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Regularization in Matrix Relevance Learning

This study presents a regularization scheme for metric adaptation methods in Learning Vector Quantization (LVQ) to prevent oversimplification of distance measures. The regularization aims to enhance classification performance and learning dynamics by preventing overfitting. The methodology includes matrix learning in LVQ and Generalized LVQ (GLVQ), with an emphasis on minimizing the cost function. Experimental results demonstrate the effectiveness of the proposed scheme in preventing instabilities, improving generalization, and deriving discriminative visualizations. Applications include enhancing the Vector Quantization process in artificial neural networks.

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Regularization in Matrix Relevance Learning

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  1. Regularization in Matrix Relevance Learning Petra Schneider, Kerstin Bunte, Han Stiekema, Barbara Hammer, Thomas Villmann, and Michael Biehl TNN, 2010 Presented by Hung-Yi Cai 2011/6/29

  2. Outlines • Motivation • Objectives • Methodology • Experiments • Conclusions • Comments

  3. Motivation • Matrix learning tends to perform an overly strong feature selection which may have negative impact on the classification performance and the learning dynamics.

  4. Objectives To propose a regularization scheme for metric adaptation methods in LVQ to prevent the algorithms from oversimplifying the distance measure. The standard motivation for regularization is to prevent a learning system from overfitting.

  5. Methodology • Matrix Learning in LVQ • LVQ aims at parameterizing a distance-based classification scheme in terms of prototypes. • Learning aims at determining weight locations for the prototypes such that the given training data are mapped to their corresponding class labels.

  6. Methodology • Matrix Learning in GLVQ • Matrix learning in GLVQ is derived as a minimization of the cost function

  7. Methodology • Regularized cost function • The approach can easily be applied to any LVQ algorithm with an underlying cost function . • In case of GMLVQ, the extended cost function… • The update rule for the metric parameters…

  8. Experiments Artificial Data

  9. Experiments • Real-Life Data • Pima Indians Diabetes

  10. Experiments • Real-Life Data • Glass Identification

  11. Experiments • Real-Life Data • Letter Recognition

  12. Conclusions • The proposed regularization scheme prevents oversimplification, eliminates instabilities in the learning dynamics, and improves the generalization ability of the considered metric adaptation algorithms. • The new method turns out to be advantageous to derive discriminative visualizationsby means of GMLVQ with a rectangular matrix.

  13. Comments • Advantages • Improving the VQ in the ANN. • Drawbacks • It’s very difficult to understand. • Applications • Learning Vector Quantization

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