I have a number of ordered lists, most containing the same elements. I want to find the most probable order of the elements from the lists (samples).
Example:
l1={ a, b, f, h, z }
l2={ c, e, h, x, z }
l3={ a, e, y, z }
l4={ b, e, f, z }
The result should be:
R={a, b, c, e, f, h, x, y, z}; or
R={ a,b,c,e,f,h,y,x,z }
The elements have no information regarding their natural order. The order should be learned from the lists, and in some cases the order in a list may contradict other lists, so I need the most probable order. I have about 175,000 lists, for about 1.8 million elements (total, 260k unique), the number of elements per list varies.
I have already tried building a directed graph where the edges have the number of lists that connect the vertices in such order, and then went through all the paths to find the most probable sequence. This approach works well for small problems, but it is way too complex for a problem this large.
Any pointers, please, will be greatly appreciated.
Thanks.
Juan