Spatial and Anatomical Regularization of SVM: A General Framework for Neuroimaging Data

Rémi Cuingnet 1 Joan Alexis Glaunès 2 Marie Chupin 1 Habib Benali 3 Olivier Colliot 1
1 ARAMIS - Algorithms, models and methods for images and signals of the human brain
UPMC - Université Pierre et Marie Curie - Paris 6, Inria de Paris, ICM - Institut du Cerveau et de la Moëlle Epinière = Brain and Spine Institute
Abstract : This paper presents a framework to introduce spatial and anatomical priors in SVM for brain image analysis based on regularization operators. A notion of proximity based on prior anatomical knowledge between the image points is defined by a graph (e.g. brain connectivity graph) or a metric (e.g. Fisher metric on statistical manifolds). A regularization operator is then defined from the graph Laplacian, in the discrete case, or from the Laplace-Beltrami operator, in the continuous case. The regularization operator is then introduced into the SVM, which exponentially penalizes high frequency components with respect to the graph or to the metric and thus constrains the classification function to be smooth with respect to the prior. It yields a new SVM optimization problem whose kernel is a heat kernel on graphs or on manifolds. We then present different types of priors and provide efficient computations of the Gram matrix. The proposed framework is finally applied to the classification of brain magnetic resonance (MR) images (based on gray matter concentration maps and cortical thickness measures) from 137 patients with Alzheimer's disease and 162 elderly controls. The results demonstrate that the proposed classifier generates less-noisy and consequently more interpretable feature maps with high classification performances.
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Rémi Cuingnet, Joan Alexis Glaunès, Marie Chupin, Habib Benali, Olivier Colliot. Spatial and Anatomical Regularization of SVM: A General Framework for Neuroimaging Data. IEEE Transactions on Pattern Analysis and Machine Intelligence, Institute of Electrical and Electronics Engineers, 2013, 35 (3), pp.682 - 696. ⟨10.1109/TPAMI.2012.142⟩. ⟨hal-00790079⟩

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