# Can any one give explanation on LSA and what is different from NMF?

LSA is better way for extracted new concepts from large text documents collections .. in the following example :

i have spend lot of time in Google to get explanation about the following My questions are:

The result matrix Vtk .. similarity matrix can be build based on cosine similarity for all documents .. now how do we use this matrix for document clustering ?

can some one give a brief explanation how can we get Ak matrix .. is this matrix contain the original Term-Document matrix with reduced version?

thanks for any suggestion

## 1 Answer

You never compute Ak. Too expensive. It will usually be less sparse than A, so even worse. Ak is a reconstruction of the original term-document matrix.

For clustering, you could use V_k, the documents x topics matrix.

But usually you wouldn't even do clustering, you would hope the topics (factors) already are what you are looking for.

As a matter of fact, you can formalize k-means the very same way, as a matrix decomposition. Uk is the matrix storing your centroids, sigma is identity, and Vk is a binary matrix with exactly one 1 for every document. k-means is a matrix factorization.

• regard this note : For clustering, you could use V_k, the documents x topics matrix. .. so is k-means working on this matrix .. is this right? – Ray ben Nov 16 '16 at 18:38
• Do you mean im using NMF (non-negative matrix factorization) where NMF give two matrices are U and V and applying k-means. is this right or do you mean some thing else? – Ray ben Nov 16 '16 at 18:45
• No. I am saying that k-means is also a variant of NMF. And why would you apply NMF twice in a row? You certainly can, but it lacks any good reason to do so. – Has QUIT--Anony-Mousse Nov 17 '16 at 0:27
• ok, so the result matrix Vk for documents x Topics ... how do we clustering similar documents .. ? can i use cosine to find ( documents x documents ) matrix similarity based in cosine .. then applying such algorithm ? what do you think about that ? thanks – Ray ben Nov 17 '16 at 7:49
• You have the "clusters" right there in the matrix. You are done. – Has QUIT--Anony-Mousse Nov 17 '16 at 7:52