We present a statistical analysis of a large set of absorption spectra of phytoplankton, measured in natural samples collected from ocean water, in conjunction with detailed pigment concentrations. We processed the absorption spectra with a sophisticated neural network method suitable for classifying complex phenomena, the so-called self-organizing maps (SOM) proposed by Kohonen [Kohonen, Self Organizing Maps (Springer-Verlag, 1984)]. The aim was to compress the information embedded in the data set into a reduced number of classes characterizing the data set, which facilitates the analysis. By processing the absorption spectra, we were able to retrieve well-known relationships among pigment concentrations and to display them on maps to facilitate their interpretation. We then showed that the SOM enabled us to extract pertinent information about pigment concentrations normalized to chlorophyll a. We were able to propose new relationships between the fucoxanthin/Tchl-a ratio and the derivative of the absorption spectrum at 510 nm and between the Tchl-b/Tchl-a ratio and the derivative at 640 nm. Finally, we demonstrate the possibility of inverting the absorption spectrum to retrieve the pigment concentrations with better accuracy than a regression analysis using the Tchl-a concentration derived from the absorption at 440 nm. We also discuss the data coding used to build the self-organizing map. This methodology is very general and can be used to analyze a large class of complex data.