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Two types of spatiotemporal chaos exhibited by ensembles of coupled nonlinear oscillators are analyzed using independent component analysis (ICA). For diffusively coupled complex Ginzburg-Landau oscillators that exhibit smooth amplitude patterns, ICA extracts localized one-humped basis vectors that reflect the characteristic hole structures of the system, and for nonlocally coupled complex Ginzburg-Landau oscillators with fractal amplitude patterns, ICA extracts localized basis vectors with characteristic gap structures. Statistics of the decomposed signals also provide insight into the complex dynamics of the spatiotemporal chaos.
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We study Lyapunov vectors (LVs) corresponding to the largest Lyapunov exponents in systems with spatiotemporal chaos. We focus on characteristic LVs and compare the results with backward LVs obtained via successive Gram-Schmidt orthonormalizations. Systems of a very different nature such as coupled-map lattices and the (continuous-time) Lorenz `96 model exhibit the same features in quantitative and qualitative terms. Additionally we propose a minimal stochastic model that reproduces the results for chaotic systems. Our work supports the claims about universality of our earlier results [I. G. Szendro et al., Phys. Rev. E 76, 025202(R) (2007)] for a specific coupled-map lattice.
Extreme events such as rogue wave in optics and fluids are often associated with the merging dynamics of coherent structures. We present experimental and numerical results on the physics of extreme events appearance in a spatially extended semiconductor microcavity laser with intracavity saturable absorber. This system can display deterministic irregular dynamics only thanks to spatial coupling through diffraction of light. We have identified parameter regions where extreme events are encountered and established the origin of this dynamics in the emergence of deterministic spatiotemporal chaos, through the correspondence between the proportion of extreme events and the dimension of the strange attractor.
Independent component analysis (ICA) has been widely used for blind source separation in many fields such as brain imaging analysis, signal processing and telecommunication. Many statistical techniques based on M-estimates have been proposed for estimating the mixing matrix. Recently, several nonparametric methods have been developed, but in-depth analysis of asymptotic efficiency has not been available. We analyze ICA using semiparametric theories and propose a straightforward estimate based on the efficient score function by using B-spline approximations. The estimate is asymptotically efficient under moderate conditions and exhibits better performance than standard ICA methods in a variety of simulations.
Compositional data represent a specific family of multivariate data, where the information of interest is contained in the ratios between parts rather than in absolute values of single parts. The analysis of such specific data is challenging as the application of standard multivariate analysis tools on the raw observations can lead to spurious results. Hence, it is appropriate to apply certain transformations prior further analysis. One popular multivariate data analysis tool is independent component analysis. Independent component analysis aims to find statistically independent components in the data and as such might be seen as an extension to principal component analysis. In this paper we examine an approach of how to apply independent component analysis on compositional data by respecting the nature of the former and demonstrate the usefulness of this procedure on a metabolomic data set.
Fast Independent Component Analysis (FastICA) is a component separation algorithm based on the levels of non-Gaussianity. Here we apply the FastICA to the component separation problem of the microwave background including carbon monoxide (CO) line emissions that are found to contaminate the PLANCK High Frequency Instrument (HFI) data. Specifically we prepare 100GHz, 143GHz, and 217GHz mock microwave sky maps including galactic thermal dust, NANTEN CO line, and the Cosmic Microwave Background (CMB) emissions, and then estimate the independent components based on the kurtosis. We find that the FastICA can successfully estimate the CO component as the first independent component in our deflection algorithm as its distribution has the largest degree of non-Gaussianity among the components. By subtracting the CO and the dust components from the original sky maps, we will be able to make an unbiased estimate of the cosmological CMB angular power spectrum.
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