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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.
Because the minimization over all possible sets of cluster centers is prohibitively complex, the distortion is computed in practice by generating a set of cluster centers using a standard clustering algorithm and computing the distortion using the result. The pseudo-code for the jump method with an input set of p-dimensional data points X is:
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.
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 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 ]
Such a model can be trained with the expectation-maximization algorithm on an unlabeled set of hand-written digits, and will effectively cluster the images according to the digit being written. The same model could then be used to recognize the digit of another image simply by holding the parameters constant, computing the probability of the ...
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]
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.