In the higher-order algorithms, only a small number of super edges are used to construct the sparse affinity model, and the higher-order affinity model only considers the single-order higher-order similarity relationship. In order to solve these two problems, based on the normalized cut algorithm and by using the transductive learning technique, a full higher-order affinity model and a full multi-order affinity model are constructed from the two perspectives of normalized and non-normalized Laplacian matrixes. A Transductive learning framework is constructed based on the normalized cut algorithm, and it is showed how the framework trains the full similarity in the algorithm. The final result shows that the full similarity between the super edges in the algorithm can be applied as a simple form. Based on this, the multi-order full similarity relation is merged, and a fully similar multi-order affinity model with multi-order information is proposed. The constructed full higher-order affinity model and the full multi-order affinity model are applied to the framework of the normalized cut algorithm, and a full affinity higher-order normalized cut algorithm and a fully affinity multi-order normalized cut algorithm are proposed. In the two higher-order affinity models, the full affinity tensor is in the form of sparse tensor inverse and the inverse matrix can be transformed into the sparse tensor feature decomposition problem in the normalized cut. In the experimental part, the proposed algorithm is applied to motion segmentation and compared with the existing higher-order algorithms. The results show the advantages of the propesed algorithm.