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Matched Signal Detection on Graphs: Theory and Application to Brain Network Classification
Chenhui Hu1,2, Lin Cheng3, Jorge Sepulcre1, Georges El Fakhri1, Yue M. Lu2, and Quanzheng Li1
1Center for Advanced Medical Imaging Science, NMMI, Radiology, Massachusetts General Hospital, Boston, MA 02114, USA
sepulcre@nmr.mgh.harvard.edu
elfakhri@pet.mgh.harvard.edu
Li.Quanzheng@mgh.harvard.edu
2School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA 02138
yuelu@seas.harvard.edu
3Department of Engineering, Trinity College, Hartford, CT 06106, USA
lin.cheng@trincoll.edu
Abstract. We develop a matched signal detection (MSD) theory for signals with an intrinsic structure described by a weighted graph. Hypothesis tests are formulated under different signal models. In the simplest scenario, we assume that the signal is deterministic with noise in a subspace spanned by a subset of eigenvectors of the graph Laplacian. The conventional matched subspace detection can be easily extended to this case. Furthermore, we study signals with certain level of smoothness. The test turns out to be a weighted energy detector, when the noise variance is negligible. More generally, we presume that the signal follows a prior distribution, which could be learnt from training data. The test statistic is then the difference of signal variations on associated graph structures, if an Ising model is adopted. Effectiveness of the MSD on graph is evaluated both by simulation and real data. We apply it to the network classification problem of Alzheimer’s disease (AD) particularly. The preliminary results demonstrate that our approach is able to exploit the sub-manifold structure of the data, and therefore achieve a better performance than the traditional principle component analysis (PCA).
Keywords: Matched subspace detection, graph-structured data, graph Laplacian, brain networks, classification, Alzheimer’s disease
LNCS 7917, p. 1 ff.
lncs@springer.com
© Springer-Verlag Berlin Heidelberg 2013