Coursera-Mathematics for Machine Learning: PCA Week4-2

上次我们已经知道

So now we need to set this to zero in order to find our $\beta_{in}$βin​ parameters and this is 0 if and only if the $\beta_{in}$βin​ parameters are given by $\widetilde X_n$Xn​ which we are going to define as equation D. What this means is that the optimal coordinates of $\widetilde X_n$Xn​ with respect to our basis are the orthogonal projections of the coordinates of our original data point onto the $i_{th}$ith​ basis vector that spans our principal subspace.

Reformulation of the objective

Finding the basis vectors that span the principal subspace