How can I assign a point from a matrix to a group in another matrix

I have two matrixes, randMatrix and matrix1.

matrix1 is 150x5.

randMatrix consist of matrix1 values shuffled, they're the same numbers in different order.

In column 5 of matrix1 theres 50: 1s, 50: 2, and 50: 3s. Those numbers are in group 1 the first 50 numbers in matrix1, group 2 is the next 50 numbers and group 3 the remaining 50 numbers.

Each number in randMatrix is a point.

How can I know which corresponds to which number in randMatrix corresponds to group1, group2 and group3?

Heres matrix1

https://pastebin.com/a8N0x1ym

[DGM]

When you say the values are shuffled, is randMatrix a random permutation of matrix1's elements, or is it a random permutation of matrix1's row vectors?

When you say "Each number in randMatrix is a point" do you mean each individual element, or each row vector?

If it's a fully elementwise random permutation, I don't see how a unique mapping can be recovered unless you were in control of the process which randomized it. If it's a row-wise permutation, then it should be possible to figure out a mapping, provided the rows are unique.

[Whale Chicken]

When I say shuffled I mean that it’s a random permutation of matrix1 elements on both row and columns. It’s the same elements, just shuffled around. Each number in randMatrix is a point, meaning each individual element.

Answer 1

[DGM]

The short answer is that you can't. If it's elementwise, I don't see that there is enough uniqueness between sets to determine any practial amount of mapping.

% I renamed the matrix M
% let's ignore col 5 since it's not unique anyway
A = M(1:50,1:4);
B = M(51:100,1:4);
C = M(101:150,1:4);

% these are values which are unique within each set
% i.e. after removing repeated values, this is how many would be left
% this already tells us that the intersectons are significant
um = unique(M); % 74/600 (12%) unique
ua = unique(A); % 45/200 (22.5%) unique (contains 1,3)
ub = unique(B); % 58/200 (29%) unique (contains 1,2,3)
uc = unique(C); % 53/200 (26.5%) unique (contains 2,3)

% this is how many of those values are a member of only one set
uniquetoa = numel(setdiff(setdiff(ua,ub),uc)) % 6/45 (13%)
uniquetob = numel(setdiff(setdiff(ub,ua),uc)) % 1/58 (1.7%)
uniquetoc = numel(setdiff(setdiff(uc,ub),ua)) % 8/53 (15%)

There is simply too much intersection between the sets. There are nearly two dozen unique numbers which are a member of all three sets. For instance, if you had a 1.5 in the permuted array, there would be no way to tell which set it originally came from. This intersection of sets A, B, and C constitutes a full 43% of M.

iabc = intersect(intersect(ua,ub),uc); % 23 values
miabc = ismember(M,iabc);
sum(miabc(:)) % 323/750 (43%)

If you can accept some lost information and want to recover as much of a mapping as you can, then you can probably see how far you can get:

% let's take a random permutation
Mp = M(randperm(numel(M)));

% look for membership
ia = ismember(Mp,ua);
ib = ismember(Mp,ub);
ic = ismember(Mp,uc);

% remove values which are ambiguous
% these are now maps identifying which elements 
% unambiguously belong to which set
iau = ia & ~(ib | ic);
ibu = ib & ~(ia | ic);
icu = ic & ~(ib | ia);

sum(iau(:)) % 50 elements mapped
sum(ibu(:)) % 1 element mapped
sum(icu(:)) % 18 elements mapped

(50 + 1 + 18)/numel(Mp) % 9.2% mapped

<10% recovery doesn't seem very good to me.

[Whale Chicken]

This is close to what I was looking for. Thank you very much for your time and help :)