Mining of Massive Datasets

In this chapter we shall explore the idea of dimensionality reduction in more detail. We begin with a discussion of eigenvalues and their use in “principal component analysis” (PCA). We cover singular-value decomposition, a more powerful version of UV-decomposition. Finally, because we are always interested in the largest data sizes we can handle, we look at another form of decomposition, called CUR-decomposition, which is a variant of singular-value decomposition that keeps the matrices of the decomposition sparse if the original matrix is sparse.