I'm investigation various techniques used in document clustering and I would like to clear some doubts concerning PCA (principal component analysis) and LSA (latent semantic analysis).
First thing - what are the differences between them? I know that in PCA, SVD decomposition is applied to term-covariance matrix, while in LSA it's term-document matrix. Is there anything else?
Second - what's their role in document clustering procedure? From what I have read so far, I deduce that their purpose is reduction of the dimensionality, noise reduction and incorporating relations between terms into the representation. After executing PCA or LSA, traditional algorithms like k-means or agglomerative methods are applied on the reduced term space and typical similarity measures, like cosine distance are used. Please correct me if I'm wrong.
Third - does it matter if the TF/IDF term vectors are normalized before applying PCA/LSA or not? And should they be normalized again after that?
Fourth - let's say I have performed some clustering on the term space reduced by LSA/PCA. Now, how should I assign labels to the result clusters? Since the dimensions don't correspond to actual words, it's rather a difficult issue. The only idea that comes to my mind is computing centroids for each cluster using original term vectors and selecting terms with top weights, but it doesn't sound very efficient. Are there some specific solutions for this problem? I wasn't able to find anything.
I will be very grateful for clarifying these issues.