Linear Algebraic Models

Abstract

This chapter presents some of the fundamental linear algebraic tools for large scale data analysis and machine learning. Specifically, the focus will fall on large scale linear algebra, including iterative, approximate and randomized algorithms for basic linear algebra computations and matrix functions. Algorithms of such type are mostly pass-efficient, requiring only a constant number of passes over the matrix data for creating samples or sketches, and other work. Most these algorithms require at least two passes for their efficient performance guarantees, with respect to error or failure probability. Such a one-pass algorithm is close to the streaming model of computation, where there is one pass over the data, and resource bounds are sublinear in the data size.