Large amount of information in hyperspectral images (HSI) generally makes their analysis (e.g., principal component analysis, PCA) time consuming and often requires a lot of random access memory (RAM) and high computing power. This is particularly problematic for analysis of large images, containing millions of pixels, which can be created by augmenting series of single images (e.g., in time series analysis). This tutorial explores how data reduction can be used to analyze time series hyperspectral images much faster without losing crucial analytical information. Two of the most common data reduction methods have been chosen from the recent research. The first one uses a simple randomization method called randomized sub-sampling PCA (RSPCA). The second implies a more robust randomization method based on local-rank approximations (rPCA). This manuscript exposes the major benefits and drawbacks of both methods with the spirit of being as didactical as possible for a reader. A comprehensive comparison is made considering the amount of information retained by the PCA models at different compression degrees and the performance time. Extrapolation is also made to the case where the effect of time and any other factor are to be studied simultaneously.