mona {cluster} R Documentation

## MONothetic Analysis Clustering of Binary Variables

### Description

Returns a list representing a divisive hierarchical clustering of a dataset with binary variables only.

mona(x)

### Arguments

 x data matrix or data frame in which each row corresponds to an observation, and each column corresponds to a variable. All variables must be binary. A limited number of missing values (NAs) is allowed. Every observation must have at least one value different from NA. No variable should have half of its values missing. There must be at least one variable which has no missing values. A variable with all its non-missing values identical, is not allowed.

### Details

mona is fully described in chapter 7 of Kaufman and Rousseeuw (1990). It is "monothetic" in the sense that each division is based on a single (well-chosen) variable, whereas most other hierarchical methods (including agnes and diana) are "polythetic", i.e. they use all variables together.

The mona-algorithm constructs a hierarchy of clusterings, starting with one large cluster. Clusters are divided until all observations in the same cluster have identical values for all variables.
At each stage, all clusters are divided according to the values of one variable. A cluster is divided into one cluster with all observations having value 1 for that variable, and another cluster with all observations having value 0 for that variable.

The variable used for splitting a cluster is the variable with the maximal total association to the other variables, according to the observations in the cluster to be splitted. The association between variables f and g is given by a(f,g)*d(f,g) - b(f,g)*c(f,g), where a(f,g), b(f,g), c(f,g), and d(f,g) are the numbers in the contingency table of f and g. [That is, a(f,g) (resp. d(f,g)) is the number of observations for which f and g both have value 0 (resp. value 1); b(f,g) (resp. c(f,g)) is the number of observations for which f has value 0 (resp. 1) and g has value 1 (resp. 0).] The total association of a variable f is the sum of its associations to all variables.

This algorithm does not work with missing values, therefore the data are revised, e.g. all missing values are filled in. To do this, the same measure of association between variables is used as in the algorithm. When variable f has missing values, the variable g with the largest absolute association to f is looked up. When the association between f and g is positive, any missing value of f is replaced by the value of g for the same observation. If the association between f and g is negative, then any missing value of f is replaced by the value of 1-g for the same observation.

### Value

an object of class "mona" representing the clustering. See mona.object for details.