How many possible solution K-means have of n points and K cluster?



I am currently studying about K-means clustering and while studying I understand that.

K-means Clustering - k-means clustering aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean, serving as a prototype of the cluster.

I understand it can have a different solution when we assign n points into a different cluster.I want to know how many solutions can possible for K-means clustering.


Hi @ankit81195,

I may be wrong but I think that there could be infinite solutions to the problem. It would depend on the initialization of the centroids and the value of k.


Hi @ankit81195,

You have to understand from a business perspective.

The number of clusters depends on the users who are running the model, the person can create as many clusters, but number os possible solution is infinite and you have to choose the solution which gives you minimum intra-cluster distance and maximum inter-cluster distance. As there are infinite iterations possible, you have to choose the number of the desired combination of initial centroid positions.

There is a trade-off in it though. Higher the combination of initial centroid positions more precise solution you will get but it will also take more time to solve the problem.

Hope this answer your query.