This study presents a method for estimating secondary phytoplankton pigments from satellite ocean color observations. We first compiled a large training data set composed of 12,000 samples; each sample is composed of 10 in situ phytoplankton high-performance liquid chromatography (HPLC)-measured pigment concentrations, GlobColour products of chlorophyll-a concentration, and remote sensing reflectance (Rrs($\lambda$)) data at different wavelengths, in addition to advanced very high resolution radiometer sea surface temperature measurements. The resulting data set regroups a large variety of encountered situations between 1997 and 2014. The nonlinear relationship between the in situ and satellite components was identified using a self-organizing map, which is a neural network classifier. As a major result, the self-organizing map enabled reliable estimations of the concentration of chlorophyll-a and of nine different pigments from satellite observations. A cross-validation procedure showed that the estimations were robust for all pigments (R$^2$>0.75 and an average root-mean-square error=0.016mg/m$^3$). A consistent association of several phytoplankton pigments indicating phytoplankton group specific dynamic was shown at a global scale. We also showed the uncertainties for the estimation of each pigment.