Advances in Self-Organizing Maps and Learning Vector Quantization

This paper proposes a variant of the generalized learning vector quantizer (GLVQ) optimizing explicitly the area under the receiver operating characteristics (ROC) curve for binary classification problems instead of the classification accuracy, which is frequently not appropriate for classifier evaluation. This is particularly important in case of overlapping class distributions, when the user has to decide about the trade-off between high true-positive and good false-positive performance. The model keeps the idea of learning vector quantization based on prototypes by stochastic gradient descent learning. For this purpose, a GLVQ-based cost function is presented, which describes the area under the ROC-curve in terms of the sum of local discriminant functions. This cost function reflects the underlying rank statistics in ROC analysis being involved into the design of the prototype based discriminant function. The resulting learning scheme for the prototype vectors uses structured inputs, i.e. ordered pairs of data vectors of both classes. Keywords Learning vector quantization • ROC analysis • AUC optimization 1 IntroductionClassification learning belongs to the most important tasks in machine learning. The respective mathematical basis is the Bayesian decision theory (Berger 1993). Bayes B T. Villmann

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