If i start clustering in k-means for some data using initial centroids, lets assume 10 centroids to create 10 clusters, is it possible that it will end with 8 or 9 clusters?
Yes, it is possible for the k-means to converge to fewer than k clusters, in your case 8 or 9, depending on the data and the initial choice of centroids. This can happen if some of the centroids are initialized too close to each other, leading the algorithm to merge them into a single cluster. The final number of clusters will depend on the relative distances between the data points and the centroids, and how the centroids are updated in each iteration.
Yes initially, we can decide K as we want to classify the clusters.
Let us assume you give one of the centroid as infinity (w.r.t data) . Then none of the data points will be mapped to it. Causing one less centroid in next iteration.
I think yes, because for the k-means to converge to fewer than k clusters, follows center limit theorem.
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