1 Principal Component Analysis: Data Reduction and Simplification

The primary purpose of principal component analysis (PCA) is to reduce the dimension of a large data set containing interrelated variables into a more concise data set that retains most of the existing variations. The objective of this paper is to intuitively and mathematically explain why this analysis works and how it can be applied to experimental data. A 6061 aluminum rod with attached strain gages was subjected to a torsion test using a Tinius Olsen Bench Type Torsion Testing Machine and torque, shear strain (γ), and angle of twist (φ) were measured and recorded from the test. Although the relationships among the three measured variables are well known, PCA was performed on the test data to rediscover these correlations. The results of the analysis did indeed identify the most significant relationships within the test data, and revealed the material linearity of the test specimen. I