Deep neural networks with voice entry estimation heuristics for voice separation in symbolic music representations

In this study we explore the use of deep feedforward neural networks for voice separation in symbolic music representations. We experiment with different network architectures, varying the number and size of the hidden layers, and with dropout. We integrate two voice entry estimation heuristics that estimate the entry points of the individual voices in the polyphonic fabric into the models. These heuristics serve to reduce error propagation at the beginning of a piece, which, as we have shown in previous work, can seriously hamper model performance. The models are evaluated on the 48 fugues from Johann Sebastian Bach’s The Well-Tempered Clavier and his 30 inventions—a dataset that we curated and make publicly available. We find that a model with two hidden layers yields the best results. Using more layers does not lead to a significant performance improvement. Furthermore, we find that our voice entry estimation heuristics are highly effective in the reduction of error propagation, improving performance significantly. Our best-performing model outperforms our previous models, where the difference is significant, and, depending on the evaluation metric, performs close to or better than the reported state of the art

Methodological Issues in Building, Training, and Testing Artificial Neural Networks

We review the use of artificial neural networks, particularly the feedforward multilayer perceptron with back-propagation for training (MLP), in ecological modelling. Overtraining on data or giving vague references to how it was avoided is the major problem. Various methods can be used to determine when to stop training in artificial neural networks: 1) early stopping based on cross-validation, 2) stopping after a analyst defined error is reached or after the error levels off, 3) use of a test data set. We do not recommend the third method as the test data set is then not independent of model development. Many studies used the testing data to optimize the model and training. Although this method may give the best model for that set of data it does not give generalizability or improve understanding of the study system. The importance of an independent data set cannot be overemphasized as we found dramatic differences in model accuracy assessed with prediction accuracy on the training data set, as estimated with bootstrapping, and from use of an independent data set. The comparison of the artificial neural network with a general linear model (GLM) as a standard procedure is recommended because a GLM may perform as well or better than the MLP. MLP models should not be treated as black box models but instead techniques such as sensitivity analyses, input variable relevances, neural interpretation diagrams, randomization tests, and partial derivatives should be used to make the model more transparent, and further our ecological understanding which is an important goal of the modelling process. Based on our experience we discuss how to build a MLP model and how to optimize the parameters and architecture.Comment: 22 pages, 2 figures. Presented in ISEI3 (2002). Ecological Modelling in pres