Euclidean Distance (KNN)

This formula measures the ordinary straight-line distance between two points in a feature space by taking the difference in each coordinate, squaring those differences, adding them up, and then square-rooting the result. The squaring makes every coordinate difference positive and gives larger mismatches more influence, while the square root returns the total to the original scale. In k-nearest neighbours, this is useful because points with smaller Euclidean distance are usually more similar under equal-weighted numeric features.

Use it when your data points are numeric and each feature is measured on a comparable scale, such as height/weight data, coordinates, sensor readings, or simple embedding vectors. It is a common default choice in k-nearest neighbours for classification or regression when you want “closest in ordinary geometry” to mean “most similar.”

• Forgetting to square the coordinate differences before adding them
• Mixing up the order of subtraction and thinking it changes the final distance
• Using Euclidean distance on features with very different scales without normalizing first