The purpose of this paper is to develop the theory of principal components analysis succinctly from the fundamentals of matrix algebra and multivariate statistics. Principal components analysis is sometimes used as a descriptive technique to explain the variance-covariance or correlation structure of a dataset. However, most often, it is used as a dimensionality reduction technique to visualize a high dimensional dataset in a lower dimensional space. Principal components analysis accomplishes this by using the first few principal components, provided that they account for a substantial proportion of variation in the original dataset. In the same way, the first few principal components can be used as inputs into a cluster analysis in order to combat the curse of dimensionality and optimize the runtime for large datasets. The application portion of this paper will apply these methods to a US Crime 2018 dataset extracted from the Uniform Crime Reports on the FBI’s website.
Galkande (Iresha) Premarathna
Date of Degree
Master of Science (MS)
Mathematics and Statistics
Science, Engineering and Technology
Silva, D. (2020). Theory of principal components for applications in exploratory crime analysis and clustering [Master’s thesis, Minnesota State University, Mankato]. Cornerstone: A Collection of Scholarly and Creative Works for Minnesota State University, Mankato. https://cornerstone.lib.mnsu.edu/etds/996/
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