Given a mixture of signals we aim to estimate the source signals by using specific assumptions on their time-frequency behaviour or statistical characteristics. Since dimensionality reduction will be used to first reduce the dimension of the time-frequency data of the mixture, before the reduced data is decomposed into different components, the interaction of the reduction and the decomposition is a crucial point. Decomposition techniques like ISA or NNMF require the input data to be entry-wise non-negative, but the use of dimensionality reduction techniques might cause negative entries in the low-dimensional representation. This is why we are interested in non-negative dimensionality reduction methods.
In this talk we show that dimensionality reduction methods which can be written as an optimization problem with rotational invariant cost functional can easily be converted into non-negativity preserving methods.