Why is it not advised to use k-means for classification? It seems like a trivial extension of k-means clustering if you have labelled training data is to assign each centroid a label, and given a new piece of test data to classify it to the label corresponding to the centroid with the closest distance.
However, I could not find much online about the (ab)use of k-means clustering for this purpose, and people advise using just k-nearest neighbors or SVMs directly.
Why would (ab)using k-means clustering via this relatively straightforward method not yield good results?
 A: Where is the benefit of doing this?
A cluster found by KMeans may contain many different labels, so you decrease quality!
Just so nearest-neighbor classification.
But if you look into kNN classification literature, you will find different ways of reducing the "training" set. I am certain there is at least one paper suggesting to use k-means with a very large k to reduce redundancy in your training data. But you need to smartly handle clusters that contain more than one label.
A: I would say that k-means could be advised for classifitation following a different approach:
Let $C$ be the number of classes and $K$ the number of clusters. Now, follow these steps:


*

*Apply K-means clustering to the training data in each class seperately, using $K$ clusters per class.

*Assign a class label to each of the $C*K$ clusters.

*Classify observation $x$ to the class of the closest cluster.


I saw it on "The Elements of Statistical Learning". I changed the notation a little bit. It seems like a nice approach for classification that reduces data observations by using clusters.
A: Kmeans Clustering is a Cluster Algorithm to separate your data into different clusters. 
Of course you can assign each cluster a representing class. When you got an additional unknow point you calculate the distance to the nearest centroid (cluster center) and add this point to this cluster/class.
What does it mean is, that you would use for this classification task a k nearest neighbor approach, where you just look at the centers of the clusters as possible neighbors. 
So what we've got is a pretty simple classifier and of course there are better ways to classify data. 
