Nonnegative Factorization of a Data Matrix as a Motivational Example for Basic Linear Algebra
Helena Šmigoc
Linear algebra is a classical subject routinely taught to students not majoring in mathematics. As lecturers we are tasked to motivate our subject by producing convincing and interesting examples that are still within the understanding and knowledge of our students. In this talk we will present a motivating example in which matrix multiplication is explicated by examination of a nonnegative decomposition of a term-by-document matrix. We will explore the meaning of the entries in the decomposition, find natural interpretations of intermediate quantities that arise in several different ways of writing the matrix product, and show the utility of various matrix operations. This example gives the students a glimpse of the power of an advanced linear algebraic technique used in modern data science.
