icmiMatrix {praznik}

Conditional mutual information matrix with a common variable

Description

Calculates conditional mutual information between each feature and the decision given each other feature, that is

I(X_i;Y|X_j).

Usage

icmiMatrix(X, Y, threads = 0)

Arguments

X

Attribute table, given as a data frame with either factors (preferred), booleans, integers (treated as categorical) or reals (which undergo automatic categorisation; see below for details). Single vector will be interpreted as a data.frame with one column. NAs are not allowed.

Y

Decision attribute; should be given as a factor, but other options are accepted, exactly like for attributes. NAs are not allowed.

threads

Number of threads to use; default value, 0, means all available to OpenMP.

Value

A numerical matrix with scores, with row and column names copied from X.

Note

The method requires input to be discrete to use empirical estimators of distribution, and, consequently, information gain or entropy. To allow smoother user experience, praznik automatically coerces non-factor vectors in inputs, which requires additional time, memory and may yield confusing results – the best practice is to convert data to factors prior to feeding them in this function. Real attributes are cut into about 10 equally-spaced bins, following the heuristic often used in literature. Precise number of cuts depends on the number of objects; namely, it is n/3, but never less than 2 and never more than 10. Integers (which technically are also numeric) are treated as categorical variables (for compatibility with similar software), so in a very different way – one should be aware that an actually numeric attribute which happens to be an integer could be coerced into a n-level categorical, which would have a perfect mutual information score and would likely become a very disruptive false positive.

Diagonal is always zero with this score. The function name comes from the reasoning that this is an "interaction-CMI" showing how feature pairs interact in explaining the decision.

Examples

icmiMatrix(iris[,-5],iris[,5])