Hierarchical Extraction of Independent Subspaces of Unknown Dimensions

Abstract. Independent Subspace Analysis (ISA) is an extension of Independent Component Analysis (ICA) that aims to linearly transform a random vector such as to render groups of its components mutually independent. A recently proposed fixed-point algorithm is able to locally perform ISA if the sizes of the subspaces are known, however global convergence is a serious problem as the proposed cost function has additional local minima. We introduce an extension to this algorithm, based on the idea that the algorithm converges to a solution, in which subspaces that are members of the global minimum occur with a higher frequency. We show that this overcomes the algorithm's limitations. Moreover, this idea allows a blind approach, where no a priori knowledge of subspace sizes is required. Assuming an independent random vector S that is mixed by an unknown mixing matrix A, Independent Component Analysis (ICA) denotes the task of recovering S, given only the mixed signals, X = AS. It is kn...

• Type: Journal
• Year: 2009
• Where: IDA
• Authors: Peter Gruber, Harold W. Gutch, Fabian J. Theis
• Keywords: IDA 2009, Independent Component Analysis, Independent Subspace Analysis, Information Technology, Random Vectors