Many scientific disciplines rely on dimensionality reduction techniques for computationally
less expensive handling of multivariate data sets. In particular, Principal Component
Analysis (PCA) is a popular method that can be used to discover the underlying low-
dimensional manifolds in high-dimensional data sets. PCA-derived manifolds are formed by
projecting the original data set onto a new basis spanned by the first few Principal
Components (PCs). In many cases, it is crucial that the manifold maintains certain …