Independent Subspace Analysis Using Locally Linear Embedding

While Independent Subspace Analysis provides a means of blindly separating sound sources from a single channel signal, it does have a number of problems. In particular the amount of information required for separation of sources varies with the signal. This is as a result of the variance-based nature of Principal Component Analysis, which is used for dimensional reduction in the Independent Subspace Analysis algorithm. In an attempt to overcome this problem the use of a non-variance based dimensional reduction method, Locally Linear Embedding, is proposed. Locally Linear Embedding is a geometry based dimensional reduction technique. The use of this approach is demonstrated by its application to single channel source separation, and its merits discussed. 1. INDEPENDENT SUBSPACE ANALYSIS Independent Subspace Analysis (ISA) provides a means of blind sound source separation from single channel mixtures [1]. ISA represents sound sources as low dimensional subspaces in the time-frequency plane. The single channel mixture is assumed to result from the sum of a number of unknown independent sources. The single channel mixture is converted to a timefrequency representation such as a spectrogram by means of carrying out a Short Time Fourier Transform on the signal and retaining only the magnitude values. The resulting spectrogram is then assumed to result from the superposition of l unknown independent spectrograms. Further each independent spectrogram is assumed to be represented as the outer product of an invariant frequency basis function fj and a corresponding time basis function tj. This yields: