Nonlinear approaches to Independent Component Analysis

Lee, Te-Won
February 2000
AIP Conference Proceedings;2000, Vol. 501 Issue 1, p302
Academic Journal
Recently, there has been a great interest in statistical models for learning data representations. A popular method for this task is Independent Component Analysis (ICA) which has been successfully applied for the blind separation of mixed sounds and the analysis of biomedical signals. ICA relies on strong assumptions such as the linear mixing model, the requirement that the number of sensors are equal or greater than the number of sources, and that there is no additive noise. Some of the constraints are violated in practical applications and in order to relax the assumptions new methods need to be developed which involve nonlinear unmixing or inference solutions. In this paper, we summarize some techniques that involve nonlinear ICA solutions. Two approaches are presented to tackle the nonlinear mixing case, and nonlinear ICA solutions are summarized for overcomplete representation as well as additive noise problems. © 2000 American Institute of Physics.


Related Articles

  • An Introduction to Virtual-Based ICA Algorithm. Ariaei, A. Mohajerin; Moghadam, K. Rezaei; Kahaei, M. H. // International Journal of Signal & Image Processing;2010, Vol. 1 Issue 2, p104 

    In this paper, we develop a new method to deal with Independent Component Analysis (ICA) problems with non-square mixing matrices. This is performed by incorporating some virtual signals produced by nonlinear functions. Using simulation results, the effectiveness of the proposed algorithm is...

  • Variances of parameters obtained from nonlinear curve fits. Anton, A. Brad // Review of Scientific Instruments;Mar91, Vol. 62 Issue 3, p832 

    An analytical expression, is derived that quantifies the variances of parameters obtained from curve fits in terms of the variances of the individual data. In contrast to solutions of this problem offered previously, this solution accounts rigorously for nonlinear dependence of the fitting...

  • Effects of the linear mismatch and nonlinear asymmetry in the nonlinear coupler. Wang, Y.; Lee, C.K. // Applied Physics B: Lasers & Optics;2001, Vol. 72 Issue 4, p417 

    Abstract. Two types of nonlinear couplers exhibit identical coupling behaviors if their corresponding characteristic parameters and linear mismatches are of equal values but opposite signs. Complete power transfer can be attained in a nonlinear coupler when their characteristic parameters,...

  • Filtration-consistent nonlinear expectations and related g-expectations. Coquet, François; Hu, Ying; Mémin, Jean; Peng, Shige // Probability Theory & Related Fields;2002, Vol. 123 Issue 1, p1 

    From a general definition of nonlinear expectations, viewed as operators preserving monotonicity and constants, we derive, under rather general assumptions, the notions of conditional nonlinear expectation and nonlinear martingale. We prove that any such nonlinear martingale can be represented...

  • Instability of a Homogeneous Plastic Flow and Strain Localization in Structurally Inhomogeneous Media. Badaeva, V. F.; Kaminskii, P. P.; Khon, Yu. A. // Technical Physics Letters;Jan2001, Vol. 27 Issue 1, p6 

    Changes in the internal structure of a deformed medium are described, in addition to the defect densities, by the kinetic variables (order parameters) related to the collective modes of the macroscopic plastic deformation. The kinetic equations for two order parameters represent a system of...

  • Nonlinear Functional Analysis and Its Applications (Book). Ky Fan // American Scientist;Mar/Apr88, Vol. 76 Issue 2, p214 

    Reviews the book "Nonlinear Functional Analysis and Its Applications," edited by S.P. Singh.

  • NON-LINEAR CHARACTERIZATION OF MEMORYLESS SSP AMPLIFIERS. Ali, N.T. // Active & Passive Electronic Components;Sep2002, Vol. 25 Issue 3, p249 

    This paper describes a testbed, which is able to generate all of the standard test signals used for characterising non-linear amplifiers. The testbed is shown to be sufficiently linear to avoid any possible masking of the non-linear effects of the amplifier under test. All the standard tests:...

  • ON THE TREATMENT OF CERTAIN RECURRENT NON-LINEARITIES IN REGRESSION ANALYSIS. Dhrymes, Phoebus J. // Southern Economic Journal;Oct66, Vol. 33 Issue 2, p187 

    Examines the recurrent non-linearities in regression analysis. Elimination of the error term in the autoregressive structure; Classical properties of error terms; Specification of the error term.

  • Invariant Property of Roughly Contractive Mappings. Hoang Xuan Phu; Tran Van Truong // Vietnam Journal of Mathematics;2000, Vol. 28 Issue 3, p275 

    Presents the invariant property of roughly contractive mappings. Application on the fixed-point theorems in non-linear functional analysis; Invariant points in Euclidian norm; Theorems supporting the model.


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics