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Let's say I have many 1-dimensional vectors of the same dimension which I want to compare to each other. What I'm really looking for is to check whether they are all very similar, or not, and to derive a score based on the overall similarity (a mean of similarities?).

I don't need to try to align the vectors, I just want to correlate them from start to end to each other.

I have to perform this computation a large number of times, and it must be very fast. The vectors are small (100 units) and float-based. I am using Python. Is there a trick other than to compare each vector to each other vectors and take the worst correlation for each?

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One possibility is to do a Principal Components Analysis (PCA) and look at the percentage of the variance explained by the first component. If all your variables are measuring the same thing with just a little variation then the proportion will be close to 1. If there is more variation and multiple different things being measured then it will be lower.

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