experimental protocol used with the T-DSN [@hutchinson2012deep].

With 183 classes the all-pairs approach for generalized eigenvector extraction is unwieldy, so we used a randomized procedure to select from which class pairs to extract features, by randomly positioning the class labels on a hypercube and extracting generalized eigenvectors only for immediate hyperneighbors. For $k$ classes this results in $O (k \log k)$ generalized eigenvalue problems. Although we did not attempt a thorough exploration of different strategies for subproblem selection, the hypercube heuristic yielded better results for a given feature budget than either uniform random selection over all class pairs or stratified random selection over class pairs ensuring equal numbers of denominator or numerator classes. The resulting performance for five different choices of random hypercube is shown in the row of Table \[tab:timitres\] denoted GEM. We show both multiclass error rate as well as cross entropy, the objective we are actually optimizing.

The random subproblem selection creates an opportunity to ensemble, and empirically the resulting classifiers are sufficiently diverse that ensembling yields a substantial improvement. In Table \[tab:timitres\], denoted GEM ensemble, we show the performance of the ensemble prediction of the 5 classifiers using the geometric mean prediction (this is the prediction 