# What is USV In NLP?

3 SVD Based Methods

For this class of methods to find word embeddings (otherwise known as word vectors), we first loop over a massive data set and accumulate word co-occurrence counts in some form of a matrix X and then perform Singular Value Decomposition on X to get a USV^T decomposition. We then use the rows of U as the word embeddings for all words in our dictionary. Let us discuss a few choices of X.

Above is the excerpt from the standford univ cs224n lecture 1 notes.

Above USV refer to what? There's no prior explanation about it so I ask here.

## 1 Answer

USV^T refers to the result of the singular value decomposition (SVD).

An m times n matrix X can be written with the help of three matrices

X = USV^T,

where U is an m times m unitary matrix, S is a diagonal m times n matrix with real entries called singular values, and V is a unitary n times n matrix. The ^T is the Hermitean transpose. SVD has applications, e.g, in optimization problems, principal component analysis, etc. Wikipedia has quite a long article.