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. 2015 Oct:9349:702-709.
doi: 10.1007/978-3-319-24553-9_86. Epub 2015 Nov 18.

Disentangling Disease Heterogeneity with Max-Margin Multiple Hyperplane Classifier

Erdem Varol  1 , Aristeidis Sotiras  1 , Christos Davatzikos  1
Affiliations

Disentangling Disease Heterogeneity with Max-Margin Multiple Hyperplane Classifier

Erdem Varol et al. Med Image Comput Comput Assist Interv. 2015 Oct.

Abstract

There is ample evidence for the heterogeneous nature of diseases. For example, Alzheimer's Disease, Schizophrenia and Autism Spectrum Disorder are typical disease examples that are characterized by high clinical heterogeneity, and likely by heterogeneity in the underlying brain phenotypes. Parsing this heterogeneity as captured by neuroimaging studies is important both for better understanding of disease mechanisms, and for building subtype-specific classifiers. However, few existing methodologies tackle this problem in a principled machine learning framework. In this work, we developed a novel non-linear learning algorithm for integrated binary classification and subpopulation clustering. Non-linearity is introduced through the use of multiple linear hyperplanes that form a convex polytope that separates healthy controls from pathologic samples. Disease heterogeneity is disentangled by implicitly clustering pathologic samples through their association to single linear sub-classifiers. We show results of the proposed approach from an imaging study of Alzheimer's Disease, which highlight the potential of the proposed approach to map disease heterogeneity in neuroimaging studies.

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Figures

Fig. 1
Fig. 1
Heterogeneity due to the presence of two clusters. Left: Result obtained by linear SVM (small margin). Right: Result obtained by separately classifying each cluster (large margin). Solid lines correspond to the classifier, dashed lines indicate margin, while highlighted linear segments define the separating convex polytope.
Fig. 2
Fig. 2
Sythetic data experiments: Left: Data, optimal polytope classifier and the cluster assignments, Middle: Cross-validated adjusted Rand index across folds. Right: Cross-validated classification accuracy. Note: K = 1 corresponds to linear SVM.
Fig. 3
Fig. 3
Top: a) Gray Matter Group Differences (p<0.05) between CN and AD. Shape glossary: pentagon=caudate, ellipse=insula, square=thalamus, triangle=left cuneus, hexagon=right hippocampus b) Group differences (p<0.05) between CN vs. 3 subtypes of AD c). Group differences (p<0.05) between 3 different AD subtypes. Color-map: Right group compared to left group [ Red: loses volume]/[ Cyan: gains volume] — Bottom: Left: Imaging features projected along the 3 faces of the polytope classifier, CN, AD group 1, AD group 2, AD group 3. Middle: Cross-validated adjusted Rand index across folds. Right: Cross-validated classification acccuracy.
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