1. Intelligent Database Systems Lab 國立雲林科技大學 National Yunlin University of Science and Technology 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. Intelligent Database Systems Lab N.Y.U.S.T. I. M. 2 Outlines  Motivation  Objectives  Methodology  Experiments  Conclusions  Comments

3. Intelligent Database Systems Lab N.Y.U.S.T. I. M. 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. Intelligent Database Systems Lab N.Y.U.S.T. I. M. 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. Intelligent Database Systems Lab N.Y.U.S.T. I. M. 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. 5

6. Intelligent Database Systems Lab N.Y.U.S.T. I. M. Methodology Matrix Learning in GLVQ Matrix learning in GLVQ is derived as a minimization of the cost function 6

7. Intelligent Database Systems Lab N.Y.U.S.T. I. M. 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… 7

8. Intelligent Database Systems Lab N.Y.U.S.T. I. M.  Artificial Data Experiments 8

9. Intelligent Database Systems Lab N.Y.U.S.T. I. M.  Real-Life Data ─ Pima Indians Diabetes Experiments 9

10. Intelligent Database Systems Lab N.Y.U.S.T. I. M. Experiments  Real-Life Data ─ Glass Identification 10

11. Intelligent Database Systems Lab N.Y.U.S.T. I. M. Experiments  Real-Life Data ─ Letter Recognition 11

12. Intelligent Database Systems Lab N.Y.U.S.T. I. M. 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 visualizations by means of GMLVQ with a rectangular matrix.

13. Intelligent Database Systems Lab N.Y.U.S.T. I. M. 13 Comments  Advantages ─ Improving the VQ in the ANN.  Drawbacks ─ It’s very difficult to understand.  Applications ─ Learning Vector Quantization