Principal component analysis (PCA)

- [Instructor] Singular value decomposition … is a linear algebra method that you can use … to decompose a matrix into three resultant matrices. … You do this in order to reduce information … redundancy and noise. … SVD is most commonly used for principal component analysis. … And that's the machine learning method we're about … to discuss in this section. … But first let me give you a brief refresher … in case you have taken linear algebra. … You'll recognize how SVD works. … You can see here we've got our original matrix. … This is our original dataset. … It's called A. … And we decompose it into three resultant matrices: … U, S, and V. … U is the left orthogonal matrix and it holds … all of the important non-information redundant … information about the observations in the original dataset. … V is the right orthogonal matrix and it hold … all of the important non-redundant information … on features in the original dataset. … S, this is the diagonal matrix and it contains … all of the information about the decomposition processes …