Pearlmutter, Barak A. and Šmigoc, Helena (2017) Nonnegative Factorization of a Data Matrix as a Motivational Example for Basic Linear Algebra. Working Paper. arXiv.

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Abstract

We present a motivating example for matrix multiplication based on factoring a data matrix. Traditionally, matrix multiplication is motivated by applications in physics: composing rigid transformations, scaling, sheering, etc. We present an engaging modern example which naturally motivates a variety of matrix manipulations, and a variety of different ways of viewing matrix multiplication. We exhibit a low-rank non-negative decomposition (NMF) of a "data matrix" whose entries are word frequencies across a corpus of documents. We then 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.

Item Type:	Monograph (Working Paper)
Additional Information:	Cite as: arXiv:1706.09699 [math.HO]
Keywords:	Nonnegative Matrix Factorization (NMF); Topic Modeling; Data Mining; Matrix Multiplication;
Academic Unit:	Faculty of Science and Engineering > Computer Science
Item ID:	10254
Identification Number:	https://doi.org/10.1007/978-3-319-66811-6_15
Depositing User:	Barak Pearlmutter
Date Deposited:	28 Nov 2018 16:56
Publisher:	arXiv
URI:	https://arxiv.org
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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