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- The term 'distance' is used in Knn. Are these distance functions required to satisfy the properties of a metric?

Hi,

Just curious as to whether distances 'd' , used in Knn ; K nearest neighbors, in Machine Learning, are required to be metrics in the Mathematical Sense, i.e., if they are required to satisfy, in a space A:

##d: A \times A \rightarrow \mathbb R^{+} \cup \{0\} ;

d(a,a)=0 ;

d(a,b)=d(b,a) ; d(a,c) < d(a,b)+d(b,c) ##

?

Just curious as to whether distances 'd' , used in Knn ; K nearest neighbors, in Machine Learning, are required to be metrics in the Mathematical Sense, i.e., if they are required to satisfy, in a space A:

##d: A \times A \rightarrow \mathbb R^{+} \cup \{0\} ;

d(a,a)=0 ;

d(a,b)=d(b,a) ; d(a,c) < d(a,b)+d(b,c) ##

?