chep 11 exc

[Tausif3787]

i am trying to do the exercise from the book where i face difficulties to understand the code. please check below, i mentioned which part i can't understand

!git clone https://github.com/UniprJRC/DSwithMATLAB.git
xtable = readtable("C:\Italy Education\2nd smtr\matlab\v1\DSwithMATLAB\matlabfilesuk\ch11PCA\SpesaFatt.xlsx")
data = xtable{:,:};
n=size(data,1); x1=data(:,1);x2=data(:,2);
meanData = mean(data)

xTilde = data - meanData
s= xTilde'*xTilde/(n-1) %coverience matrix

plot(x1,x2,'o','LineWidth',3)
xlabel('X1 = Advertising spend (millione)')
ylabel('X2 = Revenue (millione)')
hold('on')

confLevEllipses = [0.5 0.75 0.90 0.99]
for i=1:length(confLevEllipses)
ellipse(meanData,s,confLevEllipses(i))
end
axis equal

from this part i can't understand what is happening.
[Vini,Lambdaini] = eig(s);
[~,ord]=sort(diag(Lambdaini),'descend');
Lambda = Lambdaini(ord,ord);
V=Vini(:,ord)

[MarcoRianiUNIPR]

In the part

[Vini,Lambdaini] = eig(s);
[~,ord]=sort(diag(Lambdaini),'descend');
Lambda = Lambdaini(ord,ord);
V=Vini(:,ord)

we compute the eigenvalues/eigevectors of the covariance matrix S (s in your notation)
The code

[~,ord]=sort(diag(Lambdaini),'descend');
Lambda = Lambdaini(ord,ord);
V=Vini(:,ord)

is necessary to order the eigenvalues in such a way that the first is in position 1,1 of matrix Lambda, the second is in position 2,2 of matrix Lambda....the first eigenvector must be in the first colum of V ...

The matrix of the eigevenctors will be used to find the equation of the line which passes throught the majoir axis of the ellipse.

For everyone: the files and the book go together in the sense that the description of what the code does is fully explained in the book

Another comment is:
your code
readtable("C:\Italy Education\2nd smtr\matlab\v1\DSwithMATLAB\matlabfilesuk\ch11PCA\SpesaFatt.xlsx")just works on your computer but does not work in another computer without that specific path.
It is always a good practice to avoid writing code that cannot be exported!

[Tausif3787]

thanks professor.