Manhattan distance

In many situations, measuring the shortest distance between two points using the Euclidean distance measure will not truly represent the similarity or closeness between two points—for example, if two data points represent locations on a map, then the actual distance from point A to point B using ground transportation, such as a car or taxi, will be more than the distance calculated by the Euclidean distance. For situations such as these, we use Manhattan distance, which marks the longest route between two points and is a better reflection of the closeness of two points in the context of source and destination points that can be traveled to in a busy city. The comparison between the Manhattan and Euclidean distance measures is shown in the following plot:

Note that the Manhattan distance will always be equal or larger than the corresponding Euclidean distance calculated.