12
$\begingroup$

I would like to code a kmeans clustering in python using pandas and scikit learn. In order to select the good k, I would like to code the Gap Statistic from Tibshirani and al 2001 (pdf).

I would like to know if I could use inertia_ result from scikit and adapt the gap statistic formula without having to recode all the distances calculation.

Does anyone know the inertia formula used in scikit / know an easy way to recode the gap statistic using high level distance functions?

$\endgroup$
2
  • 1
    $\begingroup$ I think this question has sufficient statistical content to be on-topic for CV, but note that it requires fairly sophisticated programming & Python knowledge as well. It may be difficult to get a good answer. You may want to ask for / be willing to settle for pseudocode as well, &/or you may need to split this question up into 2 parts, 1 here about the statistical aspects & 1 part on Stack Overflow about the Python programming aspects. (Or maybe not, I don't know for sure, but I just want to give you fair warning; we'll see how it goes.) $\endgroup$ Dec 2, 2013 at 16:49
  • 1
    $\begingroup$ This question needs the term "inertia" be defined. It looks like its coined within python. $\endgroup$
    – ttnphns
    Dec 2, 2013 at 17:21

1 Answer 1

9
$\begingroup$

I guess I found my answer for kmeans clustering:

By looking at the git source code, I found that for scikit learn, inertia is calculated as the sum of squared distance for each point to it's closest centroid, i.e., its assigned cluster. So $I = \sum_{i}(d(i,cr))$ where $cr$ is the centroid of the assigned cluster and $d$ is the squared distance.

Now the formula of gap statistic involves $$ W_k = \sum_{r=1}^{k}\frac 1 {(2*n_r) }D_r $$ where $D_r$ is the sum of the squared distances between all points in cluster $r$.

By introducing $+c$, $-c$ in the squared distance formula ($c$ being the centroid of cluster $r$ coordinates), I have a term that corresponds to Inertia (as in scikit) + a term that disappears if each $c$ is the barycentre of each cluster (which it is supposed to be in kmeans). So I guess $W_k$ is in fact scikit Inertia.

I have still two questions:

  1. Do you think my calculus is correct? (For example, I don't know if it holds for hierarchical clustering.)
  2. If I am correct above, I have coded the gap statistic (as difference of log inertias between estimation and clustering) and it performs badly especially on the iris dataset, has anyone tried it?
$\endgroup$
4
  • 2
    $\begingroup$ It is best not to pose questions in your answers. If this isn't really the answer to your question, but just a partial solution to clarify the real question, it would be better to edit your question & paste this information in. $\endgroup$ Feb 4, 2014 at 2:16
  • 1
    $\begingroup$ @Scratch did you ever get a python implementation of the gap statistic to work on the Iris data set? I am struggling with the same issue. $\endgroup$
    – Zelazny7
    Feb 25, 2014 at 0:23
  • $\begingroup$ Yes I coded one a few month ago. How can I send you that ? $\endgroup$
    – Scratch
    Feb 25, 2014 at 8:40
  • 1
    $\begingroup$ Should not be formula be this $$W_k = \sum_{r=1}^{k}\frac {D_r} {(2*n_r) }$$ ? $\endgroup$
    – Biswanath
    Jun 3, 2014 at 15:06

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.