What is local minima in K-means clustering?

What is local minima in K-means clustering?

One such local minimum puts two centers at one true cluster, and the third center in the middle of the other two true clusters. For general k, one local minimum puts multiple centers at a true cluster, and one center in the middle of multiple true clusters.

Does k-means always converge to the global minima why why not?

There are (at least) two different settings which satisfy the stationary condition of k-means. here the objective is 1/4. If k-means would be initialized as the first setting then it would be stuck.. and that’s by no means a global minimum.

How to avoid local minima in kmeans stack?

This Cross Validated post has a good discussion on why you cannot escape local minima. A common hack used by many, and the one you are doing by setting n_init = 100 is to run K-means multiple times and then choosing the run that gives the lowest error.

What can be done to avoid falling into local minima?

What else can be done to avoid falling into local minima. I appreciate your help. I’m afraid that with the k-means algorithm, you cannot entirely avoid local minima; you can only try to minimize your chances of getting one. This Cross Validated post has a good discussion on why you cannot escape local minima.

Why does k-means give the global minimum?

As a matter of fact this is a saddle point (try center1 = 1 + epsilon and center1 = 1 – epsilon) here the objective is 1/4. If k-means would be initialized as the first setting then it would be stuck.. and that’s by no means a global minimum. You can use a variant of previous example to create two different local minima.

Is there an algorithm to find the global minima?

There are multiple algorithms for finding a solution. There is an obvious approach to find the global optimum: enumerating all k^n possible assignments – that will yield a global minimum, but in exponential runtime. Much more attention was put to finding an approximate solution in faster time.