Nearest and k-nearest Neighbor Classification COMPE 467 - Pattern Recognition
1-NN Rule: Given an unknown sample X decide if for That is, assign X to category if the closest neighbor of X is from category i.
k-NN rule: instead of looking at the closest sample, we look at k nearest neighbors to X and we take a vote. The largest vote wins. k is usually taken as an odd number so that no ties occur.
Distance Measures(Metrices) Non-negativity Reflexivity when only x=y Symmetry Triangle inequality Euclidian distance satisfies. Not always a meaningful measure. Consider 2 features with different units scaling problem. Scale of changed to half.
Minkowski Metric A general definition norm – City block (Manhattan) distance norm – Euclidian Scaling: Normalize the data by re-scaling (Reduce the range to 0-1) (equivalent to changing the metric) Y b X a
References • R.O. Duda, P.E. Hart, and D.G. Stork, Pattern Classification, New York: John Wiley, 2001. • N. Yalabık, “Pattern Classification with Biomedical Applications Course Material”, 2010.