Effective Euclidean distance calculation

Question

I have an array MxN, where Mis the number of observations, and Nis the dimension of each vector. From this array of vectors I need to calculate the Euclidean distance mean, and minimumbetween the vectors.

In my understanding, this requires me to calculate the distances _M C ₂ , which is O (n ^{min (k, nk)} ). Mine Mis ~ 10,000 and mine Nis ~ 1000, and this calculation takes ~ 45 seconds.

Is there a more efficient way to calculate distances meanand min? Perhaps a probabilistic method? I don't need it to be accurate, just close.

Answer 1

You did not indicate where your vectors come from, nor what you will use meanand median. Here are some general notes. Limited ranges, error tolerances, and discrete values ​​may allow a more efficient approach.

The distance meanbetween the points M sounds quadratically, O (M ^ 2). But M / N is 10, quite small, and N is huge, so the data probably resembles a hairy sphere in a 1e3 space. Computing the centroid of points M, and then calculating the distances M to the centroid, can be useful in your problem area, it’s hard to say.

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