Difference between Manhattan distance and Euclidean distance

・In Japanese

■What is Manhattan distance and Euclidean distance?

Both the Manhattan distance and the Euclidean distance represent the distance between two points on coordinates. The Manhattan distance represents the distance between two points when moving parallel to each of the x and y axes, and the Euclidean distance represents the straight line distance between the two points. The index that determines the size of such a vector is called norm.



The origin of the name is that the Manhattan distance is likened to moving across the grid-like Manhattan streets, and the Euclidean distance comes from the name of an ancient Greek mathematician.

■Properties of Manhattan Distance and Euclidean Distance

If the distance from the origin is 1, the Manhattan distance and Euclidean distance are as follows.

■Uses of Manhattan Distance and Euclidean Distance

Used for loss calculation in Lasso regression and Ridge regression.

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