Supervised Multidimensional Scaling and its Application in MRI-Based Individual Age Predictions

It has been a popular trend to decode individuals' demographic and cognitive variables based on MRI. Features extracted from MRI data are usually of high dimensionality, and dimensionality reduction (DR) is an effective way to deal with these high-dimensional features. Despite many supervised DR techniques for classification purposes, there is still a lack of supervised DR techniques for regression purposes. In this study, we advanced a novel supervised DR technique for regression purposes, namely, supervised multidimensional scaling (SMDS). The implementation of SMDS includes two steps: (1) evaluating pairwise distances among entities based on their labels and constructing a new space through a distance-preserving projection; (2) establishing an explicit linear relationship between the feature space and the new space. Based on this linear relationship, DR for test entities can be performed. We evaluated the performance of SMDS first on a synthetic dataset, and the results indicate that (1) SMDS is relatively robust to Gaussian noise existing in the features and labels; (2) the dimensionality of the new space exerts negligible influences upon SMDS; and (3) when the sample size is small, the performance of SMDS deteriorates with the increase of feature dimension. When applied to features extracted from resting state fMRI data for individual age predictions, SMDS was observed to outperform classic DR techniques, including principal component analysis, locally linear embedding and multidimensional scaling (MDS). Hopefully, SMDS can be widely used in studies on MRI-based predictions. Furthermore, novel supervised DR techniques for regression purposes can easily be developed by replacing MDS with other nonlinear DR techniques.