Abstract
Robust clustering of data into overlapping linear subspaces is a common problem. Here we consider 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 present an algorithm that identifies these subspaces using an EM procedure, where the E-step calculates posterior probabilities assigning data points to lines and M-step repositions the lines to match the points assigned to them. This method, combined with a transformation into a sparse domain and an L 1-norm optimisation, constitutes a blind source separation algorithm for the under-determined case.
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© 2004 Springer-Verlag Berlin Heidelberg
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O’Grady, P.D., Pearlmutter, B.A. (2004). Soft-LOST: EM on a Mixture of Oriented Lines. In: Puntonet, C.G., Prieto, A. (eds) Independent Component Analysis and Blind Signal Separation. ICA 2004. Lecture Notes in Computer Science, vol 3195. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30110-3_55
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DOI: https://doi.org/10.1007/978-3-540-30110-3_55
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