The Relationship of Euclidean Distance and Gaussian Distribution – Machine Learning Tutorial

By | February 6, 2021

Can we compute a probability by distance? In this tutorial, we will discuss the relationship of duclidean distance and gaussian distribution, which will help us to convert a distance to a probability.

Euclidean Distance

Euclidean distance can be defined as:

Euclidean distance in tensorflow

In tensorflow, we can compute it easily.

Calculate Euclidean Distance in TensorFlow: A Step Guide – TensorFlow Tutoria

Gaussian Distribution

Gaussian distribution is defined as:

the equation of Gaussian Distribution

Here is a tutorial on it.

An Introduction to Gaussian Distribution or Normal Distribution – Machine Learning Tutorial

The Relationship of Euclidean Distance and Gaussian Distribution

We can find the euclidean distance is a scalar value. As to gaussian distribution, \((x-\mu)^2\) measures the distance from \(x\) to the center \(\mu\).

If we replace \((x-\mu)^2\) using euclidean distance,we can build a bridge between euclidean distance and gaussian distribution. Here is an example:

The Relationship of Euclidean Distance and Gaussian Distribution - Machine Learning Tutorial

Here we will compute \(p(c|w)\) based on the euclidean distance.

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