Monika Doerfler

Monika Doerfler, Franz Luef, Henry McNulty

In this short note, we study the impact of data augmentation on the smoothness of principal components of high-dimensional datasets. Using tools from quantum harmonic analysis, we show that eigenfunctions of operators corresponding to augmented data sets lie in the modulation space $M^1(\mathbb{R}^d)$, guaranteeing smoothness and continuity. Numerical examples on synthetic and audio data confirm the theoretical findings. While interesting in itself, the results suggest that manifold learning and feature extraction algorithms can benefit from systematic and informed augmentation principles.

Monika Doerfler, Thomas Grill, Roswitha Bammer et al.

When convolutional neural networks are used to tackle learning problems based on music or, more generally, time series data, raw one-dimensional data are commonly pre-processed to obtain spectrogram or mel-spectrogram coefficients, which are then used as input to the actual neural network. In this contribution, we investigate, both theoretically and experimentally, the influence of this pre-processing step on the network's performance and pose the question, whether replacing it by applying adaptive or learned filters directly to the raw data, can improve learning success. The theoretical results show that approximately reproducing mel-spectrogram coefficients by applying adaptive filters and subsequent time-averaging is in principle possible. We also conducted extensive experimental work on the task of singing voice detection in music. The results of these experiments show that for classification based on Convolutional Neural Networks the features obtained from adaptive filter banks followed by time-averaging perform better than the canonical Fourier-transform-based mel-spectrogram coefficients. Alternative adaptive approaches with center frequencies or time-averaging lengths learned from training data perform equally well.