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An Algorithm for a Large Scale Constrained Eigenvalue Problem
Student-Run Research Seminar| Speaker: | Yunshen Zhou, UC Davis |
| Related Webpage: | https://www.math.ucdavis.edu/~yszhou/ |
| Location: | 2112 MSB |
| Start time: | Thu, Jan 25 2018, 12:10PM |
In many applications such as normalized cut, transductive learning and outlier removal, we need to solve a problem of minimizing a Rayleigh quotient with linear constraints. We first show how to eliminate the linear constraints by orthogonal projection, and then reformulate it as a equivalent quadratic eigenvalue problem (QEP). We reduce the QEP by the Lanczos algorithm and then solve the eigenvalues and eigenvectors of the reduced QEP by linearization and use the eigenvalues and eigenvectors to approximate the solution of the CRQ. We also give the convergence analysis for the algorithm. Numerical examples and applications of image segmentation are given to show the efficiency of the proposed approach.
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