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# Lieven de lathauwer thesis writing

by Berkant Savas. 2003

“. This report is a masters thesis written at the Department of Mathematics, Linköping University. Two different classification algorithms for handwritten digit recognition have been thoroughly analysed. The first algorithm uses Higher Order Singular Value Decomposition (HOSVD) of the training digits. “

This report is a masters thesis written at the Department of Mathematics, Linköping University. Two different classification algorithms for handwritten digit recognition have been thoroughly analysed. The first algorithm uses Higher Order Singular Value Decomposition (HOSVD) of the training digits. The second algorithm relies on a specific distance measure, which is invariant to different transformations, called Tangent Distance (TD). This algorithm was modified in the implementation part by the use of numerical derivatives and an approximation of the blurring operator. Two more classification algorithms were constructed by combining the first two algorithms. All constructed algorithms have been tested with good performance for some of them. The best results were achieved by the Tangent Distance classifier with an error rate of 3 %. Finally the results of a few other classifiers are presented and compared with the test results obtained in this report.

by Examensarbete Utfört I Numerisk Analys, Berkant Savas, Examensarbete Utfört I Numerisk Analys, Supervisor Lars Eldén, Examiner Lars Eldén, Berkant Savas. 2003

“. This report is a masters thesis written at the Department of Mathematics, Linköping University. Two different classification algorithms for handwritten digit recognition have been thoroughly analysed. The first algorithm uses Higher Order Singular Value Decomposition (HOSVD) of the training digits. “

This report is a masters thesis written at the Department of Mathematics, Linköping University. Two different classification algorithms for handwritten digit recognition have been thoroughly analysed. The first algorithm uses Higher Order Singular Value Decomposition (HOSVD) of the training digits. The second algorithm relies on a specific distance measure, which is invariant to different transformations, called Tangent Distance (TD). This algorithm was modified in the implementation part by the use of numerical derivatives and an approximation of the blurring operator. Two more classification algorithms were constructed by combining the first two algorithms. All constructed algorithms have been tested with good performance for some of them. The best results were achieved by the Tangent Distance classifier with an error rate of 3 %. Finally the results of a few other classifiers are presented and compared with the test results obtained in this report.

he nth mode. It is easy to verify that different n–ranks of a higher order tensor are not necessarily equal as is the case considering matrices. There is a second way of defining the rank of a tensor =-=[2]-=-, but the definition will be omitted in this context. Scalar product, orthogonality and norm The scalar product for vectors is generalized to include tensors of any order in a straightforward way. Def.

## Refereed Publications

1. Convergence and Acceleration of the Regularized Alternating Least-Squares Algorithm for Tensor Approximation (With Xiaofei Wang), submitted. (arxiv.org/abs/1507.04721 )
• Low Rank Approximation of Tensors via Sparse Optimization (With Xiaofei Wang), submitted. (arxiv.org/abs/1504.05273 )

• Adaptive Low Rank Approximation of Tensors (With Xiaofei Wang), 2015 IEEE International Conference on Computer Vision Workshop (ICCVW), pp. 939-945, Santiago, Chile, 2015

• Higher Order Orthogonal Iteration with Random Projections for Low Multilinear Rank Tensors (With Deonnia N. Pompey), in I. Hotz, T. Schultz (eds.), Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, Mathematics and Visualization, pp. 93-106, Springer International Publishing Switzerland, 2015.

• Iterative Methods for Symmetric Outer Product Tensor Decompositions (With Na Li and Christina Glenn), Electronic Transactions on Numerical Analysis, 44, pp. 124-139, 2015. (arxiv.org/abs/1312.7629 )

• Tensor Restricted Isometry Property for Multilinear Sparse System for Gene Interactions (With Alexandra Fry), in the Proceedings of the IEEE Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, November 2014.

• New Algorithms for Tensor Decomposition based on a Reduced Functional. (With Stefan Kindermann ), Numerical Linear Algebra and Applications, 21 (3), pp. 542-570, 2014. (arxiv.org/abs/1109.3832 )

• Source Apportionment of Time and Size Resolved Ambient Particulate Matter. (With Philip Hopke. Na Li, Kumar Pramod and Steven Smith), J. Chemometrics and Intelligent Laboratory Systems, 129, pp. 15-20, 2013.

• Some Convergent Results of the Regularized Alternating Least-Squares for Tensor Decomposition. (With Stefan Kindermann and Na Li), Linear Algebra and Applications, 438 (2), pp. 796-812, 2013. (arxiv.org/abs/1109.3831 )

• Solving Multilinear Systems via Tensor Inversion. (With Michael Brazell, Na Li and Christino Tamon), SIAM Matrix Analysis, 34-2 (2013), pp. 542-570. (arxiv.org/abs/1109.3830 ) or (simax )

• Video Detection Anomaly via Low-Rank and Sparse Decompositions. (With Jiebo Luo and Lam Tran ), in the Proceedings of the IEEE New York Image Processing Workshop, Rochester, November 2012.

