ICL Criterion for Model-Based Clustering

ICL (Integrated Complete-data Likelihood) for parameterized Gaussian mixture models fitted by EM algorithm initialized by model-based hierarchical clustering.

Usage

mclustICL(data, G = NULL, modelNames = NULL, 
          initialization = list(hcPairs = NULL, 
                                subset = NULL, 
                                noise = NULL), 
          x = NULL, ...)

# S3 method for mclustICL
summary(object, G, modelNames, ...)

Arguments

data

A numeric vector, matrix, or data frame of observations. Categorical variables are not allowed. If a matrix or data frame, rows correspond to observations and columns correspond to variables.

G

An integer vector specifying the numbers of mixture components (clusters) for which the criteria should be calculated. The default is G = 1:9.

modelNames

A vector of character strings indicating the models to be fitted in the EM phase of clustering. The help file for mclustModelNames describes the available models. The default is:

c("E", "V"): for univariate data
mclust.options("emModelNames"): for multivariate data (n > d)
c("EII", "VII", "EEI", "EVI", "VEI", "VVI"): the spherical and diagonal models for multivariate data (n <= d)

initialization

A list containing zero or more of the following components:

hcPairs: A matrix of merge pairs for hierarchical clustering such as produced by function hc. For multivariate data, the default is to compute a hierarchical clustering tree by applying function hc with modelName = "VVV" to the data or a subset as indicated by the subset argument. The hierarchical clustering results are to start EM. For univariate data, the default is to use quantiles to start EM.
subset: A logical or numeric vector specifying a subset of the data to be used in the initial hierarchical clustering phase.

x

An object of class 'mclustICL'. If supplied, mclustICL will use the settings in x to produce another object of class 'mclustICL', but with G and modelNames as specified in the arguments. Models that have already been computed in x are not recomputed. All arguments to mclustICL except data, G and modelName are ignored and their values are set as specified in the attributes of x. Defaults for G and modelNames are taken from x.

...

Futher arguments used in the call to Mclust. See also mclustBIC.

object

An integer vector specifying the numbers of mixture components (clusters) for which the criteria should be calculated. The default is G = 1:9.

Value

Returns an object of class 'mclustICL' containing the the ICL criterion for the specified mixture models and numbers of clusters.

The corresponding print method shows the matrix of values and the top models according to the ICL criterion. The summary method shows only the top models.

References

Biernacki, C., Celeux, G., Govaert, G. (2000). Assessing a mixture model for clustering with the integrated completed likelihood. IEEE Trans. Pattern Analysis and Machine Intelligence, 22 (7), 719-725.

Scrucca L., Fop M., Murphy T. B. and Raftery A. E. (2016) mclust 5: clustering, classification and density estimation using Gaussian finite mixture models, The R Journal, 8/1, pp. 289-317.

