1. By Fernando Seoane, April 25 th, 2006 Demo for Non-Parametric Classification Euclidean Metric Classifier with Data Clustering

2. By Fernando Seoane, April 25 th, 2006 Data Classification by Similarity The similarities among the data is the basis of this type of classification –Similar data is classified together Similar term in the mathematical sense, it must be mathematically defined –In the metric Space: Euclidean Distance, Manhattan distance, etc Nearest-Neighbor approach

3. By Fernando Seoane, April 25 th, 2006 Classification Method Training data Class a Training data Class b Cluster Partitioning Cluster Centers a Cluster Centers b Unclassified data Neighbor Evaluation Minimum distance Data classified as Class a Data classified as Class b Steps  A priori information. Classified Observations  Model Reduction to reduce computation. Use of nearest-neighbor approach. A cluster point represents a group of neighbor data points. Voronoid Tesselation Selection of no. of Cluster centers is important.  The unclassified measurements are evaluation against the clusters points.  K-nearest neighbor rule is applied for Euclidean distance and k = 1

4. By Fernando Seoane, April 25 th, 2006 K-means and K-medoid algorithms

5. By Fernando Seoane, April 25 th, 2006 Feature Space for Training Observations

6. By Fernando Seoane, April 25 th, 2006 Kmedoid Function Syntax: [result]=Kmedoid(data.X,param.c) Function: The objective function Kmedoid algorithm is to partition the data set X into c clusters Result: The calculated cluster center v i (i Є {1, 2,..c}) is the nearest data point to the mean of the data points in cluster i.

7. By Fernando Seoane, April 25 th, 2006 Cluster Partition for Case a

8. By Fernando Seoane, April 25 th, 2006 Cluster Partition for Case b

9. By Fernando Seoane, April 25 th, 2006 Cluster Partition all Cases

10. By Fernando Seoane, April 25 th, 2006 New Observations in the Feature Space

11. By Fernando Seoane, April 25 th, 2006 New Observations Classified

12. By Fernando Seoane, April 25 th, 2006 To Validate the cluster perfomance classifying the a priori training data To test the effect on the clusters perfomance the no. of cluster protoypes To try classification using the complete training data, without Cluster partitioning To Increase K in the nearest neighbor selection Improvements and Suggestions

13. By Fernando Seoane, April 25 th, 2006 The End Thank You!