A framework of latent attribute space tree classifier (LAST) is proposed in this paper. LAST transforms data from the original attribute space into the latent attribute space, which is easier for data separation or more suitable for tree classifier, so that the decision boundary of the traditional decision tree can be extended and its generalization ability can be improved. This paper presents two SVD (singular value decomposition) oblique decision tree (SODT) algorithms based on the LAST framework. SODT first performs SVD on global and/or local data to construct orthogonal latent attribute space. Then, traditional decision tree or tree nodes are built in that space.Finally, SODT obtains the approximately optimal oblique decision tree of the original space. SODT can not only handle datasets with similar or different distribution between global and local data, but also can make full use of the structure information of the labelled and unlabelled data and produce the same classification results no matter how the observations are arranged. Besides, the time complexity of SODT is identical to that of the univariate decision tree. Experimental results show that compared with the traditional univariate decision tree algorithm C4.5 and the oblique decision tree algorithms OC1 and CART-LC, SODT gives higher classification accuracy, more stable decision tree size and comparable tree-construction time as C4.5, which is much less than that of OC1 and CART-LC.