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k-means clustering AND Mixture distribution

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In Depth: Gaussian Mixture Models | Python Data Science Handbook

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The non-probabilistic nature of [k-means](/tag/k_means_clustering) and its use of simple distance-from-cluster-center to assign cluster membership leads to poor performance for many real-world situations. We take a look at Gaussian mixture models (GMMs), which can be viewed as an extension of the ideas behind k-means, but can also be a powerful tool for estimation beyond simple clustering.

A Gaussian mixture model (GMM) attempts to find a mixture of multi-dimensional Gaussian probability distributions that best model any input dataset. In the simplest case, GMMs can be used for finding clusters in the same manner as k-means.

But because GMM contains a probabilistic model under the hood, it is also possible to find probabilistic cluster assignments (in Scikit-Learn, using predict_proba)

> Though GMM is often categorized as a clustering algorithm, fundamentally it is an algorithm for density estimation. That is to say, the result of a GMM fit to some data is technically not a clustering model, but a generative probabilistic model describing the distribution of the data.

-> a natural means of determining the optimal number of components for a given dataset

2018-03-16 About