In this paper, we introduce a new classification scheme for dual frequency polarimetric SAR data sets. A (6 x 6) polarimetric coherency matrix is defined to simultaneously take into account the full polarimetric information from both images. This matrix is composed of the two coherency matrices and their cross-correlation. A decomposition theorem is applied to both images to obtain 64 initial clusters based on their scattering characteristics. The data sets are then classified by an iterative algorithm based on a complex Wishart density function of the 6 by 6 matrix. A class number reduction technique is then applied on the 64 resulting clusters to improve the efficiency of the interpretation and representation of each class characteristics. An alternative technique is also proposed which introduces the polarimetric cross-correlation information to refine the results of classification to a small number of clusters using the conditional probability of the cross-correlation matrix. The analysis of the resulting clusters is realized by determining the rigorous change in polarimetric properties from one image to the other. The polarimetric variations are parameterized by 8 real coefficients derived from the decomposition of a special unitary operator on the Gell-Mann basis. These classification and analysis schemes are applied to full polarimetric P, L, and C bands SAR