Show that the distance ex defined in Step 4 of the PCA algorithm can be expressed as where U is a matrix of size d by (d -) such that [T( U5forms an orthogonal matrix. This is PCA algorithm! Input: Training data D= {(x,.yn),n= 1.2. . N} containing K classes Da D, , Dr.1, a new data point x Step 1 Apply PCA to each ? to yield {A1(k), Ugk)} for k-0, l. .. .. K-1. Step 2 Calculate principal components f(x- fork 0, 1.K-1. Step 3 Use the principal components to calculate the projection of x-l onto the kth (k)T subspace ,=U(k) f(k) for k=0.1 K-1 Step 4 Calculate the distance between x - /f/"and its projection Zk as and identify the target class k for data point.x using the classifier Show that the distance ex defined in Step 4 of the PCA algorithm can be expressed as where U is a matrix of size d by (d -) such that [T( U5forms an orthogonal matrix. This is PCA algorithm! Input: Training data D= {(x,.yn),n= 1.2. . N} containing K classes Da D, , Dr.1, a new data point x Step 1 Apply PCA to each ? to yield {A1(k), Ugk)} for k-0, l. .. .. K-1. Step 2 Calculate principal components f(x- fork 0, 1.K-1. Step 3 Use the principal components to calculate the projection of x-l onto the kth (k)T subspace ,=U(k) f(k) for k=0.1 K-1 Step 4 Calculate the distance between x - /f/"and its projection Zk as and identify the target class k for data point.x using the classifier