In order to enrich and improve the ability of the existing models for reasoning and predicting with 3D cardinal direction relations and enhance the usability of the existing models, and then better meet the demands of real applications for complex 3D spatial data, the inverse reasoning of 3D cardinal direction relations was studied. After deeply studying the theory of n-dimensional block algebra, an algorithm for computing the inverse of the basic 3D cardinal direction relations on the basis of 3D block algebra was devised. Theoretical analysis and the results of the example show that the proposed algorithm is correct and complete. This work can better enhance the power of intelligent analysis and processing for the complex 3D direction relations of the spatial database.
Aiming at the problems that the traditional Support Vector Machine (SVM) classifier is sensitive to outliers and has the large number of Support Vectors (SV) and the parameter of its separating hyperplane is not sparse, the Truncated hinge loss SVM with Smoothly Clipped Absolute Deviation (SCAD) penalty (SCAD-TSVM) was put forward and was used for constructing the financial early-warning model. At the same time, an iterative updating algorithm was proposed to solve the SCAD-TSVM model. Experiments were implemented on the financial data of A-share manufacturing listed companies of the Shanghai and Shenzhen stock markets. Compared to the T-2 and T-3 models constructed by SVM with L1 norm penalty (L1-SVM), SVM with SCAD penalty (SCAD-SVM) and Truncated hinge loss SVM (TSVM), the T-2 and T-3 model constructed by the SCAD-TSVM had the best sparseness and the highest accuracy of prediction, and its average accuracies of prediction with different number of training samples were higher than those of the L1-SVM, SCAD-SVM and TSVM algorithms.
To overcome the shortcomings of current methods in chromatic scan map vectorization, an interactive vectorization method was proposed. It used the color distance and line width as characteristics, and adopted the strategies such as fuzzy point selection, adjustable tracking direction and changeable tracking mode. Experiment results show that it can vectorized the chromatic scan map rapidly and interactively.