Hands-On Unsupervised Learning with Python

Gaussian mixture

Gaussian mixture is one of the most well-known soft clustering approaches, with dozens of specific applications. It can be considered the father of k-means, because the way it works is very similar; but, contrary to that algorithm, given a sample x_i ∈ X and k clusters (which are represented as Gaussian distributions), it provides a probability vector, [p(x_i ∈ C₁), ..., p(x_i ∈ C_k)].

In a more general way, if the dataset, X, has been sampled from a data-generating process, p_data, a Gaussian mixture model is based on the following assumption:

In other words, the data-generating process is approximated by the weighted sum of multivariate ...