) Since
is symmetric, the SVD of this matrix can be written as

Setting
show that the

^∗
_i
’s satisfy (9.30).

(c) Whiten one of the data sets in Table 9.9. Note that you should first center the data, so (9.29) is satisfied). Also, if you use the method from part (a),
Z
is not unique, and you should make a particular choice for this matrix.