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joshisanonymous
joshisanonymous
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I'm looking for a way to measure the overlap (or general similarity) between two categorical distributions in which some of the categories are shared between each and some are not. For example, if the counts for the two distributions look like this:

Distribution X
Category: a b c d
Count:    5 8 2 7

Distribution Y
Category: b c d e
Count:    6 9 5 3

Is there a statistic I can use to describe how similar these two distributions are? My first thought was Bhattacharyya distance (which I'm only vaguely familiar with), but that seems to be related to continuous quantitative distributions. Otherwise, what I can find for qualitative distributions through random Googling seem to all require that the two distributions have the same exact categories (e.g., Y should have the categories a b c d instead). I'd like to not exclude non-shared categories, though, as they're meaningful in my data.

EDIT: Another possibility I've come across is cross-entropy, but I don't understand it well enough to know if this is appropriate for this sort of data as most of what I find about cross-entropy seems to involve comparing how accurate two different classifiers are when applied to some data to be classified, but I don't have any classification task that I'm doing here.

I'm looking for a way to measure the overlap (or general similarity) between two categorical distributions in which some of the categories are shared between each and some are not. For example, if the counts for the two distributions look like this:

Distribution X
Category: a b c d
Count:    5 8 2 7

Distribution Y
Category: b c d e
Count:    6 9 5 3

Is there a statistic I can use to describe how similar these two distributions are? My first thought was Bhattacharyya distance (which I'm only vaguely familiar with), but that seems to be related to continuous quantitative distributions. Otherwise, what I can find for qualitative distributions through random Googling seem to all require that the two distributions have the same exact categories (e.g., Y should have the categories a b c d instead). I'd like to not exclude non-shared categories, though, as they're meaningful in my data.

I'm looking for a way to measure the overlap (or general similarity) between two categorical distributions in which some of the categories are shared between each and some are not. For example, if the counts for the two distributions look like this:

Distribution X
Category: a b c d
Count:    5 8 2 7

Distribution Y
Category: b c d e
Count:    6 9 5 3

Is there a statistic I can use to describe how similar these two distributions are? My first thought was Bhattacharyya distance (which I'm only vaguely familiar with), but that seems to be related to continuous quantitative distributions. Otherwise, what I can find for qualitative distributions through random Googling seem to all require that the two distributions have the same exact categories (e.g., Y should have the categories a b c d instead). I'd like to not exclude non-shared categories, though, as they're meaningful in my data.

EDIT: Another possibility I've come across is cross-entropy, but I don't understand it well enough to know if this is appropriate for this sort of data as most of what I find about cross-entropy seems to involve comparing how accurate two different classifiers are when applied to some data to be classified, but I don't have any classification task that I'm doing here.

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joshisanonymous
joshisanonymous
  • 405
  • 3
  • 12

Quantifying overlap between two categorical distributions with some non-identical categories

I'm looking for a way to measure the overlap (or general similarity) between two categorical distributions in which some of the categories are shared between each and some are not. For example, if the counts for the two distributions look like this:

Distribution X
Category: a b c d
Count:    5 8 2 7

Distribution Y
Category: b c d e
Count:    6 9 5 3

Is there a statistic I can use to describe how similar these two distributions are? My first thought was Bhattacharyya distance (which I'm only vaguely familiar with), but that seems to be related to continuous quantitative distributions. Otherwise, what I can find for qualitative distributions through random Googling seem to all require that the two distributions have the same exact categories (e.g., Y should have the categories a b c d instead). I'd like to not exclude non-shared categories, though, as they're meaningful in my data.