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We present an approach to feature extraction that is a generalization of the classical linear discriminant analysis (LDA) on the basis of deep neural networks (DNNs). As for LDA, discriminative features generated from independent Gaussian class conditionals are assumed. This modeling has the advantages that the intrinsic dimensionality of the feature space is bounded by the number of classes and that the optimal discriminant function is linear. Unfortunately, linear transformations are insufficient to extract optimal discriminative features from arbitrarily distributed raw measurements. The generalized discriminant analysis (GerDA) proposed in this paper uses nonlinear transformations that are learnt by DNNs in a semisupervised fashion. We show that the feature extraction based on our approach displays excellent performance on real-world recognition and detection tasks, such as handwritten digit recognition and face detection. In a series of experiments, we evaluate GerDA features with respect to dimensionality reduction, visualization, classification, and detection. Moreover, we show that GerDA DNNs can preprocess truly high-dimensional input data to low-dimensional representations that facilitate accurate predictions even if simple linear predictors or measures of similarity are used.
With the virtual environment developed here, the characteristic
sound radiation patterns of musical instruments can be experienced
in real-time. The user may freely move around a musical instrument, thereby receiving acoustic and visual feedback in real-time. The perception of auditory and visual effects is intensified by the combination of acoustic and visual elements, as well as the option of user interaction. The simulation of characteristic sound radiation patterns is based on interpolating the intensities of a multichannel recording and offers a near-natural mapping of the sound radiation patterns. Additionally, a simple filter has been developed, enabling the qualitative simulation of an instrument’s characteristic sound radiation patterns to be easily implemented within real-time 3D applications. Both methods of simulating sound radiation patterns have been evaluated for a saxophone with respect to their functionality and validity by means of spectral analysis and an auditory experiment.