Classification in each cluster after clustering? I have a labeled dataset with data under 3 classes.
Some of the instances in the dataset can be similar although they may belong to different classes.
So I tried clustering the dataset without considering the labels. Once clustering was done, the already known labels were assigned to instances in each cluster.This way I will have K clusters and each cluster has instances belonging to different classes. I wanted to know if it makes sense to apply supervised learning algorithms like LDA, QDA, SVM,kNN etc. on each of these clusters separately and identify the best performing classifier for each cluster? 
The data represents the sweat gland activity of a subject under 3 levels of physical activity say less intense, moderately intense, very intense. As the sweat gland functioning is different for different individuals (for eg., if the sweat gland density of a person is more than another, his sweat levels during a low-intensity exercise might be similar to the very intense level activity of the other who has lesser sweat gland density).In such a case, the data represents similar values but come under two labels low and high. 
Ultimately, the objective is to classify different physical activity levels(Low, moderate or high) based on the sweat gland activity.
 A: I take it that what you're asking is whether or not you should classify within the already clustered data; and I would say "probably not".
In the general case it's hard to say. It would depend on what data you have, how it behaves, and most importantly: what do your clusters represent.
Say you have a bunch of data about people, and you want to classify whether or not a person is higher than 1.8m. You do unsupervised clustering and it turns out that the clusters are mostly consistent with what you want to classify, however they actually classified the gender of the person. Now, does it make sense to do supervised classification within the cluster? Well, you'd get kind of a conditional distribution, conditioned on whether or not it is a male/female.
I think, if you have labels, that you're more likely to classify what you want to classify using a supervised method. Unsupervised clustering is usually handy when you don't have any labels, or you want to see if there are any "natural" clusters within your data.
A: You then have the problem of having to choose the appropriate cluster. Plus, some clusters may be pretty bad, e.g., too small.
There are some obvious things to try:
- label objects as class_cluster. So you get up to k times as many classes. Then train the classifier. When predicting, strip the cluster number at the end, and keep only the class prediction.
- do the opposite. Try to cluster single classes. If one class has strong clusters, then use them as above. If not, use the original class. So many classes may remain unchanged, but some classes may get split. Only keep those splits, that improve accuracy.
