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This led Wolfe to think about how to do the same thing for continuous data, and in 1965 he did so, proposing the Gaussian mixture model for clustering. [42] [43] He also produced the first software for estimating it, called NORMIX. Day (1969), working independently, was the first to publish a journal article on the approach. [44]
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
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.
The cluster center is indicated by the lighter, bigger symbol. An animation demonstrating the EM algorithm fitting a two component Gaussian mixture model to the Old Faithful dataset. The algorithm steps through from a random initialization to convergence.
Standard model-based clustering methods include more parsimonious models based on the eigenvalue decomposition of the covariance matrices, that provide a balance between overfitting and fidelity to the data. One prominent method is known as Gaussian mixture models (using the expectation-maximization algorithm).
Additionally, the nonparametric nature of this model makes it an ideal candidate for clustering problems where the distinct number of clusters is unknown beforehand. In addition, the Dirichlet process has also been used for developing a mixture of expert models, in the context of supervised learning algorithms (regression or classification ...
Fuzzy C-Means Clustering is a soft version of k-means, where each data point has a fuzzy degree of belonging to each cluster. Gaussian mixture models trained with expectation–maximization algorithm (EM algorithm) maintains probabilistic assignments to clusters, instead of deterministic assignments, and multivariate Gaussian distributions ...
Types of generative models are: Gaussian mixture model (and other types of mixture model) Hidden Markov model; Probabilistic context-free grammar; Bayesian network (e.g. Naive bayes, Autoregressive model) Averaged one-dependence estimators; Latent Dirichlet allocation; Boltzmann machine (e.g. Restricted Boltzmann machine, Deep belief network)