hc {mclust} | R Documentation

## Model-based Hierarchical Clustering

### Description

Agglomerative hierarchical clustering based on maximum likelihood criteria for MVN mixture models parameterized by eigenvalue decomposition.

### Usage

    hc(modelName, data, ...)

### Arguments

`modelName` | A character string indicating the model. Possible models: "E" : equal variance (one-dimensional) "V" : spherical, variable variance (one-dimensional) "EII": spherical, equal volume "VII": spherical, unequal volume "EEE": ellipsoidal, equal volume, shape, and orientation "VVV": ellipsoidal, varying volume, shape, and orientation
`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.
`...` | Arguments for the method-specific hc functions. See `hcE`.

### Details

Most models have memory usage of the order of the square of the number groups in the initial partition for fast execution. Some models, such as equal variance or `"EEE"`, do not admit a fast algorithm under the usual agglomerative hierarchical clustering paradigm. These use less memory but are much slower to execute.

### Value

A numeric two-column matrix in which the ith row gives the minimum index for observations in each of the two clusters merged at the ith stage of agglomerative hierarchical clustering.

### References

J. D. Banfield and A. E. Raftery (1993). Model-based Gaussian and non-Gaussian Clustering. Biometrics 49:803-821.

C. Fraley (1998). Algorithms for model-based Gaussian hierarchical clustering. SIAM Journal on Scientific Computing 20:270-281. See http://www.stat.washington.edu/mclust.

C. Fraley and A. E. Raftery (2002a). Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association 97:611-631. See http://www.stat.washington.edu/mclust.

C. Fraley and A. E. Raftery (2002b). MCLUST:Software for model-based clustering, density estimation and discriminant analysis. Technical Report, Department of Statistics, University of Washington. See http://www.stat.washington.edu/mclust.

### Note

If `modelName = "E"` (univariate with equal variances) or `modelName = "EII"` (multivariate with equal spherical covariances), then the method is equivalent to Ward's method for hierarchical clustering.

### See Also

`hcE`,..., `hcVVV`, `hclass`

### Examples

    data(iris)
    irisMatrix <- as.matrix(iris[,1:4])

    hcTree <- hc(modelName = "VVV", data = irisMatrix)
    cl <- hclass(hcTree,c(2,3))

    par(pty = "s", mfrow = c(1,1))
    clPairs(irisMatrix,cl=cl[,"2"])
    clPairs(irisMatrix,cl=cl[,"3"])

    par(mfrow = c(1,2))
    dimens <- c(1,2)
    coordProj(irisMatrix, classification=cl[,"2"], dimens=dimens)
    coordProj(irisMatrix, classification=cl[,"3"], dimens=dimens)

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