Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
SIAM Journal on Scientific Computing
Matrix approximation and projective clustering via volume sampling
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On the Nyström Method for Approximating a Gram Matrix for Improved Kernel-Based Learning
The Journal of Machine Learning Research
Tumor Invasion Margin on the Riemannian Space of Brain Fibers
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part II
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We present a novel manifold learning approach to efficiently identify low-dimensional structures, known as manifolds, embedded in large-scale, high dimensional MRI datasets for brain tumor growth prediction. The datasets consist of a series of MRI scans for three patients with tumor and progressed regions identified. We attempt to identify low dimensional manifolds for tumor, progressed and normal tissues, and most importantly, to verify if the progression manifold exists - the bridge between tumor and normal manifolds. By mapping the bridge manifold back to MRI image space, this method has the potential to predict tumor progression, thereby, greatly benefiting patient management. Preliminary results supported our hypothesis: normal and tumor manifolds are well separated in a low dimensional space and the progressed manifold is found to lie roughly between them but closer to the tumor manifold.