Euclidean Distance
The straight-line distance between two points in space, commonly used in proximity analysis (standard GIS usage).
What does Euclidean Distance tell us about?
Euclidean Distance is a measure that tells us how far apart two points are in a straight line in space. It is the most common way of calculating distance between two points in Euclidean space (the normal 2D or 3D space we’re familiar with).
Mathematically, for two points (x1,y1)(x_1, y_1)(x1,y1) and (x2,y2)(x_2, y_2)(x2,y2) in a 2D plane, the Euclidean distance is calculated as:
Distance=(x2−x1)2+(y2−y1)2\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}Distance=(x2−x1)2+(y2−y1)2
This formula can be extended to higher dimensions as well.
Practically speaking, Euclidean distance informs us of:
The degree of similarity or difference between two data points is determined by their distance from one another.
It is extensively utilized in image processing, geography, and machine learning (e.g., k-nearest neighbours, clustering, and determining the shortest path or direct distance between sites).
It facilitates the measurement of the distance between geographic coordinates in spatial analysis, which is helpful for tasks like facility location, route optimization, and feature identification.
To put it simply, Euclidean distance offers a simple, intuitive method for calculating the "as-the-crow-flies" distance between two points.
Related Keywords
Euclidean distance calculates the shortest straight-line distance between two points. In 2D:
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
In 3D, include (z_2 - z_1)^2.
The Euclidean distance in machine learning calculates the distance in a straight line between two locations in multidimensional space. The idea that nearby points are more similar is commonly employed in algorithms like KNN and clustering to evaluate similarity.
The Pythagorean theorem is used to compute the Euclidean distance, which is the straight-line ("as-the-crow-flies") distance between two locations in space. Manhattan distance, on the other hand, is the total of the absolute differences of the coordinates and is calculated by only moving along axes at right angles, much like navigating a city grid. Manhattan accommodates discrete or grid-like movement, whereas Euclidean is better for continuous spaces.
Euclidean distance is the straight-line distance between two points, found using:
\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + \dots}