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Neuroimaging has shown its effectiveness for diagnosis of Parkinson's disease (PD), and the neuroimaging-based computer-aided diagnosis (CAD) then attracts considerable attention. In a CAD system, the classifier module is one of the key components, which directly decides the classification performance. As a newly proposed classifier, the large margin distribution machine (LDM) has excellent generalization by maximizing the margin mean and minimizing the margin variance simultaneously. However, LDM still suffers from the problem of kernel selection. In this work, we propose a deep neural mapping large margin distribution machine (DNMLDM) algorithm by adopting the deep neural network (DNN) to perform a kernel mapping instead of the implicit kernel function in LDM. A two-stage joint training strategy is then developed, including the unsupervised layer-wise pre-training for DNN and then the supervised fine-tuning for all parameters in the whole networks. Two real-world PD datasets, namely the transcranial sonography (TCS) dataset and the magnetic resonance imaging (MRI) dataset, are used to evaluate the performance of DNMLDM algorithm. The experimental results show that the proposed DNMLDM outperforms all the compared algorithms on both datasets.

In this paper, we propose a sparse quadratic kernel-free least squares semi-supervised support vector machine model by adding an L1 norm regularization term to the objective function and using the least squares method, which results in a nonconvex and nonsmooth quadratic programming problem. For computational considerations, we use the smoothing technique and consensus technique. Then we adopt the proximal alternating direction method of multipliers (P-ADMM) to solve it, as well as propose a strategy of parameter selection. Then we not only derive the convergence analysis of algorithm, but also estimate the convergence rate as o ( 1 / k ) , where k is the number of iteration. This gives the best bound of P-ADMM known so far for nonconvex consensus problem. To demonstrate the efficiency of our model, we compare the proposed method with several state-of-the-art methods. The numerical results show that our model can achieve both better accuracy and sparsity.

In this paper, numerical methods to compute the Karcher means on the n-order rotation group SO(n) are considered. First, after recalling Karcher means as solutions of a kind of minimization problems on SO(n), a super-linearly convergent numerical method, namely conjugate gradient method, has been used to deal with them. By the geometric structure of SO(n), the proposed algorithm is structure preserving. Then, a variety of numerical experiments are presented to demonstrate the performance and efficiency of the proposed algorithm by comparing with a recent structure preserving method.

Thin-plate spline for robust point matching (TPS-RPM) algorithm is a famous and widely used approach in nonlinear shape registration. In this paper, we improve this approach by adopting an alternatively iterative strategy of globally affine and locally nonlinear registration. Concretely, in the affine registration step, we apply the Lie group parameterization method to globally align two shapes to assume the global similarity. In which, some suitable constraints are introduced to improve the robustness of algorithm. Then, in the locally nonlinear deformation step, we apply the thin-plate spline approach. By alternatively iterating these two steps, the proposed method not only preserves the advantages of spline methods, but also overcomes an overmatching phenomenon in shape registration. Finally, we test the proposed method on several conventional data sets with comparison of TPS-RPM. The experimental results validate that our method is really effective for nonlinear shape registration as well as more robust.