Unsupervised Learning and Training Data
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