Non-negative dimensionality reduction for audio signal separation by NNMF and ICA

Many relevant applications of signal processing rely on the separation of sources from a mixture of signals without a prior knowledge about the mixing process. Given a mixture of signals f = Σ_i f_i, the task of signal separation is to estimate the components f_i by using specific assumptions on their time-frequency behaviour or statistical characteristics. Time-frequency data is often very high-dimensional which affects the performance of signal separation methods quite significantly. Therefore, the embedding dimension of the time-frequency representation of f should be reduced prior to the application of a decomposition strategy, such as independent component analysis (ICA) or non-negative matrix factorization (NNMF). In other words, a suitable dimensionality reduction method should be applied, before the data is decomposed and then back-projected. But the choice of the dimensionality reduction method requires particular care, especially in combination with ICA and NNMF, since non-negative input data are required. In this paper, we introduce a generic concept for the construction of suitable non-negative dimensionality reduction methods. Furthermore, we discuss the two different decomposition strategies NNMF and ICA for single channel signal separation in combination with non-negative principal component analysis (NNPCA), where our main interest is in acoustic signals with transitory components.