Gaussian Mixture Model Explained: What are they & when to use?

The Gaussian mixture model, also known as the Mixture of Gaussian, is not a model but a probability distribution. GMM machine learning algorithms help classify data into various categories based on a probability distribution. The idea was popularised and brought to the forefront by Duda and Hart in 1973. Today, it has made its way into multiple fields like marketing, finance, etc. 

If you’re looking forward to knowing more about the Gaussian mixture model, this piece talks about the model, its uses, applications in real life, and much more. So, keep reading to learn more about gaussian mixture model!

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What is Clustering?

A range of values in a given data set can be grouped into clusters relevant to machine learning, called clustering. There are multiple methods for measuring it, including hierarchical clustering, K-means clustering, Gaussian mixture model, etc.

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What is a Gaussian distribution?

A Gaussian distribution, also called ‘normal distribution’, is a symmetric probability distribution. The symmetry is about its mean, which refers to the data closer to the mean value occurring more frequently in a given data set. If represented graphically, a Gaussian distribution resembles a bell-shaped curve. Here’s what it looks like:

Source

Understanding what the Gaussian mixture model is

Any unsupervised data set includes many data point sets following the Gaussian distribution, which means the data set can have multiple peaks. Thus extracting data from such a vast set is only possible by putting the Gaussian mixture model to play.

GMM is a probabilistic model representing the normal distribution of a population subset within a larger set. It is essentially an ‘unsupervised’ learning algorithm. The term ‘Gaussian’ indicates Gaussian distribution itself, a convenient distribution in terms of mathematics and popularity. 

The ‘Mixture’ indicates a mix of multiple Gaussian distributions. Each Gaussian in a Gaussian mixture model is identifiable by k ∈ {1,…, K}, and the ‘K’ is the total number of Gaussian clusters in a particular set.

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Every Gaussian has specific parameters, namely:

• Mean μ: It is the centre of the distribution.
• Covariance Σ: It defines the width of the distribution.
• Mixing probability π: It represents the size of the Gaussian function, i.e., how small or big it’ll be.

The parameters are graphically represented below:

Source

The graph describes three separate Gaussian functions, and thus K will be 3. 

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Expectation Maximisation: what is it?

E indicates ‘Expectation’ and M indicates ‘Maximisation,’ a powerful implementation that estimates the GMM parameters. The ‘E’ helps the user find the GMM parameters, while ‘M’ helps determine any scope for new data points to be added.

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Gaussian mixture model python: Key steps

There are three crucial steps to using the Gaussian mixture model. These are:

Step 1: Determine the covariance matrix that describes how one Gaussian can be related to the others. The more the similarity between two Gaussian sets, the greater the closeness of the means will be.

Step 2: Find out the total Gaussian number in each group. This way, it defines the total number of clusters in each set.

Step 3: Choose the hyperparameters; these help to separate data optimally by putting GMM to use. Furthermore, it helps decide if the Gaussian’s covariance matrix takes a diagonal shape or is symmetric.

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Gaussian mixture model: What are its applications?

The application of the Gaussian mixture model is mainly linked with fields like image, video, audio, and signal because any minute change in data points of such fields can bring drastic changes to the entire data set. Thus, GMM can be used for signal processing and abstracting multiple attributes of the signal data. Furthermore, GMM has also found its use in speech recognition,  computer vision, and image processing to help detect anomalies and segment images.

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