“Computational Methods for Support Vector Machine Classification and Large-Scale Kalman Filtering”

Document Type

Presentation Abstract

Presentation Date

4-29-2013

Abstract

The first half of this talk focuses on computational methods for solving the bound and equality constrained quadratic program within the support vector machine classifier. An augmented Lagrangian approach will be presented, in which all the constraints are incorporated into the objective function to yield an unconstrained quadratic program, allowing us to apply the conjugate gradient method. This method outperforms other state-of-the-art methods on three image test cases.

The second half of this talk focuses on computational methods for large-scale Kalman filtering applications. The Kalman filter (KF) is a method for solving a dynamic, coupled system of equations. Standard KF is often infeasible in large-scale implementations due to the storage requirements and inverse calculations of large, dense covariance matrices. The use of the conjugate gradient (CG) method within various forms of the Kalman filter will be discussed for low-rank approximations of the covariance matrices, with low storage requirements. In test cases, the CG-based KF methods perform similarly in root-mean-square error when compared to the standard KF methods, when these implementations are feasible.

Additional Details

Doctoral Dissertation Defense. Link to the presenter's dissertation.

Dissertation Committee:
John Bardsley, Chair (Mathematical Sciences),
Jon Graham (Mathematical Sciences),
Jesse Johnson (Computer Science),
Albert Parker (Mathematical Sciences, MSU),
David Patterson (Mathematical Sciences) Monday, April 29, 2013
3:10 pm in Math 103

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