On the Construction of Non-Negative Dimensionality Reduction Methods

Abstract

Many relevant applications of signal processing rely on the separation of sources from a mixture of signals without prior knowledge about the mixing process. Given a mixture of signals, the task of signal separation is to estimate the mixture components by using specific assumptions on their time-frequency behaviour or statistical characteristics. Time-frequency data is often very high-dimensional, which reduces the performance of signal separation methods quite significantly. Therefore, the embedding dimension of the signal's time-frequency representation 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 NNMF and certain types of ICA, since they require non-negative input data. 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 ICA and NNMF for single channel signal separation. We apply the resulting methods to the separation of acoustic signals with transitory components. Key words and phrases: Non-negative dimensionality reduction, signal separation , independent component analysis, non-negative matrix factorization 2 S. KRAUSE-SOLBERG AND A. ISKE 2000