Hellinger distance

Ever wondered how to measure differences between two things?

Imagine you're comparing two playlists of songs to see how similar they are. You want a way to quantify that similarity or difference.

Think of it like comparing the playlists by looking at how many songs each playlist shares and how these similarities relate to the rest of the songs in each playlist. The formula for Bhattacharyya distance helps us do this by considering the square root of the sum of the squares of the differences between corresponding probabilities.

Example

If Playlist A has a probability of 0.8 for song X and Playlist B has a probability of 0.6 for the same song, the Bhattacharyya distance for song X would be √(0.8² + 0.6²).

Remember this

The Bhattacharyya distance gives us a numerical value to understand how similar two probability distributions are, like comparing playlists based on shared songs.

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

Related concepts

Kolmogorov–Smirnov test

Ever wondered how scientists know if two things are the same or not?

Cross-entropy H(p,q) = -Σ p(x) log q(x) measures how well q approximates p

Ever wondered how well we can guess the outcome of a random event?

Culture of India

How can we measure differences between two things?

Conditional probability

P(A|B) = P(A ∩ B) / P(B)

the Lp norm ball shape changes as p goes from 1 to 2 to infinity

How does the shape of a ball change as we measure distance differently?

Great-circle distance

Ever wondered how to measure distance on a globe?

Swipe through more Machine Learning concepts

Open Pocket Polymath