I have 100000 observations with two variables on each, age on the range of 18-80 and interactions on the range of 1-1500. I want to find 4 bins based on the age variable, where the number of observations in each bin is roughly similar (any bin can deviate up to 20% from the mean number in a bin, which is 100000/4=25000).
There are multiple binning options with this constraint. I would like to find the binning option, where the mean of interactions in each bin is very similar across bins. More mathematically, I'd like to do the following. For each bin $b$ I define $\mu_{b}$ as the mean of interactions for the observations in that bin and $\mu_{b,all}$ as the distribution of $\mu_{b}$. Then I need to do the following:
$$minimize \hspace{0.2cm} var(\mu_{b,all})$$
The bin ranges must not overlap and should span the entire interval. For instance, the 4 bins could be:
- 18-30
- 31-45
- 46-57
- 58-80
Is there a method that would easily do this? Or any suggestions on how to do it?
interactions) within each bin. Since you seem to be asking for something impossible, perhaps it would be more useful to edit your post to explain why you're trying to do this, so people could help you figure out an effective approach. – whuber Jun 30 '15 at 20:49interactionsin the bin relative to $\mu_i$). You are asking for a one-dimensional constrained clustering algorithm. It is especially helpful that you have quantified your constraints. – whuber Jun 30 '15 at 21:11