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A Splitting Approach to Dimensionality Reduction with Non-Negativity Constraints
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In many applications there is an increasing demand for effective methods to estimate the components from a mixture of transitory signals. In recent years, different techniques were developed for doing so, among them Independent Subspace Analysis (ISA), which in particular seems to be a very promising tool in combination with dimensionality reduction methods.
The basic idea is to first reduce the dimension of the data obtained from a short-time Fourier transform (STFT), before the reduced data is decomposed into different components, each assigned to one of the source signals. This decomposition is based on methods as Independent Component Analysis (ICA) or Non-Negative Matrix Factorization (NNMF).
For the application of NNMF, however, non-negative dimensionality reduction methods are required in order to obtain non-negative output from non-negative input data (e.g., non-negative spectrogram from the STFT).
Therefore, we are interested in modifying existent dimensionality reduction methods, such as Principal Component Analysis (PCA), to obtain non-negativity preserving methods.
This talk discusses a splitting approach for the construction of a non-negative dimensionality reduction method relying on PCA.
Supporting numerical examples concerning the separation of audio signals are presented for illustration.