Sort column vectors of a matrix and extract a new vector from a maximal criterion

I do have a huge nx4 matrix M in which its column vectors are listed according to given categories. All column vectors from the same category have their first 2 row elements the same(below Example shows 5 I-to V distinct categories) . I need to extract another line vector V built only from the maximal values on the fourth row elements of each vector category(shown with asterisc below them *).V has same elements as nr. of categories. I need to extract V vector

M

<----cat I--------> <----cat II--------> <---cat III----> <----cat IV-----> <---cat III---->

1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 _

1 1 1 1 2 2 2 2 4 4 4 1 1 1 2 2 2 _ 2Rows define category vector

1 2 3 4 1 2 3 4 1 2 3 2 3 4 1 2 3

---------------------------------------------------------------------------------------------------------

31 16 15 9 10 8 13 6 16 11 4 9 4 10 6 17 15 Row with maximal criterion to sort

* * * * * Max value of fourth row of each category

M=[1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2;1,1,1,1,2,2,2,2,4,4,4,1,1,1,2,2,2;1,2,3,4,1,2,3,4,1,2,3,2,3,4,1,2,3;31,16,15,9,10,8,13,6,16,11,4,9,4,10,6,17,15];
V=[31,13,16, 10, 17];

[Stephen23]

"I do have a huge nx4 matrix M..."

But your examples show a 4xN matrix.

Your data would be easier to work with if it were oriented as an Nx4 matrix.

[Radu Mihail]

Thank you very much Stephen! Yes I transposed a fracțion of a Matrix. Thank you for advice

[Radu Mihail]

Thank you very much Stephen! Yes I transposed a fracțion of a Matrix. Thank you for advice

Answer 1

[Stephen23]

M = [1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2; 1,1,1,1,2,2,2,2,4,4,4,1,1,1,2,2,2; 1,2,3,4,1,2,3,4,1,2,3,2,3,4,1,2,3; 31,16,15,9,10,8,13,6,16,11,4,9,4,10,6,17,15];
[~,~,X] = unique(M(1:2,:).','rows','stable');
V = accumarray(X(:),M(4,:),[],@max)

V = 5×1

31 13 16 10 17

or

Y = splitapply(@max,M(4,:).',X(:))

Y = 5×1

31 13 16 10 17

Your data would be easier to work with if it were oriented as an Nx4 matrix.