Elbow Test using AIC/BIC for identifying number of clusters using GMM

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How to select number of clusters using GMM when the elbow test (AIC/BIC vs n_components) results in a graph like this?










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  • 6 seems to be what you are looking for, if you are looking for a test there are a few, for ex. using clusGap statistic.
    – user2974951
    Sep 25 at 8:51
















up vote
6
down vote

favorite
1












enter image description here



How to select number of clusters using GMM when the elbow test (AIC/BIC vs n_components) results in a graph like this?










share|cite|improve this question























  • 6 seems to be what you are looking for, if you are looking for a test there are a few, for ex. using clusGap statistic.
    – user2974951
    Sep 25 at 8:51












up vote
6
down vote

favorite
1









up vote
6
down vote

favorite
1






1





enter image description here



How to select number of clusters using GMM when the elbow test (AIC/BIC vs n_components) results in a graph like this?










share|cite|improve this question















enter image description here



How to select number of clusters using GMM when the elbow test (AIC/BIC vs n_components) results in a graph like this?







aic bic generalized-moments






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edited Sep 25 at 9:13









Ferdi

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3,39342151










asked Sep 25 at 8:29









psangam

332




332











  • 6 seems to be what you are looking for, if you are looking for a test there are a few, for ex. using clusGap statistic.
    – user2974951
    Sep 25 at 8:51
















  • 6 seems to be what you are looking for, if you are looking for a test there are a few, for ex. using clusGap statistic.
    – user2974951
    Sep 25 at 8:51















6 seems to be what you are looking for, if you are looking for a test there are a few, for ex. using clusGap statistic.
– user2974951
Sep 25 at 8:51




6 seems to be what you are looking for, if you are looking for a test there are a few, for ex. using clusGap statistic.
– user2974951
Sep 25 at 8:51










1 Answer
1






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Welcome to CV!



This plot shows how the AIC and BIC change as a function of the number of clusters. While the AIC continuous to decrease with a larger number of clusters, you can see that the BIC stops decreasing after $k=6$ clusters. For this reason, you could choose $k = 6$.



Another way to choose the 'best' number of clusters is by considering the elbow(s) of the figure. The elbow of a function is a point after which the decrease becomes notably smaller. An elbow is a heuristic, so there is no exact way to determine which value best describes this point. For example, one could argue that the AIC & BIC both stop decreasing as much after $k = 5$ clusters, while someone else might argue that this is after $k = 6$ clusters. You could even argue that the biggest decrease has already happened after $k = 2$ clusters.



Lastly, you don't have to choose any number of clusters just because AIC/BIC/whatever suggested you do so. If you have some a priori reason to assume that there should be $k = 3$ clusters, then that might be a better choice.



In short: An elbow in this context is a heuristic guide to decide the number of clusters if you have no other reason to assume a certain number of clusters.






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    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    4
    down vote



    accepted










    Welcome to CV!



    This plot shows how the AIC and BIC change as a function of the number of clusters. While the AIC continuous to decrease with a larger number of clusters, you can see that the BIC stops decreasing after $k=6$ clusters. For this reason, you could choose $k = 6$.



    Another way to choose the 'best' number of clusters is by considering the elbow(s) of the figure. The elbow of a function is a point after which the decrease becomes notably smaller. An elbow is a heuristic, so there is no exact way to determine which value best describes this point. For example, one could argue that the AIC & BIC both stop decreasing as much after $k = 5$ clusters, while someone else might argue that this is after $k = 6$ clusters. You could even argue that the biggest decrease has already happened after $k = 2$ clusters.



    Lastly, you don't have to choose any number of clusters just because AIC/BIC/whatever suggested you do so. If you have some a priori reason to assume that there should be $k = 3$ clusters, then that might be a better choice.



    In short: An elbow in this context is a heuristic guide to decide the number of clusters if you have no other reason to assume a certain number of clusters.






    share|cite|improve this answer
























      up vote
      4
      down vote



      accepted










      Welcome to CV!



      This plot shows how the AIC and BIC change as a function of the number of clusters. While the AIC continuous to decrease with a larger number of clusters, you can see that the BIC stops decreasing after $k=6$ clusters. For this reason, you could choose $k = 6$.



      Another way to choose the 'best' number of clusters is by considering the elbow(s) of the figure. The elbow of a function is a point after which the decrease becomes notably smaller. An elbow is a heuristic, so there is no exact way to determine which value best describes this point. For example, one could argue that the AIC & BIC both stop decreasing as much after $k = 5$ clusters, while someone else might argue that this is after $k = 6$ clusters. You could even argue that the biggest decrease has already happened after $k = 2$ clusters.



      Lastly, you don't have to choose any number of clusters just because AIC/BIC/whatever suggested you do so. If you have some a priori reason to assume that there should be $k = 3$ clusters, then that might be a better choice.



      In short: An elbow in this context is a heuristic guide to decide the number of clusters if you have no other reason to assume a certain number of clusters.






      share|cite|improve this answer






















        up vote
        4
        down vote



        accepted







        up vote
        4
        down vote



        accepted






        Welcome to CV!



        This plot shows how the AIC and BIC change as a function of the number of clusters. While the AIC continuous to decrease with a larger number of clusters, you can see that the BIC stops decreasing after $k=6$ clusters. For this reason, you could choose $k = 6$.



        Another way to choose the 'best' number of clusters is by considering the elbow(s) of the figure. The elbow of a function is a point after which the decrease becomes notably smaller. An elbow is a heuristic, so there is no exact way to determine which value best describes this point. For example, one could argue that the AIC & BIC both stop decreasing as much after $k = 5$ clusters, while someone else might argue that this is after $k = 6$ clusters. You could even argue that the biggest decrease has already happened after $k = 2$ clusters.



        Lastly, you don't have to choose any number of clusters just because AIC/BIC/whatever suggested you do so. If you have some a priori reason to assume that there should be $k = 3$ clusters, then that might be a better choice.



        In short: An elbow in this context is a heuristic guide to decide the number of clusters if you have no other reason to assume a certain number of clusters.






        share|cite|improve this answer












        Welcome to CV!



        This plot shows how the AIC and BIC change as a function of the number of clusters. While the AIC continuous to decrease with a larger number of clusters, you can see that the BIC stops decreasing after $k=6$ clusters. For this reason, you could choose $k = 6$.



        Another way to choose the 'best' number of clusters is by considering the elbow(s) of the figure. The elbow of a function is a point after which the decrease becomes notably smaller. An elbow is a heuristic, so there is no exact way to determine which value best describes this point. For example, one could argue that the AIC & BIC both stop decreasing as much after $k = 5$ clusters, while someone else might argue that this is after $k = 6$ clusters. You could even argue that the biggest decrease has already happened after $k = 2$ clusters.



        Lastly, you don't have to choose any number of clusters just because AIC/BIC/whatever suggested you do so. If you have some a priori reason to assume that there should be $k = 3$ clusters, then that might be a better choice.



        In short: An elbow in this context is a heuristic guide to decide the number of clusters if you have no other reason to assume a certain number of clusters.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Sep 25 at 8:53









        Frans Rodenburg

        3,107426




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