Maximum Margin Multi-Dimensional Classification
Multi-dimensional classification (MDC) assumes heterogenous class spaces for each example, where class variables from different class spaces characterize semantics of the example along different dimensions. Due to the heterogeneity of class spaces, the major difficulty in designing margin-based MDC techniques lies in that the modeling outputs from different class spaces are not comparable to each other. In this paper, a first attempt towards maximum margin multi-dimensional classification is investigated. Following the one-vs-one decomposition within each class space, the resulting models are optimized by leveraging classification margin maximization on individual class variable and model relationship regularization across class variables. We derive convex formulation for the maximum margin MDC problem, which can be tackled with alternating optimization admitting QP or closed-form solution in either alternating step. Experimental studies over real-world MDC data sets clearly validate effectiveness of the proposed maximum margin MDC techniques.