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

- Convergence and Acceleration of the Regularized Alternating Least-Squares Algorithm for Tensor Approximation (With Xiaofei Wang), submitted. (arxiv.org/abs/1507.04721 )

## Thesis

- 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

- Block Tensor Decomposition for Source Apportionment of Air Pollution. (With P. Hopke. M. Leung, N. Li) (arxiv.org/abs/1110.4133 )

*Proceedings of the 5th Pacific Institute for Mathematical Sciences 2001 Industrial Problem Solving Workshop,*University of Washington, Seattle, 2001.