Name
Abstract | ||
|---|---|---|
Independent Subspace Analysis (ISA) is a generalization of ICA. It tries to find a basis in which a given random vector can be decomposed into groups of mutually independent random vectors. Since the first introduction of ISA, various algorithms to solve this problem have been introduced, however a general proof of the uniqueness of ISA decompositions remained an open question. In this contribution we address this question and sketch a proof for the separability of ISA. The key condition for separability is to require the subspaces to be not further decomposable (irreducible). Based on a decomposition into irreducible components, we formulate a general model for ISA without restrictions on the group sizes. The validity of the uniqueness result is illustrated on a toy example. Moreover, an extension of ISA to subspace extraction is introduced and its indeterminacies are discussed. |
Year | Venue | Keywords |
|---|---|---|
2007 | ICA | irreducible component,general model,isa decomposition,general proof,open question,independent subspace analysis,group size,independent random vector,uniqueness result,random vector |
Field | DocType | Volume |
Uniqueness,Combinatorics,Irreducible component,Algebra,Subspace topology,Irreducibility,Linear subspace,Multivariate random variable,Independent component analysis,Mathematics,Independence (probability theory) | Conference | 4666 |
ISSN | ISBN | Citations |
0302-9743 | 3-540-74493-2 | 10 |
PageRank | References | Authors |
0.69 | 7 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Harold W. Gutch | 1 | 45 | 4.60 |
| Fabian J. Theis | 2 | 931 | 85.37 |