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The different approaches used for target decomposition (TD) theory in radar polarimetry are reviewed and three main types of theorems are introduced: those based on Mueller matrix, those using an eigenvector analysis of the coherency matrix, and those employing coherent decomposition of the scattering matrix. Support vector machine (SVM), as a novel approach in pattern recognition, has demonstrated success in many fields. A new algorithm of target classification, by combining target decomposition and the support vector machine, is proposed. To conduct the experiment, the polarimetric synthetic aperture radar (SAR) data are used. Experimental results show that it is feasible and efficient to target classification by applying target decomposition to extract scattering mechanisms, and the effects of kernel function and its parameters on the classification efficiency are significant.