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.