How to split a matrix based on array similarity

I have matrix A as follows:

A = [123  223  225  123
123  223  224  123
123  223  225  123
123  225  123  23
123  223  224  123
123  223  224  123
123  223  225  123
123  223  224  123
123  223  123  23
];

I want to find similar rows and have their row numbers in another set of matrices:

A1 = [1;2;3;4];
A2 = [5;6;7];
A3 = [8];
A4 = [9];

% numbers inside matrices A1 to A4 refers to row numbers in matrix A

Answer 1

[michio]

I am not sure how you define "similarity" but you can try out clustering functions available in Statistics and Machine Learning Toolbox to partition rows in A into k clusters.

 clusterdata(A,'maxclust',4)

or

 kmeans(A,4)