Recently, a high dimensional classification framework has been proposed to introduce spatial structure information in classical single kernel support vector machine optimization scheme for brain image analysis. However, during the construction of spatial kernel in this framework, a huge adjacency matrix is adopted to determine the adjacency relation between each pair of voxels and thus it leads to very high computational complexity in the spatial kernel calculation. The method is improved in this manuscript by a new construction of tensorial kernel wherein a 3-order tensor is adopted to preserve the adjacency relation so that calculation of the above huge matrix is avoided, and hence the computational complexity is significantly reduced. The improvement is verified by experimental results on classification of Alzheimer patients and cognitively normal controls.

Recently, a high dimensional classification framework has been proposed to introduce spatial and anatomical priors in classical single kernel support vector machine optimization scheme, wherein the sequential minimal optimization (SMO) training algorithm is adopted, for brain image analysis. However, to satisfy the optimization conditions required in the single kernel case, it is unreasonably assumed that the spatial regularization parameter is equal to the anatomical one. In this letter, this approach is improved by combining SMO algorithm with multiple kernel learning to avoid that assumption and optimally estimate two parameters. The improvement is comparably demonstrated by experimental results on classification of Alzheimer patients and elderly controls.