Absent multiple kernel learning

Multiple kernel learning (MKL) optimally combines the multiple channels of each sample to improve classification performance. However, existing MKL algorithms cannot effectively handle the situation where some channels are missing, which is common in practical applications. This paper proposes an absent MKL (AMKL) algorithm to address this issue. Different from existing approaches where missing channels are firstly imputed and then a standard MKL algorithm is deployed on the imputed data, our algorithm directly classifies each sample with its observed channels. In specific, we define a margin for each sample in its own relevant space, which corresponds to the observed channels of that sample. The proposed AMKL algorithm then maximizes the minimum of all sample-based margins, and this leads to a difficult optimization problem. We show that this problem can be reformulated as a convex one by applying the representer theorem. This makes it readily be solved via existing convex optimization packages. Extensive experiments are conducted on five MKL benchmark data sets to compare the proposed algorithm with existing imputation-based methods. As observed, our algorithm achieves superior performance and the improvement is more significant with the increasing missing ratio.