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We present a novel technique to overcome the limitations of the applicability of principal component analysis to typical real-life data sets, especially astronomical spectra. Our new approach addresses the issues of outliers, missing information, large number of dimensions and the vast amount of data by combining elements of robust statistics and recursive algorithms that provide improved eigensystem estimates step by step. We develop a generic mechanism for deriving reliable eigenspectra without manual data censoring, while utilizing all the information contained in the observations. We demonstrate the power of the methodology on the attractive collection of the Visible Imaging Multi-Object Spectrograph (VIMOS) Very Large Telescope (VLT) Deep Survey spectra that manifest most of the challenges today, and highlight the improvements over previous workarounds, as well as the scalability of our approach to collections with sizes of the Sloan Digital Sky Survey and beyond. [ABSTRACT FROM AUTHOR]