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If we use k-means in a dataset where k is equal to the number of points in the dataset, and each cluster is made out of only a point. Considering that we have given a distance method, we can classify a test instance associating it with the cluster whose centroid is nearest to that given point. The centroids are not changing in the test phase.

With what automatic classification method is the above strategy similar to?

Yes, this is a homework. My answer was knn, is this correct? But I do not know how to argue this properly.

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Your case is where K=number of points in dataset :

K-means: Lets suppose, there are 10 data points and k=10, so you have 10 clusters. the new test point will be matched with the cluster nearest to it
KNN: If K=1, then the new test point classified will be same as in K-means.

So, if there is one data-point per cluster, then your given answer ie. knn is technically correct, if we take k=1.

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