Deriving statistical significance maps from support vector machine (SVM) classifiers, in order to elucidate features that significantly contribute to the classification.
Support vector machines (SVM) have been used extensively and in diverse contexts as high-dimensional multi-variate systems. Our group has applied SVMs in multiple projects ranging from brain decoding and lie detection using fMRI1 to prediction of development of dementia using MRI 2,3 to individualized diagnosis of schizophrenia 4,5. A persistent challenge with high-dimensional machine learning methods like SVM, when applied to medical imaging, has been the ability to understand the imaging features that most importantly determine the classification status. This is of paramount importance not only because clinicians need to be able to appreciate the information used to determine the status of a patient beyond the output of a “black box” (machine learning algorithm), but also because understanding the imaging features that drive classification ultimately provides leads to the better understanding of the neurobiological underpinnings of diseases.
Identifying brain regions that significantly contribute to the classification/group separation requires computationally expensive permutation testing. In this project we showed that the results of SVM-permutation testing can be analytically approximated. This approximation leads to more than a thousand-fold speedup of the permutation testing procedure, thereby rendering it feasible to perform such tests quickly on standard computers. The details of this work are described in 6,7.
The basis of the analytic approximation of statistical significance maps is two key indigts:
- Davatzikos, C., et al. Classifying spatial patterns of brain activity for lie-detection. NeuroImage 28, 663-668 (2005).
- Fan, Y., Batmanghelich, N., Clark, C.M., Davatzikos, C. & the Alzheimer’s Disease Neuroimaging Initiative. Spatial patterns of brain atrophy in MCI patients, identified via high-dimensional pattern classification, predict subsequent cognitive decline. Neuroimage (one of the top 10 cited papers of 2008) 39, 1731-1743 (2008).
- Davatzikos, C., Xu, F., An, Y., Fan, Y. & Resnick, S.M. Longitudinal progression of Alzheimer's-like patterns of atrophy in normal older adults: the SPARE-AD index. Brain : a journal of neurology 132, 2026-2035 (2009).
- Gur, R., et al. Whole-brain deformation based morphometry MRI study of schizophrenia. Schizophrenia bulletin 31, 408-408 (2006).
- Koutsouleris, N., et al. Use of neuroanatomical pattern regression to predict the structural brain dynamics of vulnerability and transition to psychosis. Schizophrenia Research 123, 175-187 (2010).
- Gaonkar, B., R, T.S., Davatzikos, C. & Alzheimers Disease Neuroimaging, I. Interpreting support vector machine models for multivariate group wise analysis in neuroimaging. Medical image analysis 24, 190-204 (2015).
- Gaonkar, B. & Davatzikos, C. Analytic estimation of statistical significance maps for support vector machine based multi-variate image analysis and classification. NeuroImage 78, 270-283 (2013).