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Measure to compare two or more sets w.r.t. their similarity.


The Phi Coefficient is defined as the Pearson correlation between the binary representation of two sets \(A\) and \(B\). The binary representation for \(A\) is a logical vector of length \(p\) with the i-th element being 1 if the corresponding element is in \(A\), and 0 otherwise.

If more than two sets are provided, the mean of all pairwise scores is calculated.

This measure is undefined if one set contains none or all possible elements.


This measure requires learners with property "selected_features". The extracted feature sets are passed to mlr3measures::phi() from package mlr3measures.

If the measure is undefined for the input, NaN is returned. This can be customized by setting the field na_value.


This Measure can be instantiated via the dictionary mlr_measures or with the associated sugar function msr():


Meta Information

  • Type: "similarity"

  • Range: \([-1, 1]\)

  • Minimize: FALSE

See also

Dictionary of Measures: mlr_measures for a complete table of all (also dynamically created) Measure implementations.

Other similarity measures: mlr_measures_sim.jaccard