Nonlinear Clustering as an Unsupervised Learning Scheme

Principal Component Analysis (PCA) is an usupervised learning algorithm to decompose high-dimensional data into lower dimensions. In standard PCA, this decomposition is a linear transformation performed by means of Eigenvectors. As a nonlinear extension, Kernel PCA allows nonlinear transformations and thus nonlinear classifications by means of a projection into height-dimensional spaces. In this BA/MA or as RA, the objective is to compare Principal Component Analysis (PCA) with a Kernel PCA and an IPCA which uses varying loadings, based on two different applications. These two applications have already been implemented by using the conventional PCA, which is why the required input/data for these applications is provided. Finally, the idea is to try to link Kernel PCA with the idea of IPCA, that is, with time-varying loadings. This study should thus find the relative merits of a Kernel PCA and IPCA when compared to a conventional PCA.