IEEE Trans Pattern Anal Mach Intell. 2013 Mar;35(3):682-96. doi: 10.1109/TPAMI.2012.142. Epub 2012 Jun 26.
This paper presents a framework to introduce spatial and anatomical priors in SVM for brain image analysis based on regularization operators. A notion of proximity based on prior anatomical knowledge between the image points is defined by a graph (e.g., brain connectivity graph) or a metric (e.g., Fisher metric on statistical manifolds). A regularization operator is then defined from the graph Laplacian, in the discrete case, or from the Laplace-Beltrami operator, in the continuous case. The regularization operator is then introduced into the SVM, which exponentially penalizes high-frequency components with respect to the graph or to the metric and thus constrains the classification function to be smooth with respect to the prior. It yields a new SVM optimization problem whose kernel is a heat kernel on graphs or on manifolds. We then present different types of priors and provide efficient computations of the Gram matrix. The proposed framework is finally applied to the classification of brain Magnetic Resonance (MR) images (based on Gray Matter (GM) concentration maps and cortical thickness measures) from 137 patients with Alzheimer's Disease (AD) and 162 elderly controls. The results demonstrate that the proposed classifier generates less-noisy and consequently more interpretable feature maps with high classification performances.
本文提出了一种基于正则化算子的 SVM 框架，用于在脑图像分析中引入空间和解剖先验。基于图像点之间先验解剖知识的接近度概念可以通过图（例如脑连接图）或度量（例如统计流形上的 Fisher 度量）来定义。然后从图拉普拉斯算子（离散情况）或拉普拉斯-贝尔特拉米算子（连续情况）定义正则化算子。然后将正则化算子引入 SVM 中，该算子对图或度量的高频分量进行指数惩罚，从而约束分类函数相对于先验平滑。这产生了一个新的 SVM 优化问题，其核是图或流形上的热核。然后，我们提出了不同类型的先验，并提供了 Gram 矩阵的有效计算。最后，将提出的框架应用于 137 名阿尔茨海默病（AD）患者和 162 名老年对照者的脑磁共振（MR）图像（基于灰质（GM）浓度图和皮质厚度测量值）分类。结果表明，所提出的分类器生成的特征图噪声更小，因此更具可解释性，且分类性能更高。
