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The Expectation Maximization Algorithm: A short tutorial, A self-contained derivation of the EM Algorithm by Sean Borman. The EM Algorithm, by Xiaojin Zhu. EM algorithm and variants: an informal tutorial by Alexis Roche. A concise and very clear description of EM and many interesting variants.
Divisive Clustering: Top-down approach. Large clusters are split into smaller clusters. [3] Density-based Clustering: A structure is determined by the density of data points. [4] DBSCAN; Distribution-based Clustering: Clusters are formed based on mathematical methods from data. [1] Expectation-maximization algorithm; Collocation; Stemming Algorithm
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]
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.
When developing new algorithms or index structures, the existing components can be easily reused, and the type safety of Java detects many programming errors at compile time. ELKI is a free tool for analyzing data, mainly focusing on finding patterns and unusual data points without needing labels.
The parameters of the model, and for =, …,, are typically estimated by maximum likelihood estimation using the expectation-maximization algorithm (EM); see also EM algorithm and GMM model. Bayesian inference is also often used for inference about finite mixture models. [ 2 ]
This training algorithm is an instance of the more general expectation–maximization algorithm (EM): the prediction step inside the loop is the E-step of EM, while the re-training of naive Bayes is the M-step.
Also, the convergence of the algorithm in higher dimensions with a finite number of the stationary (or isolated) points has been proved. [5] [7] However, sufficient conditions for a general kernel function to have finite stationary (or isolated) points have not been provided. Gaussian Mean-Shift is an Expectation–maximization algorithm. [8]