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I've studied the k-means algorithm and I know how it works.
Just curious,is there any situation that this algorithm will go into an infinite loop,say if we have some particular bad choices for initial centroid points? I could only imagine a situation k-means will get to local minimum with bad initial choices.
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Yes. It converges but not coverage to the same result and not coverage with the same speed. It proves mathematically that the iterated running of finding the centers in k-means is converges.
K-means fails because the objective function which it attempts to minimize measures the true clustering solution as worse than the manifestly poor solution shown here. The Euclidean distance entails that the average of the coordinates of data points in a cluster is the centroid of that cluster (algorithm line 15).
There are essentially three stopping criteria that can be adopted to stop the K-means algorithm: Centroids of newly formed clusters do not change. Points remain in the same cluster. Maximum number of iterations are reached.
K-means fails to find a good solution where MAP-DP succeeds; this is because K-means puts some of the outliers in a separate cluster, thus inappropriately using up one of the K = 3 clusters. This happens even if all the clusters are spherical, equal radii and well-separated.
No. k-means has an upper bound of O(nkd) in d-dimensional space.
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