Clustering normalization of the distance between the trajectories does not work

[Ovewh]

I attempted to normalize the distance between each trajectory since the spread would be larger towards the end of the trajectory.

1. Calculate a mean distance from the cluster for the trajectories for each timestep along the trajectories.

do t=1,ntime
   distances=0
   do j=1,ncluster
     do i=1,n
       distances=distances+distance2(yl(t,i),xl(t,i),yclust(t,j),xclust(t,j))
     end do
   end do
   meandistance(t) = distances/(n*ncluster)
end do

2. Calculate a mean distance for the trajectories and each cluster for each timestep along the trajectories.

do t=1,ntime
   do j=1,ncluster
      distances=0
       do i=1,n
          distances=distances+distance2(yl(t,i),xl(t,i),yclust(t,j),xclust(t,j))
       end do
       meandistance(t,j) = distances/(n)
   end do
end do

Then divide by this mean distance when before check where distance is less than mindistance

However then every trajectory get assign to one cluster.

[Ovewh]

Implemented improved way of doing the normalization using the standard deviation of the distance from the center of mass trajectory.

  do t=1,ntime
    tempdist=0.
    do i=1,n
      tempdist=tempdist+distance2(yl(t,i),xl(t,i),ycenter(t),xcenter(t))
    end do
    mdist=tempdist/n
    tempdev=0.
    do i=1,n
      tempdev=tempdev+(distance2(yl(t,i),xl(t,i),ycenter(t),xcenter(t))-mdist)**2
    end do
    stddev(t)=sqrt(tempdev/n)
  end do

With normalization

Root mean squared distance as function of clusters

5 clusters:

16 clusters:

Without normalization

Root mean squared distance as function of clusters

5 clusters:

16 clusters: