Maximal Discrepancy for Support Vector Machines

Stability Evaluation of Brain Changes in Parkinson's Disease Based on Machine Learning

Structural MRI (sMRI) has been widely used to examine the cerebral changes that occur in Parkinson's disease (PD). However, previous studies have aimed for brain changes at the group level rather than at the individual level. Additionally, previous studies have been inconsistent regarding the changes they identified. It is difficult to identify which brain regions are the true biomarkers of PD. To overcome these two issues, we employed four different feature selection methods [ReliefF, graph-theory, recursive feature elimination (RFE), and stability selection] to obtain a minimal set of relevant features and nonredundant features from gray matter (GM) and white matter (WM). Then, a support vector machine (SVM) was utilized to learn decision models from selected features. Based on machine learning technique, this study has not only extended group level statistical analysis with identifying group difference to individual level with predicting patients with PD from healthy controls (HCs), but also identified most informative brain regions with feature selection methods. Furthermore, we conducted horizontal and vertical analyses to investigate the stability of the identified brain regions. On the one hand, we compared the brain changes found by different feature selection methods and considered these brain regions found by feature selection methods commonly as the potential biomarkers related to PD. On the other hand, we compared these brain changes with previous findings reported by conventional statistical analysis to evaluate their stability. Our experiments have demonstrated that the proposed machine learning techniques achieve satisfactory and robust classification performance. The highest classification performance was 92.24% (specificity), 92.42% (sensitivity), 89.58% (accuracy), and 89.77% (AUC) for GM and 71.93% (specificity), 74.87% (sensitivity), 71.18% (accuracy), and 71.82% (AUC) for WM. Moreover, most brain regions identified by machine learning were consistent with previous findings, which means that these brain regions are related to the pathological brain changes characteristic of PD and can be regarded as potential biomarkers of PD. Besides, we also found the brain abnormality of superior frontal gyrus (dorsolateral, SFGdor) and lingual gyrus (LING), which have been confirmed in other studies of PD. This further demonstrates that machine learning models are beneficial for clinicians as a decision support system in diagnosing PD.

In-sample and out-of-sample model selection and error estimation for support vector machines

In-sample approaches to model selection and error estimation of support vector machines (SVMs) are not as widespread as out-of-sample methods, where part of the data is removed from the training set for validation and testing purposes, mainly because their practical application is not straightforward and the latter provide, in many cases, satisfactory results. In this paper, we survey some recent and not-so-recent results of the data-dependent structural risk minimization framework and propose a proper reformulation of the SVM learning algorithm, so that the in-sample approach can be effectively applied. The experiments, performed both on simulated and real-world datasets, show that our in-sample approach can be favorably compared to out-of-sample methods, especially in cases where the latter ones provide questionable results. In particular, when the number of samples is small compared to their dimensionality, like in classification of microarray data, our proposal can outperform conventional out-of-sample approaches such as the cross validation, the leave-one-out, or the Bootstrap methods.