Optimization of K-NN by feature weight learning

The Euclidean distance is usually chosen as the similarity measure in the conventional similarity metrics, which usually relates to all attributes. The smaller the distance is, the greater the similarity is. All the features of each vector have different functions in describing samples. So we can decide different function of every feature by using feature weight learning, that is, introduce feature weight parameters to the distance formula. Feature weight learning can be viewed as a linear transformation for a set of points in the Euclidean space. The numerical experiments applied in K-NN algorithm prove the validity of this learning algorithm.