Surrogate regret bounds for generalized classification performance metrics

We consider optimization of generalized performance metrics for binary classification by means of surrogate losses. We focus on a class of metrics, which are linear-fractional functions of the false positive and false negative rates (examples of which include $F_{\beta}$-measure, Jaccard similarity coefficient, AM measure, and many others). Our analysis concerns the following two-step procedure. First, a real-valued function $f$ is learned by minimizing a surrogate loss for binary classification on the training sample. It is assumed that the surrogate loss is a strongly proper composite loss function (examples of which include logistic loss, squared-error loss, exponential loss, etc.). Then, given $f$, a threshold $\widehat{\theta}$ is tuned on a separate validation sample, by direct optimization of the target performance metric. We show that the regret of the resulting classifier (obtained from thresholding $f$ on $\widehat{\theta}$) measured with respect to the target metric is upperbounded by the regret of $f$ measured with respect to the surrogate loss. We also extend our results to cover multilabel classification and provide regret bounds for micro- and macro-averaging measures. Our findings are further analyzed in a computational study on both synthetic and real data sets.Comment: 22 page

A Multiple-Expert Binarization Framework for Multispectral Images

In this work, a multiple-expert binarization framework for multispectral images is proposed. The framework is based on a constrained subspace selection limited to the spectral bands combined with state-of-the-art gray-level binarization methods. The framework uses a binarization wrapper to enhance the performance of the gray-level binarization. Nonlinear preprocessing of the individual spectral bands is used to enhance the textual information. An evolutionary optimizer is considered to obtain the optimal and some suboptimal 3-band subspaces from which an ensemble of experts is then formed. The framework is applied to a ground truth multispectral dataset with promising results. In addition, a generalization to the cross-validation approach is developed that not only evaluates generalizability of the framework, it also provides a practical instance of the selected experts that could be then applied to unseen inputs despite the small size of the given ground truth dataset.Comment: 12 pages, 8 figures, 6 tables. Presented at ICDAR'1