title: Matched signal detection on graphs: theory and application to brain network classification.
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).
authors.forename: Chenhui
authors.initials: C
authors.lastname: Hu
authors.forename: Lin
authors.initials: L
authors.lastname: Cheng
authors.forename: Jorge
authors.initials: J
authors.lastname: Sepulcre
authors.forename: Georges
authors.initials: G
authors.lastname: El Fakhri
authors.forename: Yue M
authors.initials: YM
authors.lastname: Lu
authors.forename: Yue M
authors.initials: YM
authors.lastname: Lu
mesh_terms: D000465:Algorithms; D000544:Alzheimer Disease / Q000000981:diagnostic imaging* / Q000378:metabolism; D000814:Aniline Compounds; D052160:Benzothiazoles / Q000493:pharmacokinetics; D001921:Brain / Q000000981:diagnostic imaging* / Q000378:metabolism; D001931:Brain Mapping / Q000379:methods*; D063132:Connectome / Q000379:methods*; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods; D009415:Nerve Net / Q000000981:diagnostic imaging*; D009434:Neural Pathways / Q000000981:diagnostic imaging; D010363:Pattern Recognition, Automated / Q000379:methods*; D049268:Positron-Emission Tomography / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D013844:Thiazoles; D014018:Tissue Distribution
chemical_list: C475519:2-(4'-(methylamino)phenyl)-6-hydroxybenzothiazole; D000814:Aniline Compounds; D052160:Benzothiazoles; D013844:Thiazoles