Unsupervised Parameter Estimation of Non Linear Scaling for Improved Classification in the Dissimilarity Space

The non-linear scaling of given dissimilarities, by raising them to a power in the (0,1) interval, is often useful to improve the classification performance in the corresponding dissimilarity space. The optimal value for the power can be found by a grid search across a leave-one-out cross validation of the classifier: a procedure that might become costly for large dissimilarity matrices, and is based on labels, not permitting to capture the global effect of such a scaling. Herein, we propose an entirely unsupervised criterion that, when optimized, leads to a suboptimal but often good enough value of the scaling power. The criterion is based on a trade-off between the dispersion of data in the dissimilarity space and the corresponding intrinsic dimensionality, such that the concentrating effects of the power transformation on both the space axes and the spatial distribution of the objects are rationed.