# Euclidean Distance

## Definition of Euclidean Distance

Euclidean Distance: The Euclidean distance between two points is the length of the straight line between them.

## What is Euclidean Distance used for?

Euclidean Distance is a mathematical tool used to measure the distance between two points in a multidimensional space. It is also known as the “straight line” or “as-the-crow-flies” distance, due to its direct route from one point to another. This distance can be useful for comparing different datasets and determining how similar or different they are from each other, allowing us to detect patterns and find correlations between them. Furthermore, this metric is was commonly used in Machine Learning algorithms for clustering and classification tasks, such as K-Means Clustering and Nearest Neighbor Classification.

The most basic form of Euclidean Distance calculation is the Pythagorean Theorem which states that the sum of the squares of the sides of a right triangle equal the square of its hypotenuse (a^2 + b^2 = c^2). Using this formula, we can calculate distances by taking two points in space and connecting them with a line, then measuring the length of that line (the hypotenuse). However, when dealing with higher dimensions, we must use variations of this equation that are more complex but still yield accurate results.

Another application of Euclidean Distance involves finding out how close two vectors are in terms not just their magnitude but also their direction. This often requires transforming matrices into a form called Orthogonal Matrix where only those entries that represent angles between vectors need to be calculated. By doing so it’s possible to determine similarity between two datasets by examining their angles relative to each other.

Overall, Euclidean Distance provides an efficient way for data scientists and machine learning practitioners alike to compare various data sets among themselves and make effective decisions on which ones can be useful going forward. It’s easy enough to compute given its relatively simple equation so it often serves as a reliable starting point when first analyzing any type of dataset.