Deriving statistical significance maps for SVM based image classification and group comparisons.

Population based pattern analysis and classification for quantifying structural and functional differences between diverse groups has been shown to be a powerful tool for the study of a number of diseases, and is quite commonly used especially in neuroimaging. The alternative to these pattern analysis methods, namely mass univariate methods such as voxel based analysis and all related methods, cannot detect multivariate patterns associated with group differences, and are not particularly suitable for developing individual-based diagnostic and prognostic biomarkers. A commonly used pattern analysis tool is the support vector machine (SVM). Unlike univariate statistical frameworks for morphometry, analytical tools for statistical inference are unavailable for the SVM. In this paper, we show that null distributions ordinarily obtained by permutation tests using SVMs can be analytically approximated from the data. The analytical computation takes a small fraction of the time it takes to do an actual permutation test, thereby rendering it possible to quickly create statistical significance maps derived from SVMs. Such maps are critical for understanding imaging patterns of group differences and interpreting which anatomical regions are important in determining the classifier's decision.