The Least-Squares Mixed-Norm Support Vector Classifier

Support vector machines (SVMs) are powerful new tools for data classification and regression analysis. A number of different variations exist for the SVMs, one of which is the least-squares support vector classifier (LS-SVC). The LS-SVC enjoys the advantage of training without quadratic programming. This paper presents the least-squares mixed-norm support vector classifier (LS m-SVC) which is a generalized form of the conventional LS-SVC by incorporating both 1-norm and 2-norm classification errors into the design problem. Using the method of Lagrange multipliers, we have derived a form suitable for efficient implementation. It is found that the decision boundary of the LS m-SVC concides with that of the LS-SVC exactly, whereas the classification margin of the former is proportional to the (1 + C1/C2)-1 factor. Some demonstrative examples are given to show the relation between the newly developed LS m-SVC and conventional LS-SVC.