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.

基于MRI解码个人的人口统计和认知变量已成为一种流行的趋势。从MRI数据中提取的特征通常具有较高的维数，而降维（DR）是处理这些高维特征的有效方法。尽管有许多用于分类目的的监督DR技术，但仍缺乏用于回归的监督DR技术目的。在这项研究中，我们出于回归目的提出了一种新型的监督DR技术，即监督多维缩放（SMDS）。SMDS的实现包括两个步骤：（1）根据实体的标签评估实体之间的成对距离，并通过保距投影构造新空间；（2）在特征空间和新空间之间建立显式线性关系。基于此线性关系，可以执行测试实体的DR。我们首先在综合数据集上评估了SMDS的性能，结果表明：（1）SMDS对特征和标签中存在的高斯噪声具有相对强健的性能；（2）新空间的尺寸对SMDS的影响可忽略不计；（3）当样本量较小时，SMDS的性能会随着特征尺寸的增加而降低。当将其应用于从静止状态fMRI数据中提取的用于个体年龄预测的特征时，观察到SMDS优于传统的DR技术，包括主成分分析，局部线性嵌入和多维缩放（MDS）。希望SMDS可以广泛用于基于MRI的预测研究中。此外，通过将MDS替换为其他非线性DR技术，可以轻松开发用于回归目的的新型监督DR技术。SMDS可以广泛用于基于MRI的预测研究中。此外，通过将MDS替换为其他非线性DR技术，可以轻松开发用于回归目的的新型监督DR技术。SMDS可以广泛用于基于MRI的预测研究中。此外，通过将MDS替换为其他非线性DR技术，可以轻松开发用于回归目的的新型监督DR技术。