Incorporation of radius-info can be simple with SimpleMKL

Recent research has shown the benefit of incorporating the radius of the Minimal Enclosing Ball (MEB) of training data into Multiple Kernel Learning (MKL). However, straightforwardly incorporating this radius leads to complex learning structure and considerably increased computation. Moreover, the notorious sensitivity of this radius to outliers can adversely affect MKL. In this paper, instead of directly incorporating the radius of MEB, we incorporate its close relative, the trace of data scattering matrix, to avoid the above problems. By analyzing the characteristics of the resulting optimization, we show that the benefit of incorporating the radius of MEB can be fully retained. More importantly, our algorithm can be effortlessly realized within the existing MKL framework such as SimpleMKL. The mere difference is the way to normalize the basic kernels. Although this kernel normalization is not our invention, our theoretic derivation uncovers why this normalization can achieve better classification performance, which has not appeared in the literature before. As experimentally demonstrated, our method achieves the overall best learning performance in various settings. In another perspective, our work improves SimpleMKL to utilize the information of the radius of MEB in an efficient and practical way.