Optimal N-ary ECOC Matrices for Ensemble Classification

A new recursive construction of
$N$
-ary error-correcting output code (ECOC) matrices for ensemble classification methods is presented, generalizing the classic doubling construction for binary Hadamard matrices. Given any prime integer
$N$
, this deterministic construction generates base-
$N$
symmetric square matrices
$M$
of prime-power dimension having optimal minimum Hamming distance between any two of its rows and columns. Experimental results for six datasets demonstrate that using these deterministic coding matrices for
$N$
-ary ECOC classification yields comparable and in many cases higher accuracy compared to using randomly generated coding matrices. This is particular true when
$N$
is adaptively chosen so that the dimension of
$M$
matches closely with the number of classes in a dataset, which reduces the loss in minimum Hamming distance when
$M$
is truncated to fit the dataset. This is verified through a distance formula for
$M$
which shows that these adaptive matrices have significantly higher minimum Hamming distance in comparison to randomly generated ones.