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For a dataset I wanted to pick-out some most representative points from it. Lets say the first point could be centroid, next could be the one farthest from it in the data-set(To get variance in data) & so on. Can anybody name if there exists any algorithm of such kind or any other. The representative power of sample could be its ability to best explain population variance

I wanted a sample which best describes the variance or the spread-out of population data in vector space. In terms of eucledian distance I wanted set of possible points having maximum distance with each other

Thanks for the help

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    $\begingroup$ I don't think "representative" is defined clearly enough here for us to be of much help. Do you want statistics to summarize the data? (Probably, the basic answer would be to compute the different order moments). Or are they supposed to be points of data themselves? $\endgroup$
    – Ziddletwix
    Commented Jun 5, 2020 at 11:21
  • $\begingroup$ The algorithm should give the points that are in dataset itself. Say if I want 10 points from population it should best represent data in terms of variance. $\endgroup$
    – Nishant
    Commented Jun 5, 2020 at 12:24
  • $\begingroup$ What would be the problem with simple random selection? In what sense do you mean the word "explain" (population variance) in your question? $\endgroup$
    – whuber ♦
    Commented Jun 5, 2020 at 13:01
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    $\begingroup$ For that, we would need a quantitative definition of "versatility." It's unlikely that maximizing some criterion, such as some measure of being "spread-out," would be "representative" in any sense: by construction it would be as unrepresentative of the spreading as possible! $\endgroup$
    – whuber ♦
    Commented Jun 5, 2020 at 14:35
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    $\begingroup$ In a similar vein, see here: flothesof.github.io/farthest-neighbors.html for a better approach to that problem $\endgroup$
    – dc3726
    Commented Jun 5, 2020 at 15:07

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In order to get a sample from your data which is representative in the way you describe it, you could apply a bootstrap algorithm, which in essence amounts to sampling from the empirical distribution of your data.

Bootstrapping simply involves sampling with replacement from your data. Intuitively if you employ such a method, as the number of draws you make from your data increases, the empirical distributions of your data and your sample should draw nearer.

Here is some pseudocode to apply the bootstrap:

for i in desired number of samples from data
    #pick a random number from a uniform distribution with range 1:length of your data
    #use this number as an index to get a data point
    #append the data point you indexed to your sample
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  • $\begingroup$ Your idea is good but this would be helpful if wanted representative distribution. But rather I wanted a sample which best describes the variance or the spread-out of population data in vector space. In terms of eucledian distance I wanted set of possible points having maximum distance with each other $\endgroup$
    – Nishant
    Commented Jun 5, 2020 at 14:25

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