Soft-LOST: EM on a Mixture of Oriented Lines

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 the M-step repositions the lines to match the points assigned to them. This method, combined with a transformation into a sparse domain and an L1-norm optimisation, constitutes a blind source separation algorithm for the under-determined case.

• Type: Conference
• Year: 2004
• Where: ICA
• Authors: Paul D. O'Grady, Barak A. Pearlmutter
• Keywords: Blind Source Separation, ICA 2004, Linear Subspaces, One-dimensional Subspaces