1. On Utillizing LVQ3-Type Algorithms to Enhance Prototype Reduction Schemes Sang-Woon Kim and B. John Oommen* Myongji University, Carleton University*

2. Workshop on PRIS’ 2002 Outline of the Study Introduction Overview of the Prototype Reduction Schemes The Proposed Reduction Method Experiments & Discussions Conclusions

3. Workshop on PRIS’ 2002 Introduction (1) The Nearest Neighbor (NN) Classifier : A widely used classifier, which is simple and yet one of the most efficient classification rules in practice. However, its application often suffers from the computational complexity caused by the huge amount of information.

4. Workshop on PRIS’ 2002 Introduction (2) Solving strategies to the problem : Reducing the size of the design set without sacrificing the performance. Accelerating the speed of computation by eliminating the necessity of calculating many distances. Increasing the accuracy of the classifiers designed with limited samples.

5. Workshop on PRIS’ 2002 Motivation of the Study zIn NN classifications, prototypes near the boundary play more important roles. zThe prototypes need to be moved or adjusted towards the classification boundary. zThe proposed approach is based on this philosophy, namely that of creating and adjusting.

6. Workshop on PRIS’ 2002 Prototype Reduction Schemes - Conventional Approaches - The Condensed Nearest Neighbor (CNN) : The RNN, SNN, ENN, mCNN rules The Prototypes for Nearest Neighbor (PNN) classifiers The Vector Quantization (VQ) & Bootstrap (BT) techniques The Support Vector Machines (SVM)

7. Workshop on PRIS’ 2002 A Graphical Example (PNN)

8. Workshop on PRIS’ 2002 LVQ3 Algorithm An improved LVQ algorithm : Learning Parameters : Initial vectors Learning rates : Iteration numbers Training Set = Placement + Optimizing:

9. Workshop on PRIS’ 2002 Support Vector Machines (SVM) The SVM has a capability of extracting vectors which support the boundary between two classes, and they can satisfactorily represent the global distribution structure.

10. Workshop on PRIS’ 2002 Extension by Kernels

11. Workshop on PRIS’ 2002 The Proposed Method First, the CNN, PNN, VQ, SVM are employed to select initial prototype vectors. Next, an LVQ3-type learning is performed to adjust the prototypes: Perform the LVQ3 with Tip to select w Perform the LVQ3 with Tip to select e Repeat the above steps to obtain the best w* and e* Finally, determine the best prototypes by invoking the learning n times with Tip and Tio.

12. Workshop on PRIS’ 2002 Experiments The proposed method is tested with artificial and real benchmark design data sets, and compared with the conventional methods. The one-against-all NN classifier is designed. Benchmark data sets :

13. Workshop on PRIS’ 2002

15. Experimental Results (3)

16. Workshop on PRIS’ 2002 Experimental Results (4)

17. Workshop on PRIS’ 2002 Data Compression Rates

18. Workshop on PRIS’ 2002 Classification Error Rates (%) - Before Adjusting -

19. Workshop on PRIS’ 2002 Classification Error Rates (%) - After Adjusting with LVQ3 -

20. Workshop on PRIS’ 2002 Conclusions The method provides a principled way of choosing prototype vectors for designing NN classifiers. The performance of a classifier trained with the method is better than that of the CNN, PNN, VQ, and SVM classifier. The future work is to expand this study into large data set problems such as data mining and text categorization.