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The on-line textbook: Information Theory, Inference, and Learning Algorithms, by David J.C. MacKay includes simple examples of the EM algorithm such as clustering using the soft k-means algorithm, and emphasizes the variational view of the EM algorithm, as described in Chapter 33.7 of version 7.2 (fourth edition).
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.
Second, it is conceptually close to nearest neighbor classification, and as such is popular in machine learning. Third, it can be seen as a variation of model-based clustering, and Lloyd's algorithm as a variation of the Expectation-maximization algorithm for this model discussed below. k-means clustering examples
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]
Several of these models correspond to well-known heuristic clustering methods. For example, k-means clustering is equivalent to estimation of the EII clustering model using the classification EM algorithm. [8] The Bayesian information criterion (BIC) can be used to choose the best clustering model as well as the number of clusters. It can also ...
The mixture of experts, being similar to the gaussian mixture model, can also be trained by the expectation-maximization algorithm, just like gaussian mixture models. Specifically, during the expectation step, the "burden" for explaining each data point is assigned over the experts, and during the maximization step, the experts are trained to ...
The expectation–maximization algorithm can be treated as a special case of the MM algorithm. [1] [2] However, in the EM algorithm conditional expectations are usually involved, while in the MM algorithm convexity and inequalities are the main focus, and it is easier to understand and apply in most cases. [3]
Assign each non-core point to a nearby cluster if the cluster is an ε (eps) neighbor, otherwise assign it to noise. A naive implementation of this requires storing the neighborhoods in step 1, thus requiring substantial memory. The original DBSCAN algorithm does not require this by performing these steps for one point at a time.