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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.
The optimization of full-scale biogas plant operation is of great importance to make biomass a competitive source of renewable energy. The implementation of innovative control and optimization algorithms, such as Nonlinear Model Predictive Control, requires an online estimation of operating states of biogas plants. This state estimation allows for optimal control and operating decisions according to the actual state of a plant. In this paper such a state estimator is developed using a calibrated simulation model of a full-scale biogas plant, which is based on the Anaerobic Digestion Model No.1. The use of advanced pattern recognition methods shows that model states can be predicted from basic online measurements such as biogas production, CH4 and CO2 content in the biogas, pH value and substrate feed volume of known substrates. The machine learning methods used are trained and evaluated using synthetic data created with the biogas plant model simulating over a wide range of possible plant operating regions. Results show that the operating state vector of the modelled anaerobic digestion process can be predicted with an overall accuracy of about 90%. This facilitates the application of state-based optimization and control algorithms on full-scale biogas plants and therefore fosters the production of eco-friendly energy from biomass.
