Non-uniqueness of solutions of 1-norm support vector classification in dual form

Most of previous research efforts on support vector machines (SVMs) were directed toward efficient implementations and practical applications. In this work, we concentrate on a different aspect of SVMs. Specifically, we investigate the non-uniqueness of SVM solutions. The key features of this work include (1) we concentrate on the cases where the dual solutions are not unique, whereas the primal solutions are unique; (2) our test for non-uniqueness can be directly applied to data points without solving the SVC optimization problem, namely, the non-uniqueness information is obtained before any numerical optimization procedure is employed.