Two New Distance Metrics For K Nearest Neighbor Algorithm

Many machine learning algorithms, for example K Nearest Neighbor (KNN), heavily depend on the distance metric for the input data points. Distance Metric learning is to learn a distance for the input space of data from a given set of similar/dissimilar points which preserves the distance relation among the training data. Emerging research demonstrates, both empirically and theoretically, that a learned metric can significantly affect the performance in classification and clustering tasks.Here we have introduced two novel distance metrics for KNN algorithm: Sobolev and Fisher metrics. We applied these new metrics on breast cancer data from repository of UCI . The performance based on the new distance metrics was better than the usual metrics, such as: Euclidean and Manhattan.

Keywords:

K Nearest Neighbor , Sobolev , Fisher , Distance Metric