the sum of absolute differences

Euclidean distances are root sum-of-squares of differences, and manhattan distances are the sum of absolute differences.

the mathematical distance between two points, which is the sum of the absolute difference of their Cartesian coordinates

Manhattan Distance is the mathematical distance between two points, which is the sum of the absolute difference of their Cartesian coordinates.

a rectilinear distance

Unusual definitions of distance can be helpful to model certain physical situations, but are also used in theoretical mathematics: "Manhattan distance" is a rectilinear distance, named after the number of blocks north, south, east, or west a taxicab must travel on to reach a taxicab's destination on the grid of streets in parts of New York City.

the simple sum of the horizontal and vertical components

The Manhattan distance is the simple sum of the horizontal and vertical components, whereas the diagonal distance might be computed by applying the Pythagorean theorem.

The distance derived from this norm

The distance derived from this norm is called the Manhattan distance or 1 distance.

the first root of the sum of differences , and the Euclidean distance, or raised to the first power

The Manhattan distance, or 1-norm, is the first root of the sum of differences raised to the first power, and the Euclidean distance, or 2-norm, is the square root of the sum of differences raised to the second power.

the sum of absolute differences between points across all the dimensions

Manhattan Distance is the sum of absolute differences between points across all the dimensions.

the shortest distance between two points on a grid

Manhattan distance is the shortest distance between two points on a grid.

which is 30 miles away

Many residents commute to Manhattan, which is 30 miles away.

the distance between a pair of vectors

The Manhattan distance (also known as L1 norm and Taxicab Distance) - calculates the distance between a pair of vectors, as if simulating a route for a Manhattan taxi driver driving from point A to point B - who is navigating the streets of Manhattan with the grid layout and one-way streets.

The 1-norm distance

The 1-norm distance is more colorfully called the taxicab norm or Manhattan distance, because The 1-norm distance is the distance a car would drive in a city laid out in square blocks (if there are no one-way streets).

an alternative distance metric used in KNN

Manhattan distance, also known as city block distance, is an alternative distance metric used in KNN.

similarity distance

Manhattan Distance is the similarity distance that being used in this project study.

walking” distance

The manhattan distance is the actual “walking” distance as opposed to the straight line distance.

the distance a car would drive from one place to another place in a grid-based street system, whereas Euclidian distance (in two-dimensional space) is the “straight-line” distance between two points

For example, Manhattan distance is the distance a car would drive from one place to another place in a grid-based street system, whereas Euclidian distance (in two-dimensional space) is the “straight-line” distance between two points.

the distance we would have to walk in New York

The Manhattan distance (or rectangular distance) between two points is the distance we would have to walk in New York.

the path traversed represented by the line with arrow

the Manhattan distance is the path traversed represented by the line with arrow.

one mile

To calculate distances in New York City, bear in mind that 20 avenue (north-south) or 10 street blocks (east-west) are equal to one mile.

2.5 miles

Manhattan is 2.5 miles by 11 miles and has a river on either side with a total area of about 28 sq.

sum of absolute differences between expression values for genes in two sets

Manhattan distance: Distance is calculated as sum of absolute differences between expression values for genes in two sets.