Principal Component Analysis: Resources for an Essential Application of Linear Algebra

Abstract

Principal Component Analysis (PCA) is a highly useful topic within an introductory Linear Algebra course, especially since it can be used to incorporate a number of applied projects. This method represents an essential application and extension of the Spectral Theorem and is commonly used within a variety of fields, including statistics, neuroscience, and image compression. We present a synopsis of PCA and include a number of examples that can be used within upper-level mathematics courses to engage undergraduate students while introducing them to one of the most widely used applications of linear algebra.

Keywords:

• Linear algebra
• principal component analysis
• data analysis
• neuroscience
• image compression
• MATLAB

Additional information

Funding

The authors would like to thank the College of Engineering and Computational Sciences at the Colorado School of Mines for partial support to develop and implement the educational tools included within this article. Additionally, the first author thanks the National Science Foundation for support under award DMS-1211667.

Notes on contributors

Stephen Pankavich

Stephen Pankavich received his Ph.D. in Mathematical Sciences from Carnegie Mellon University in 2005 and has been interested in applications of mathematics throughout his career. He is currently an Assistant Professor at the Colorado School of Mines where he actively seeks to relate mathematics to the daily life of his undergraduate students while stressing its immense utility within science and engineering.

Rebecca Swanson

Rebecca Swanson received her Ph.D. in Mathematics from Indiana University in 2010. Prior to arriving at the Colorado School of Mines in 2012, she was an Assistant Professor at Nebraska Wesleyan University. She enjoys the beauty and elegance of discrete mathematics and the challenge of pedagogical innovation. In her free time, she also enjoys baking, running, and reading.