• Randomized tensor-based algorithm for image classification. (With Ryan Sigurdson), in the Proceedings of the IEEE Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, November 2012.

• Sparseness Constraints on Nonnegative Tensor Decomposition. (With Na Li), in the Proceedings of the IEEE Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, November 2010.

• Approximation of low rank solutions for linear quadratic control of partial differential equations. (With Kirsten Morris ) Computational Optimization and Applications, 46 (1) (2010), pp. 93-111.

• Recovery of Tensor Data from Incomplete Measurement via Compressed Sampling. (With Jason Holloway), in the 43rd IEEE Asilomar Conference on Signals, Systems, and Computers, pp. 1310-1314, Pacific Grove, November 2009.

• Low Multilinear Rank Tensor Decomposition via Semidefinite Programming. (With Lieven De Lathauwer ), in the 17th Proceedings of the European Signal Processing Conference, Glasgow, August 2009.

• Swamp reducing technique for tensor decomposition. (With Lieven De Lathauwer and Stefan Kindermann ) in the 16th Proceedings of the European Signal Processing Conference, Lausanne, August 2008.

• Patchy cost and feedback for the Hamilton-Jacobi-Bellman PDE. (With A. J. Krener ), in the 18th Proceedings of the Mathematical Theory of Networks and Systems, Blacksburg, Virginia, July 2008.

• Patchy Solution of the HJB PDE. (With Arthur J. Krener ), in A. Chiuso, A. Ferrante and S. Pinzoni, eds, Modeling, Estimation and Control, Lecture Notes in Control and Information Sciences, 364, pp. 251-270, 2007.

• Implementations of control laws for motion camouflage in a pursuit-evasion system. (With A. Asatryan, V. Attarian, Y.R. Huang, K.K. Leung, A. Joshi, V. Voroninski, M. Aboulian, K. McBride), in the Proceedings of IFIP Conference on Systems Modeling and Optimization, Cracow, July 2007. (UCLA CAM Report (06-62) ).

• Iterative solution of algebraic Riccati equations for damped systems. (With Kirsten Morris ), in the 45th Proceedings of the IEEE Conference on Decision and Control, San Diego, December 2006.

• Optimal control as a regularization method for ill-posed problems. (With Stefan Kindermann ), J. Inverse and Ill-Posed Problems, 14 (7), 2006, pp. 685-703.

• Solution of Algebraic Riccati Equations Arising in Control of Partial Differential Equations. (With Kirsten Morris ), in J. P. Zolesio and J. Cagnol, eds, Control and Boundary Analysis, Lecture Notes in Pure Appl. Math. v. 240, CRC Press, Boca Raton 2005.

• The Lax-Friedrichs Sweeping Method for Optimal Control Problem in Continuous and Hybrid Dynamics. (With Chiu-Yen Kao and Stanley Osher ), J. Nonlinear Analysis, 63 (5-7), pp. 1561-1572, 2005.

• Iterative Solution of Algebraic Riccati Equations using a Modified Newton-Klienman Method. (With Kirsten Morris ) in the 16th Proceedings of the Mathematical Theory of Networks and Systems, Brussels, July 2004.

• Solutions of Hamilton-Jacobi-Bellman Equations. (With Arthur Krener ), in the 39th Proceedings of the IEEE Conference on Decision and Control, Sydney, pp.570-574, December 2000.

## Thesis

1. Local Solutions of the Dynamic Programming Equations and the Hamilton- Jacobi-Bellman PDE. PhD Thesis, University of California, Davis, August 2002. (front.math.ucdavis.edu/math.OC/0208240 ).

## Other Manuscripts

1. Block Tensor Decomposition for Source Apportionment of Air Pollution. (With P. Hopke. M. Leung, N. Li) (arxiv.org/abs/1110.4133 )
• Tensors as Module Homomorphisms over Group Rings. (With M. Opperman, T. Penderghest, C. Tamon) (arxiv.org/abs/1005.1894 )

• Parameter Identification in Radio-Frequency Ablation. (With H. Tiesler and C. Bueskens), International Association of Applied Mathematics and Mechanics (Gesellschaft fur Angewandte Mathematik und Mechanik) March 2008

• Local Stable Manifold for the Bidirectional Discrete-Time Dynamics. (arxiv.org/abs/math/0309026 )

• Web Hosting Service Level Agreements. (With A. King et al) IBM Research Report, RC22031, January 2002. Also in Proceedings of the 5th Pacific Institute for Mathematical Sciences 2001 Industrial Problem Solving Workshop, University of Washington, Seattle, 2001.