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The objective detection of binaural interaction is of diagnostic interest for the evaluation of the central auditory processing disorder (CAPD). The β-wave of the binaural interaction component in auditory brainstem responses has been suggested as an objective measure of binaural interaction and has been shown to be of diagnostic value in the CAPD diagnosis. However, a reliable and automated detection of the β-wave capable of clinical use still remains a challenge. We propose a new machine learning approach to the detection of the CAPD that is based on adapted tight frame decompositions which are tailored for support vector machines with radial kernels. Using shift-invariant scale and morphological features of the binaurally evoked brainstem potentials, our approach provides at least comparable results to the β-wave detection in view of the discrimination of subjects being at risk for CAPD and subjects being not at risk for CAPD. Furthermore, as no information from the monaurally evoked potentials is necessary, the measurement cost is reduced by two-thirds compared to the computation of the binaural interaction component. We conclude that a machine learning approach in the form of a hybrid tight frame-support vector classification is effective in the objective detection of the CAPD.