MATLAB: Graph analysis question

curve fittingdifferentiationseperating dataStatistics and Machine Learning Toolboxturning points

I have this data:
X = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
With
Y = 0.5 1 1.5 2 2.5 3 3.5 4 1 1.5 3 3.5 4.5 5.5 6 2 4 4.5 5.5 6.5 8
This may be more of a math question rather than a matlab question. If you plot the above data you will see three distinct sets of data, is there any way I can get matlab to automatically split this data into the three seperate variables. The number of variables may change depending on the data set, the data I have provided is indicative for the real data the X axis is actually dates.
In short I need Matlab to detect how many separate data sets there are and split the data into different variables.
I've tried using a max and min point script but I didn't get very far with it.
Thanks in advance

Best Answer

After I posted my answer about cluster analysis, I noticed the following:
Are your (X,Y) data always sorted as in your example, or can the pairs be jumbled? If they are always sorted, you can just look for negative jumps in Y, using the find() and diff() commands, and separate the data wherever there is such a jump downward.
X = [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21];
Y = [0.5 1 1.5 2 2.5 3 3.5 4 1 1.5 3 3.5 4.5 5.5 6 2 4 4.5 5.5 6.5 8];
N = numel(Y);
negativeJumpIndex = find(diff([0,Y])<0);
numberNegativeJumps = numel(negativeJumpIndex);
numberClusters = numberNegativeJumps + 1;
indexToNewLine = [1 negativeJumpIndex N+1];
IDX = zeros(N,1);
for nc=1:numberClusters
    IDX(indexToNewLine(nc):indexToNewLine(nc+1)-1) = nc;
end
figure
gscatter(X,Y,IDX)
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