SVM that Maximizes the Margin in the Input Space

摘要

While the original SVM seeks the discriminative plane that maximizes the margin in the feature space (the Hilbert space), this paper investigates the framework that maximizes the margin in the input space. This framework is considered to be effective for cases in which a priori knowledge is embedded as input space estimates. In the approach taken in this paper, approximating the margin in the input space by Taylor expansion is essential. The algorithm obtained is a kind of alternating optimization comprising the step of obtaining projections onto the discriminative plane from sample points by Newton's method and the step of determining parameters of the discriminative plane by convex quadratic programming. The algorithm converges to a stably local optimal solution under comparatively lenient conditions. In addition, the optimization problem to be solved includes the original SVM as a special case. However, since the amount of computation increases as the dimensions of the input space increase in the proposed algorithm, this paper proposes a simplified algorithm obtained by combining the original SVM and the abridged proposed algorithm.