Auffermann William F, Ngan Shing-Chung, Hu Xiaoping
Department of Radiology, Center for Magnetic Resonance Research, University of Minnesota Medical School, Minneapolis 55455, USA.
Neuroimage. 2002 Oct;17(2):583-91.
Many of the statistical methods currently employed to analyze fMRI data depend on a response template. However, the true form of the hemodynamic response, and thereby the response template, is often unknown. Consequently, cluster analysis provides a complementary, template-free method for exploratory analysis of multidimensional fMRI data sets. Clustering algorithms currently being applied to fMRI data separate the data into a predefined number of clusters (k). A poor choice of k will result in erroneously partitioning well-defined clusters. Although several clustering algorithms have been successfully applied to fMRI data, techniques for statistically testing cluster separation are still lacking. To address this problem we suggest a method based on Fisher's linear discriminant and the bootstrap. Also introduced in this paper is a measure based on the projection of multidimensional data from two clusters onto the vector, maximizing the ratio of the between- to the within-cluster sums of squares. The resulting one-dimensional distribution may be readily visualized and used as a heuristic for estimating cluster homogeneity. These methods are demonstrated for the self-organizing maps clustering algorithm when applied to event-related fMRI data.
目前用于分析功能磁共振成像（fMRI）数据的许多统计方法都依赖于一个响应模板。然而，血流动力学响应的真实形式，进而响应模板，往往是未知的。因此，聚类分析为多维fMRI数据集的探索性分析提供了一种互补的、无模板的方法。目前应用于fMRI数据的聚类算法将数据分离为预定义数量的簇（k）。k的选择不当将导致错误地划分定义明确的簇。尽管几种聚类算法已成功应用于fMRI数据，但仍缺乏用于统计检验簇分离的技术。为了解决这个问题，我们提出了一种基于Fisher线性判别和自助法的方法。本文还介绍了一种基于将来自两个簇的多维数据投影到向量上的度量，该向量使簇间和簇内平方和的比率最大化。由此产生的一维分布可以很容易地可视化，并用作估计簇同质性的启发式方法。当应用于事件相关fMRI数据时，这些方法通过自组织映射聚类算法得到了验证。
