netresponse (version 1.32.2)

vdp.mixt: vdp.mixt

Description

Accelerated variational Dirichlet process Gaussian mixture.

Usage

vdp.mixt(dat, prior.alpha = 1, prior.alphaKsi = 0.01,
  prior.betaKsi = 0.01, do.sort = TRUE, threshold = 1e-05,
  initial.K = 1, ite = Inf, implicit.noise = 0, c.max = 10,
  speedup = TRUE, min.size = 5)

Arguments

dat

Data matrix (samples x features).

prior.alpha, prior.alphaKsi, prior.betaKsi

Prior parameters for Gaussian mixture model (normal-inverse-Gamma prior). alpha tunes the mean; alphaKsi and betaKsi are the shape and scale parameters of the inverse Gamma function, respectively.

do.sort

When true, qOFz will be sorted in decreasing fashion by component size, based on colSums(qOFz). The qOFz matrix describes the sample-component assigments in the mixture model.

threshold

Defines the minimal free energy improvement that stops the algorithm: used to define convergence limit.

initial.K

Initial number of mixture components.

ite

Defines maximum number of iterations on posterior update (updatePosterior). Increasing this can potentially lead to more accurate results, but computation may take longer.

implicit.noise

Adds implicit noise; used by vdp.mk.log.lambda.so and vdp.mk.hp.posterior.so. By adding noise (positive values), one can avoid overfitting to local optima in some cases, if this happens to be a problem.

c.max

Maximum number of candidates to consider in find.best.splitting. During mixture model calculations new mixture components can be created until this upper limit has been reached. Defines the level of truncation for a truncated stick-breaking process.

speedup

When learning the number of components, each component is splitted based on its first PCA component. To speed up, approximate by using only subset of data to calculate PCA.

min.size

Minimum size for a component required for potential splitting during mixture estimation.

Value

• prior
  Prior parameters of the vdp-gm model (qofz: priors on observation lables; Mu: centroids; S2: variance).
• posterior
  Posterior estimates for the model parameters and statistics.
• weights
  Mixture proportions, or weights, for the Gaussian mixture components.
• centroids
  Centroids of the mixture components.
• sds
  Standard deviations for the mixture model components (posterior modes of the covariance diagonals square root). Calculated as sqrt(invgam.scale/(invgam.shape + 1)).
• qOFz
  Sample-to-cluster assigments (soft probabilistic associations).
• Nc
  Component sizes
• invgam.shape
  Shape parameter (alpha) of the inverse Gamma distribution
• invgam.scale
  Scale parameter (beta) of the inverse Gamma distribution
• Nparams
  Number of model parameters
• K
  Number of components in the mixture model
• opts
  Model parameters that were used.
• free.energy
  Free energy of the model.

Details

Implementation of the Accelerated variational Dirichlet process Gaussian mixture model algorithm by Kenichi Kurihara et al., 2007.

ALGORITHM SUMMARY This code implements Gaussian mixture models with diagonal covariance matrices. The following greedy iterative approach is taken in order to obtain the number of mixture models and their corresponding parameters:

1. Start from one cluster, $T = 1$. 2. Select a number of candidate clusters according to their values of "Nc" = \sum_{n=1}^N q_{z_n} (z_n = c) (larger is better). 3. For each of the candidate clusters, c: 3a. Split c into two clusters, c1 and c2, through the bisector of its principal component. Initialise the responsibilities q_{z_n}(z_n = c_1) and q_{z_n}(z_n = c_2). 3b. Update only the parameters of c1 and c2 using the observations that belonged to c, and determine the new value for the free energy, F{T+1}. 3c. Reassign cluster labels so that cluster 1 corresponds to the largest cluster, cluster 2 to the second largest, and so on. 4. Select the split that lead to the maximal reduction of free energy, F{T+1}. 5. Update the posterior using the newly split data. 6. If FT - F{T+1} < \epsilon then halt, else set T := T +1 and go to step 2.

The loop is implemented in the function greedy(...)

References

Kenichi Kurihara, Max Welling and Nikos Vlassis: Accelerated Variational Dirichlet Process Mixtures. In B. Sch"olkopf and J. Platt and T. Hoffman (eds.), Advances in Neural Information Processing Systems 19, 761--768. MIT Press, Cambridge, MA 2007.

Examples

set.seed(123)

  # Generate toy data with two Gaussian components
  dat <- rbind(array(rnorm(400), dim = c(200,2)) + 5,
               array(rnorm(400), dim = c(200,2)))

  # Infinite Gaussian mixture model with 
  # Variational Dirichlet Process approximation
  mixt <- vdp.mixt( dat )

  # Centroids of the detected Gaussian components
  mixt$posterior$centroids

  # Hard mixture component assignments for the samples
  apply(mixt$posterior$qOFz, 1, which.max)