This paper introduces the newly developed principal component powered two-dimensional (2D) correlation spectroscopy (PC 2D-COS) as an alternative approach to 2D correlation spectroscopy taking advantage of a dimensionality reduction by principal component analysis. It is shown that PC 2D-COS is equivalent to traditional 2D correlation analysis while providing a significant advantage in terms of computational complexity and memory consumption. These features allow for an easy calculation of 2D correlation spectra even for data sets with very high spectral resolution or a parallel analysis of multiple data sets of 2D correlation spectra. Along with this reduction in complexity, PC 2D-COS offers a significant noise rejection property by limiting the set of principal components used for the 2D correlation calculation. As an example for the application of truncated PC 2D-COS a temperature-dependent Raman spectroscopic data set of a fullerene-anthracene adduct is examined. It is demonstrated that a large reduction in computational cost is possible without loss of relevant information, even for complex real world data sets.