Local Stability Analysis Of Flexible Independent Component Analysis Algorithm (original) (raw)

Flexible independent component analysis

2000

We present a exible independent component analysis (ICA) algorithm which can separate mixtures of sub-and super-Gaussian source signals with self-adaptive nonlinearities. The exible ICA algorithm in the framework of natural Riemannian gradient, is derived using the parameterized generalized Gaussian density model. The nonlinear function in the exible ICA algorithm is self-adaptive and is controlled by Gaussian exponent. Computer simulation results con rm the validity and high performance of the proposed algorithm.

A Novel Approach to Independent Component Analysis

2014

Independent component analysis (ICA) is a computational method, based on neural learning algorithm, to separate source signals from the observed mixtures by assuming that the sources are non-Gaussian in nature. Convergence speed, Area and Power are important parameters to be improved in VLSI implementation of ICA techniques, since they involve large number of iterative calculations, area and power. This paper presents a novel fast confluence adaptive independent component analysis (FCAICA) technique for separation of signals from their two observed mixtures. The reduction in area and power is achieved by hardware optimization by replacing random generator unit by means of comparator. High convergence speed is achieved by a novel optimization scheme that adaptively changes the weight vector based on the kurtosis value. To increase the number precision and dynamic range of the signals, floatingpoint (FP) arithmetic units are used. Simulation, synthesis and backend analysis are carried...

On some new ideas and algorithms for independent component analysis

2002

We propose new sufficient conditions for separation of source signals, stating that the separation is possible, if the source signals have different autocorrelation or cumulant functions (depending on time delay). We show that the problem of blind source separation of signals can be qonverted to asymmetric eigenvalue problem of ageneralized cumulant matrices if these matrices have distinct eigenvalues. We propose new algorithms, based on non-smooth analysis and optimization theory, which disperse the eigenvalues of these generalized cumulant matrices. 1Introduction The problem of independent component analysis is formulated as follows: we observe sensor signals (random variables

AN ALTERNATIVE NATURAL GRADIENT APPROACH FOR ICA BASED LEARNING ALGORITHMS IN BLIND SOURCE SEPARATION

In this paper a new formula for natural gradient based learning in blind source separation (BSS) problem is derived. This represents a different gradient from the usual one in [1], but can still considered natural since it comes from the definition of a Riemannian metric in the matrix space of parameters. The new natural gradient consists on left multiplying the standard gradient for an adequate term depending on the parameter matrix to adapt, whereas the other one considers a right multiplication. The two natural gradients have been employed in two ICA based learning algorithms for BSS and it resulted they have identical behavior.

A new fixed-point algorithm for independent component analysis

Neurocomputing, 2004

A new ÿxed-point algorithm for independent component analysis (ICA) is presented that is able blindly to separate mixed signals with sub-and super-Gaussian source distributions. The new ÿxed-point algorithm maximizes the likelihood of the ICA model under the constraint of decorrelation and uses the method of Lee et al. (Neural Comput. 11(2) (1999) 417) to switch between sub-and super-Gaussian regimes. The new ÿxed-point algorithm maximizes the likelihood very fast and reliably. The validity of this algorithm is conÿrmed by the simulations and experimental results.

Blind Source Separation and Independent Component Analysis: A Review

2005

Blind source separation (BSS) and independent component analysis (ICA) are generally based on a wide class of unsupervised learning algorithms and they found potential applications in many areas from engineering to neuroscience. A recent trend in BSS is to consider problems in the framework of matrix factorization or more general signals decomposition with probabilistic generative and tree structured graphical models and exploit a priori knowledge about true nature and structure of latent (hidden) variables or sources such as spatio-temporal decorrelation, statistical independence, sparseness, smoothness or lowest complexity in the sense e.g., of best predictability. The possible goal of such decomposition can be considered as the estimation of sources not necessary statistically independent and parameters of a mixing system or more generally as finding a new reduced or hierarchical and structured representation for the observed (sensor) data that can be interpreted as physically meaningful coding or blind source estimation. The key issue is to find a such transformation or coding (linear or nonlinear) which has true physical meaning and interpretation. We present a review of BSS and ICA, including various algorithms for static and dynamic models and their applications. The paper mainly consists of three parts:

Independent component analysis based on first-order statistics

Signal Processing, 2012

This communication puts forward a novel method for independent source extraction in instantaneous linear mixtures. The method is based on the conditional mean of the whitened observations and requires some prior knowledge of the positive support of the desired source. A theoretical performance analysis yields the closed-form expression of the asymptotic interference-to-signal ratio (ISR) achieved by this technique. The analysis includes the effects of inaccuracies in the estimation of the positive support of the desired source in single-step and iterative implementations of the algorithm. Numerical experiments validate the fitness of the asymptotic approximations. As it is based on first-order statistics, the method is extremely cost-effective, which makes it an attractive alternative to second-and higher-order statistical techniques in power-limited scenarios.