Unsupervised Learning and Training Data As far as I know, we need to use training data to find out the relation between the features, also known as input values, and labels, that are output values, in supervised learning. After that, by using this relation, our learning system tries to predict labels of data samples in next data sets. 

However, there is no need to find out such a relation in unsupervised learning because the data samples do not have labels; they only consist of features. In this case, do we need a training set in unsupervised learning ?
In unsupervised learning,the learning procedure is finding similarity between training samples, and putting similar items into a same cluster,
training phase in unsupervised learning produce some sets with similar items. 
Then,in test phase the similarity is calculated for all items of each set, and check if the test item is similar to each cluster's items or not, if it was similar to at least one item, the test item belongs to that cluster.

SO... YES, we need training set and test set, the training set helps to find thresholds to find similarity