Examples

data(faithful)
faithful.ICL <- mclustICL(faithful)
faithful.ICL
#> Integrated Complete-data Likelihood (ICL) criterion: 
#>         EII       VII       EEI       VEI       EVI       VVI       EEE
#> 1 -4024.721 -4024.721 -3055.835 -3055.835 -3055.835 -3055.835 -2607.623
#> 2 -3455.814 -3460.903 -2356.273 -2350.728 -2353.254 -2346.161 -2326.710
#> 3 -3422.758 -3360.264 -2359.458 -2377.306 -2367.537 -2387.744 -2357.824
#> 4 -3265.796 -3272.457 -2371.996 -2413.391 -2402.189 -2436.318 -2468.261
#> 5 -3190.702 -3151.887 -2394.022 -2486.702 -2412.390 -2445.754 -2478.220
#> 6 -3117.441 -3061.335 -2423.024 -2486.795 -2446.878 -2472.624 -2456.239
#> 7 -3022.312 -2995.759 -2476.203 -2519.776 -2446.706 -2496.750 -2464.343
#> 8 -3007.364 -2953.728 -2488.504 -2513.529 -2492.319 -2509.675 -2502.177
#> 9 -2989.092 -2933.144 -2499.876 -2540.432 -2515.042 -2528.602 -2547.111
#>         VEE       EVE       VVE       EEV       VEV       EVV       VVV
#> 1 -2607.623 -2607.623 -2607.623 -2607.623 -2607.623 -2607.623 -2607.623
#> 2 -2323.396 -2325.768 -2320.763 -2330.000 -2325.727 -2328.163 -2322.697
#> 3 -2376.466 -2412.034 -2427.038 -2372.365 -2405.333 -2380.322 -2385.244
#> 4 -2452.689 -2459.430 -2440.279 -2414.165 -2419.889 -2385.843 -2407.555
#> 5 -2472.038 -2444.255 -2478.628 -2431.096 -2490.222 -2423.174 -2474.493
#> 6 -2503.936 -2504.770 -2489.104 -2449.583 -2481.393 -2483.772 -2491.597
#> 7 -2466.783 -2499.326 -2496.300 -2465.693 -2506.829 -2490.131 -2519.470
#> 8 -2479.790 -2526.028 -2516.572 -2489.431 -2539.783 -2497.812 -2556.115
#> 9 -2499.921 -2545.663 -2541.675 -2542.877 -2566.735 -2528.600 -2587.235
#> 
#> Top 3 models based on the ICL criterion: 
#>     VVE,2     VVV,2     VEE,2 
#> -2320.763 -2322.697 -2323.396 
summary(faithful.ICL)
#> Best ICL values:
#>              VVE,2        VVV,2       VEE,2
#> ICL      -2320.763 -2322.697467 -2323.39551
#> ICL diff     0.000    -1.934645    -2.63269
plot(faithful.ICL)

# \donttest{
# compare with
faithful.BIC <- mclustBIC(faithful)
faithful.BIC
#> Bayesian Information Criterion (BIC): 
#>         EII       VII       EEI       VEI       EVI       VVI       EEE
#> 1 -4024.721 -4024.721 -3055.835 -3055.835 -3055.835 -3055.835 -2607.623
#> 2 -3452.998 -3458.305 -2354.601 -2350.607 -2352.618 -2346.065 -2325.220
#> 3 -3377.701 -3336.598 -2323.014 -2332.687 -2332.205 -2342.366 -2314.316
#> 4 -3230.264 -3242.826 -2323.673 -2331.284 -2334.749 -2343.486 -2331.223
#> 5 -3149.394 -3129.080 -2327.059 -2350.230 -2347.564 -2351.017 -2360.659
#> 6 -3081.414 -3038.171 -2338.205 -2360.578 -2357.660 -2373.469 -2347.352
#> 7 -2990.367 -2973.374 -2356.454 -2368.513 -2372.851 -2394.696 -2369.330
#> 8 -2978.100 -2935.082 -2364.140 -2384.740 -2389.064 -2413.705 -2376.104
#> 9 -2953.359 -2919.415 -2372.790 -2398.223 -2407.224 -2432.708 -2389.609
#>         VEE       EVE       VVE       EEV       VEV       EVV       VVV
#> 1 -2607.623 -2607.623 -2607.623 -2607.623 -2607.623 -2607.623 -2607.623
#> 2 -2322.972 -2324.273 -2320.433 -2329.115 -2325.416 -2327.598 -2322.192
#> 3 -2322.103 -2342.319 -2336.271 -2325.322 -2329.648 -2339.983 -2349.696
#> 4 -2340.173 -2361.821 -2362.487 -2351.523 -2361.084 -2344.686 -2351.493
#> 5 -2347.337 -2351.828 -2368.937 -2356.856 -2368.101 -2364.900 -2379.388
#> 6 -2372.287 -2366.482 -2386.537 -2366.087 -2386.323 -2384.117 -2387.016
#> 7 -2371.175 -2379.810 -2402.220 -2379.071 -2401.270 -2398.703 -2412.440
#> 8 -2390.391 -2403.934 -2425.956 -2392.988 -2425.426 -2414.962 -2442.018
#> 9 -2406.732 -2414.089 -2448.208 -2407.500 -2446.726 -2438.876 -2460.398
#> 
#> Top 3 models based on the BIC criterion: 
#>     EEE,3     VVE,2     VEE,3 
#> -2314.316 -2320.433 -2322.103 
plot(faithful.BIC)

# }