Abstract
Robust clustering of data into linear subspaces is a frequently encountered problem. Here, we treat clustering of one-dimensional subspaces that cross the origin. This problem arises in blind source separation, where the subspaces correspond directly to columns of a mixing matrix. We propose the LOST algorithm, which identifies such subspaces using a procedure similar in spirit to EM. This line finding procedure combined with a transformation into a sparse domain and an L1-norm minimisation constitutes a blind source separation algorithm for the separation of instantaneous mixtures with an arbitrary number of mixtures and sources. We perform an extensive investigation on the general separation performance of the LOST algorithm using randomly generated mixtures, and empirically estimate the performance of the algorithm in the presence of noise. Furthermore, we implement a simple scheme whereby the number of sources present in the mixtures can be detected automatically.
Highlights
When presented with a set of observations from sensors such as microphones, the process of extracting the underlying sources is called source separation
To demonstrate the performance of the line orientation separation technique (LOST) algorithm, we investigate its separation performance when applied to speech mixtures: We use speech sources that are extracted from a commercial audio CD of poems read by their authors [30]; each source is a ten second segment of a poem, which has been down-sampled to 8 kHz; details of the extraction procedure and the poems used are presented in the appendix
The results show that a frame size of 4096 produces the worst separation performance for all three measures, which indicates that speech sampled at 8 kHz is not sufficiently sparse in this domain
Summary
When presented with a set of observations from sensors such as microphones, the process of extracting the underlying sources is called source separation. When M = N, the underlying sources, S, can be separated if one can find an unmixing matrix W such that s(t) = Wx(t), where s(t) holds the estimated sources at time t, and W = A−1 up to permutation and scaling of the rows. This problem can be described in probabilistic terms: N
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