Abdi Hervé, Dunlop Joseph P, Williams Lynne J
The University of Texas at Dallas, Richardson, 75080-3021, USA.
Neuroimage. 2009 Mar 1;45(1):89-95. doi: 10.1016/j.neuroimage.2008.11.008. Epub 2008 Nov 24.
When used to analyze brain imaging data, pattern classifiers typically produce results that can be interpreted as a measure of discriminability or as a distance between some experimental categories. These results can be analyzed with techniques such as multidimensional scaling (MDS), which represent the experimental categories as points on a map. While such a map reveals the configuration of the categories, it does not provide a reliability estimate of the position of the experimental categories, and therefore cannot be used for inferential purposes. In this paper, we present a procedure that provides reliability estimates for pattern classifiers. This procedure combines bootstrap estimation (to estimate the variability of the experimental conditions) and a new 3-way extension of MDS, called DISTATIS, that can be used to integrate the distance matrices generated by the bootstrap procedure and to represent the results as MDS-like maps. Reliability estimates are expressed as (1) tolerance intervals which reflect the accuracy of the assignment of scans to experimental categories and as (2) confidence intervals which generalize standard hypothesis testing. When more than two categories are involved in the application of a pattern classifier, the use of confidence intervals for null hypothesis testing inflates Type I error. We address this problem with a Bonferonni-like correction. Our methodology is illustrated with the results of a pattern classifier described by O'Toole et al. (O'Toole, A., Jiang, F., Abdi, H., Haxby, J., 2005. Partially distributed representations of objects and faces in ventral temporal cortex. J. Cogn. Neurosci. 17, 580-590) who re-analyzed data originally collected by Haxby et al. (Haxby, J., Gobbini, M., Furey, M., Ishai, A., Schouten, J., Pietrini, P., 2001. Distributed and overlapping representation of faces and objects in ventral temporal cortex. Science 293, 2425-2430).
当用于分析脑成像数据时，模式分类器通常会产生一些结果，这些结果可以被解释为可区分性的度量，或者是某些实验类别之间的距离。这些结果可以使用多维缩放（MDS）等技术进行分析，该技术将实验类别表示为地图上的点。虽然这样的地图揭示了类别的配置，但它并没有提供实验类别位置的可靠性估计，因此不能用于推理目的。在本文中，我们提出了一种为模式分类器提供可靠性估计的程序。该程序结合了自助估计（以估计实验条件的变异性）和一种新的MDS三元扩展，称为DISTATIS，它可用于整合由自助程序生成的距离矩阵，并将结果表示为类似MDS的地图。可靠性估计表示为：（1）反映扫描分配到实验类别准确性的容忍区间，以及（2）推广标准假设检验的置信区间。当模式分类器的应用涉及两个以上类别时，用于零假设检验的置信区间会增加I型错误。我们用类似邦费罗尼校正的方法解决了这个问题。我们用O'Toole等人（O'Toole, A., Jiang, F., Abdi, H., Haxby, J., 2005. 腹侧颞叶皮层中物体和面孔的部分分布式表征。《认知神经科学杂志》17, 580 - 590）描述的模式分类器的结果来说明我们的方法，他们重新分析了Haxby等人（Haxby, J., Gobbini, M., Furey, M., Ishai, A., Schouten, J., Pietrini, P., 2001. 腹侧颞叶皮层中面孔和物体的分布式和重叠表征。《科学》293, 2425 - 2430）最初收集的数据。
