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Say I have N people and K weeks. For each person-week, I have a vector of a fixed length filled some number between 0 and 1, summing to 1 across the whole vector (so for each person, I'll have K vectors all of the same length). I want to do two things:

1) Collapse the person-week vectors into a single number for each person representing how similar all of their week vectors are (so intuitively like a correlation matrix of all the vectors for that person, but want to collapse to single number)

2) Find people that have similar distributions of vectors

My Googling isn't turning up too much. For #1, I could just take the average correlation of the correlation matrix, but that seems like a somewhat naive approach.

Can you guys point me in the right direction?

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Why don't you simply concatenate all weeks, then take the distances between the vectors?

The mathematical properties of this are well defined and well understood (least squares).

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