A fast algorithm for the classification of high dimensional vectors was proposed. A special nonlinear feature function was used to reshape training sample sets of multi classes to low dimensional and orthogonal feature sub-spaces. Then the principle components of each feature sub-space were calculated. By projecting a new coming vector on each feature sub-space the projection residuals was calculated. The new vector was regarded as a sample of the feature sub-space with the smallest residual. This algorithm can distinguish high dimensional vectors of multi classes by one comparison and has good accuracy. Furthermore, manifold learning theory was added to the feature function to keep the accuracy and greatly reduce the dimensionality of feature sub-spaces.
