An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
Spectral Graph Theory and its Applications
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Spectral Regression: A Unified Approach for Sparse Subspace Learning
ICDM '07 Proceedings of the 2007 Seventh IEEE International Conference on Data Mining
Discrete regularization on weighted graphs for image and mesh filtering
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
IEEE Transactions on Signal Processing
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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).