  This study presents an efficient approach for incomplete data classification,
where the entries of samples are missing or masked due to privacy preservation.
To deal with these incomplete data, a new kernel function with asymmetric
intrinsic mappings is proposed in this study. Such a new kernel uses three-side
similarities for kernel matrix formation. The similarity between a testing
instance and a training sample relies not only on their distance but also on
the relation between the testing sample and the centroid of the class, where
the training sample belongs. This reduces biased estimation compared with
typical methods when only one training sample is used for kernel matrix
formation. Furthermore, centroid generation does not involve any clustering
algorithms. The proposed kernel is capable of performing data imputation by
using class-dependent averages. This enhances Fisher Discriminant Ratios and
data discriminability. Experiments on two open databases were carried out for
evaluating the proposed method. The result indicated that the accuracy of the
proposed method was higher than that of the baseline. These findings thereby
demonstrated the effectiveness of the proposed idea.
