Besides SimpleNPKL, we also propose a novel non-parametric spectral kernel learning method which can seamlessly combine manifold structure of unlabeled data and Regularized Least-Squares (RLS) to learn a new kernel. Interestingly, the new kernel matrix can be obtained analytically with the use of spectral decomposition of graph Laplacian matrix. Hence, the proposed algorithm does not require any numerical optimization solvers. Moreover, by maximizing kernel target alignment on labeled data, we can also learn model parameters automatically with a closed-form solution. For a given graph Laplacian matrix, our proposed method does not need to tune any model parameter including the tradeoff parameter in RLS and the balance parameter for unlabeled data. Extensive experiments on ten benchmark datasets show that our proposed non-parametric and parameter-free spectral kernel learning algorithm can obtain comparable performance with fine-tuned manifold regularization methods in transductive setting, and outperform multiple kernel learning in supervised setting.
Here, we directly test this hypothesis, by developing a 1st order dynamical model with non-linear interactions between function and use, and by analyzing how this model can account for actual stroke recovery data. Using a Bayesian framework, we systematically compared this model to other time-varying models with and without interactions between function and use. To train the parameters of all the models, we used data from the immediate treatment group of the EXCITE clinical trial (Wolf et al. 2006) in which use and function data were collected following two weeks of therapy in four month intervals for 2 years.
Comparison of the model evidence probabilities showed that the best fitting model was our 1st order dynamical model with the non-linear interaction between function and uses. We also predicted that the recovery process of each patient, and categorized patients into the vicious or vicious group, by using a threshold surface of long term arm use estimate. Finally, we compared model parameters before and after therapy and found that the only parameter which increased is related to the motivation to use the affected arm. Our results suggest that after rehabilitation, the interaction between function and use is a crucial factor for functional recovery.