Topology-based kernels with application to inference problems in Alzheimer's disease.
Topology-based kernels with application to inference problems in Alzheimer's disease.
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DOI：
10.1109/tmi.2011.2147327
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发表时间：
2011-10
影响因子：
10.6
通讯作者：
Singh V
中科院分区：
文献类型：
--
作者：
Pachauri D;Hinrichs C;Chung MK;Johnson SC;Singh V
阿尔茨海默病 (AD) 研究最近出现了大量的活动，重点是开发新的统计学习工具，以使用成像数据进行自动推理。其中许多技术的主力是支持向量机 (SVM) 框架（或更普遍的基于内核的方法）。作为第一步，其中大多数需要在输入示例（即图像）之间指定内核矩阵。特征空间中图像 Ii 和 Ij 之间的内积一般可以写成封闭形式，因此可以方便地视为“给定”。然而，在某些神经成像应用中，这种假设会出现问题。例如，提供高度归因数据的两个实例之间的相似性标量测量（例如皮质表面上的皮质厚度测量）是相当具有挑战性的。请注意，已知皮质厚度对于神经系统疾病具有区分作用，因此在推理框架中利用此类信息，特别是在多模态方法中，具有潜在的优势。尽管具有临床意义，但成功利用这种方法进行分类或回归的研究相对较少。受这些应用的推动，我们的论文提出了计算此类基于拓扑的属性数据的相似性矩阵的新技术。我们的想法利用最新的发展来表征由其拓扑特征的持久性驱动的信号（例如，皮质厚度），从而产生了一种简单构造核矩阵的方案。作为原理证明，在 ADNI 研究的 356 名受试者的数据集上，我们在多个统计推理任务上报告了良好的性能，而无需任何特征选择、降维或参数调整。
Alzheimer’s disease (AD) research has recently witnessed a great deal of activity focused on developing new statistical learning tools for automated inference using imaging data. The workhorse for many of these techniques is the Support Vector Machine (SVM) framework (or more generally kernel based methods). Most of these require, as a first step, specification of a kernel matrix between input examples (i.e., images). The inner product between images Ii and Ij in a feature space can generally be written in closed form, and so it is convenient to treat as “given”. However, in certain neuroimaging applications such an assumption becomes problematic. As an example, it is rather challenging to provide a scalar measure of similarity between two instances of highly attributed data such as cortical thickness measures on cortical surfaces. Note that cortical thickness is known to be discriminative for neurological disorders, so leveraging such information in an inference framework, especially within a multi-modal method, is potentially advantageous. But despite being clinically meaningful, relatively few works have successfully exploited this measure for classification or regression. Motivated by these applications, our paper presents novel techniques to compute similarity matrices for such topologically-based attributed data. Our ideas leverage recent developments to characterize signals (e.g., cortical thickness) motivated by the persistence of their topological features, leading to a scheme for simple constructions of kernel matrices. As a proof of principle, on a dataset of 356 subjects from the ADNI study, we report good performance on several statistical inference tasks without any feature selection, dimensionality reduction, or parameter tuning.