Although multiple criteria mathematical program （MCMP）, as an alternative method of classification, has been used in various real-life data mining problems, its mathematical structure of solvability is still challengeable. This paper proposes a regularized multiple criteria linear program （RMCLP） for two classes of classification problems. It first adds some regularization terms in the objective function of the known multiple criteria linear program （MCLP） model for possible existence of solution. Then the paper describes the mathematical framework of the solvability. Finally, a series of experimental tests are conducted to illustrate the performance of the proposed RMCLP with the existing methods： MCLP, multiple criteria quadratic program （MCQP）, and support vector machine （SVM）. The results of four publicly available datasets and a real-life credit dataset all show that RMCLP is a competitive method in classification. Furthermore, this paper explores an ordinal RMCLP （ORMCLP） model for ordinal multigroup problems. Comparing ORMCLP with traditional methods such as One-Against-One, One-Against-The rest on large-scale credit card dataset, experimental results show that both ORMCLP and RMCLP perform well.
Exploring the structural topology of genome-based large-scale metabolic network is essential for in- vestigating possible relations between structure and functionality.Visualization would be helpful for obtaining immediate information about structural organization.In this work,metabolic networks of 75 organisms were investigated from a topological point of view.A spread bow-tie model was proposed to give a clear visualization of the bow-tie structure for metabolic networks.The revealed topological pattern helps to design more efficient algorithm specifically for metabolic networks.This coarse- grained graph also visualizes the vulnerable connections in the network,and thus could have important implication for disease studies and drug target identifications.In addition,analysis on the reciprocal links and main cores in the GSC part of bow-tie also reveals that the bow-tie structure of metabolic networks has its own intrinsic and significant features which are significantly different from those of random networks.
