Recommended Algorithim for time based clustering












4














I am not very knowledgeable on time based clustering and wondering if any algorithms are well suited for my use case.



I have a set of exertion data (range from 0-500) and I want to cluster them along time intervals.



My problem is that I want to find point the points of time where there is major exertion differences on the time interval. I will know exactly how many grouping their should be (e.g. 5 separate clusters) but wont know where one ends and the next one starts.



Is there a good algorithm to apply in this case? I was looking at K-Means but it appears to be very good at clustering disregarding the time and I am more looking for the boundaries looking at exertion data.






algorithm k-means data-science hierarchical-clustering







share|improve this question





























    4














    I am not very knowledgeable on time based clustering and wondering if any algorithms are well suited for my use case.



    I have a set of exertion data (range from 0-500) and I want to cluster them along time intervals.



    My problem is that I want to find point the points of time where there is major exertion differences on the time interval. I will know exactly how many grouping their should be (e.g. 5 separate clusters) but wont know where one ends and the next one starts.



    Is there a good algorithm to apply in this case? I was looking at K-Means but it appears to be very good at clustering disregarding the time and I am more looking for the boundaries looking at exertion data.






    algorithm k-means data-science hierarchical-clustering







    share|improve this question



























      4












      4








      4







      I am not very knowledgeable on time based clustering and wondering if any algorithms are well suited for my use case.



      I have a set of exertion data (range from 0-500) and I want to cluster them along time intervals.



      My problem is that I want to find point the points of time where there is major exertion differences on the time interval. I will know exactly how many grouping their should be (e.g. 5 separate clusters) but wont know where one ends and the next one starts.



      Is there a good algorithm to apply in this case? I was looking at K-Means but it appears to be very good at clustering disregarding the time and I am more looking for the boundaries looking at exertion data.






      algorithm k-means data-science hierarchical-clustering







      share|improve this question















      I am not very knowledgeable on time based clustering and wondering if any algorithms are well suited for my use case.



      I have a set of exertion data (range from 0-500) and I want to cluster them along time intervals.



      My problem is that I want to find point the points of time where there is major exertion differences on the time interval. I will know exactly how many grouping their should be (e.g. 5 separate clusters) but wont know where one ends and the next one starts.



      Is there a good algorithm to apply in this case? I was looking at K-Means but it appears to be very good at clustering disregarding the time and I am more looking for the boundaries looking at exertion data.






      algorithm k-means data-science hierarchical-clustering




      algorithm k-means data-science hierarchical-clustering






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited Nov 12 at 5:39









      Kromster

      4,77164886




      4,77164886










      asked Nov 11 at 22:25









      mornindew

      5363721




      5363721
























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          I think you could get good results from a dynamic program. For each interval [i, j), let C(i, j) be a loss function that is lower when the interval values are more likely to be one cluster. Then letting L(k, r) be the minimum loss for up to k clusters of elements [0, r), we have equations



          L(1, r) = C(0, r)
          
L(k, r), k > 1 = min over s in [0, r) of L(k-1, s) + C(s, r).


          If there are O(1) values of k needed, evaluating these equations with memoization takes O(n^2) time and O(n) space where n is the number of samples.



          A plausible first choice for C(i, j) would be the statistical variance of the samples in that interval. Naively, this requires Theta(n^3) time to compute for each interval, but Welford's algorithm can be used to compute variance online if you iterate s from its greatest value to its least, so the overall algorithm would still be O(n^2).






          share|improve this answer





















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            I think you could get good results from a dynamic program. For each interval [i, j), let C(i, j) be a loss function that is lower when the interval values are more likely to be one cluster. Then letting L(k, r) be the minimum loss for up to k clusters of elements [0, r), we have equations



            L(1, r) = C(0, r)
            
L(k, r), k > 1 = min over s in [0, r) of L(k-1, s) + C(s, r).


            If there are O(1) values of k needed, evaluating these equations with memoization takes O(n^2) time and O(n) space where n is the number of samples.



            A plausible first choice for C(i, j) would be the statistical variance of the samples in that interval. Naively, this requires Theta(n^3) time to compute for each interval, but Welford's algorithm can be used to compute variance online if you iterate s from its greatest value to its least, so the overall algorithm would still be O(n^2).






            share|improve this answer


























              0














              I think you could get good results from a dynamic program. For each interval [i, j), let C(i, j) be a loss function that is lower when the interval values are more likely to be one cluster. Then letting L(k, r) be the minimum loss for up to k clusters of elements [0, r), we have equations



              L(1, r) = C(0, r)
              
L(k, r), k > 1 = min over s in [0, r) of L(k-1, s) + C(s, r).


              If there are O(1) values of k needed, evaluating these equations with memoization takes O(n^2) time and O(n) space where n is the number of samples.



              A plausible first choice for C(i, j) would be the statistical variance of the samples in that interval. Naively, this requires Theta(n^3) time to compute for each interval, but Welford's algorithm can be used to compute variance online if you iterate s from its greatest value to its least, so the overall algorithm would still be O(n^2).






              share|improve this answer
























                0












                0








                0






                I think you could get good results from a dynamic program. For each interval [i, j), let C(i, j) be a loss function that is lower when the interval values are more likely to be one cluster. Then letting L(k, r) be the minimum loss for up to k clusters of elements [0, r), we have equations



                L(1, r) = C(0, r)
                
L(k, r), k > 1 = min over s in [0, r) of L(k-1, s) + C(s, r).


                If there are O(1) values of k needed, evaluating these equations with memoization takes O(n^2) time and O(n) space where n is the number of samples.



                A plausible first choice for C(i, j) would be the statistical variance of the samples in that interval. Naively, this requires Theta(n^3) time to compute for each interval, but Welford's algorithm can be used to compute variance online if you iterate s from its greatest value to its least, so the overall algorithm would still be O(n^2).






                share|improve this answer












                I think you could get good results from a dynamic program. For each interval [i, j), let C(i, j) be a loss function that is lower when the interval values are more likely to be one cluster. Then letting L(k, r) be the minimum loss for up to k clusters of elements [0, r), we have equations



                L(1, r) = C(0, r)
                
L(k, r), k > 1 = min over s in [0, r) of L(k-1, s) + C(s, r).


                If there are O(1) values of k needed, evaluating these equations with memoization takes O(n^2) time and O(n) space where n is the number of samples.



                A plausible first choice for C(i, j) would be the statistical variance of the samples in that interval. Naively, this requires Theta(n^3) time to compute for each interval, but Welford's algorithm can be used to compute variance online if you iterate s from its greatest value to its least, so the overall algorithm would still be O(n^2).







                share|improve this answer












                share|improve this answer



                share|improve this answer










                answered Nov 12 at 13:01









                David Eisenstat

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