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The EM algorithm consists of two steps: the E-step and the M-step. Firstly, the model parameters and the () can be randomly initialized. In the E-step, the algorithm tries to guess the value of () based on the parameters, while in the M-step, the algorithm updates the value of the model parameters based on the guess of () of the E-step.
A typical finite-dimensional mixture model is a hierarchical model consisting of the following components: . N random variables that are observed, each distributed according to a mixture of K components, with the components belonging to the same parametric family of distributions (e.g., all normal, all Zipfian, etc.) but with different parameters
Model-based clustering [1] based on a statistical model for the data, usually a mixture model. This has several advantages, including a principled statistical basis for clustering, and ways to choose the number of clusters, to choose the best clustering model, to assess the uncertainty of the clustering, and to identify outliers that do not ...
The slow "standard algorithm" for k-means clustering, and its associated expectation–maximization algorithm, is a special case of a Gaussian mixture model, specifically, the limiting case when fixing all covariances to be diagonal, equal and have infinitesimal small variance.
The average silhouette of the data is another useful criterion for assessing the natural number of clusters. The silhouette of a data instance is a measure of how closely it is matched to data within its cluster and how loosely it is matched to data of the neighboring cluster, i.e., the cluster whose average distance from the datum is lowest. [8]
However, these algorithms put an extra burden on the user: for many real data sets, there may be no concisely defined mathematical model (e.g. assuming Gaussian distributions is a rather strong assumption on the data). Gaussian mixture model clustering examples
In the sum, given an observed signal mixture , the corresponding set of extracted signals and source signal model = ′, we can find the optimal unmixing matrix , and make the extracted signals independent and non-gaussian. Like the projection pursuit situation, we can use gradient descent method to find the optimal solution of the unmixing matrix.
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