Simple principal components.

Sun, Linjuan (2006). Simple principal components. PhD thesis The Open University.

DOI: https://doi.org/10.21954/ou.ro.0000fe0f

Abstract

A new technique, simple principal component analysis (SCA), is addressed by Vines (2000) to enhance the interpretation of principal components (PCs). The SCA algorithm seeks integer valued loadings vectors that have properties close to the loading vectors obtained from the principal component analysis (PCA). Simulation is used to compare the different implementations and show that SCA is better than PCA in some cases. In this thesis, I first pin down the link between SCA with Jacobi methods, then develop the concepts of a combining approach and a hybrid approach.
The results produced by SCA methods can be very good approximation to corresponding PCs whatever the structures of the data, and simple components are generally easier to interpret than PCs. In particular, the sample simulation results of SCA are generally better than PCA for any simple structures. SCA2, SCA5 and SCA6 are the best SCA methods. As the dimension of the data increases, SCA5 and SCA6 are similar. If necessary, combined and hybrid approaches can make the results of SCA more accurate. However, the results of hybrid methods are orthogonal but the combined results are generally not orthogonal.

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