Independent components in spectroscopic analysis of complex mixtures

We applied two methods of "blind" spectral decomposition (MILCA and SNICA) to quantitative and qualitative analysis of UV absorption spectra of several non-trivial mixture types. Both methods use the concept of statistical independence and aim at the reconstruction of minimally dependent components from a linear mixture. We examined mixtures of major ecotoxicants (aromatic and polyaromatic hydrocarbons), amino acids and complex mixtures of vitamins in a veterinary drug. Both MICLA and SNICA were able to recover concentrations and individual spectra with minimal errors comparable with instrumental noise. In most cases their performance was similar to or better than that of other chemometric methods such as MCR-ALS, SIMPLISMA, RADICAL, JADE and FastICA. These results suggest that the ICA methods used in this study are suitable for real life applications. Data used in this paper along with simple matlab codes to reproduce paper figures can be found at http://www.klab.caltech.edu/~kraskov/MILCA/spectraComment: 22 pages, 4 tables, 6 figure

GHICA - Risk Analysis with GH Distributions and Independent Components

Over recent years, study on risk management has been prompted by the Basel committee for regular banking supervisory. There are however limitations of some widely-used risk management methods that either calculate risk measures under the Gaussian distributional assumption or involve numerical difficulty. The primary aim of this paper is to present a realistic and fast method, GHICA, which overcomes the limitations in multivariate risk analysis. The idea is to first retrieve independent components (ICs) out of the observed high-dimensional time series and then individually and adaptively fit the resulting ICs in the generalized hyperbolic (GH) distributional framework. For the volatility estimation of each IC, the local exponential smoothing technique is used to achieve the best possible accuracy of estimation. Finally, the fast Fourier transformation technique is used to approximate the density of the portfolio returns. The proposed GHICA method is applicable to covariance estimation as well. It is compared with the dynamic conditional correlation (DCC) method based on the simulated data with d = 50 GH distributed components. We further implement the GHICA method to calculate risk measures given 20-dimensional German DAX portfolios and a dynamic exchange rate portfolio. Several alternative methods are considered as well to compare the accuracy of calculation with the GHICA one.Multivariate Risk Management, Independent Component Analysis, Generalized Hyperbolic Distribution, Local Exponential Estimation, Value at Risk, Expected Shortfall.

Noisy independent component analysis of auto-correlated components

We present a new method for the separation of superimposed, independent, auto-correlated components from noisy multi-channel measurement. The presented method simultaneously reconstructs and separates the components, taking all channels into account and thereby increases the effective signal-to-noise ratio considerably, allowing separations even in the high noise regime. Characteristics of the measurement instruments can be included, allowing for application in complex measurement situations. Independent posterior samples can be provided, permitting error estimates on all desired quantities. Using the concept of information field theory, the algorithm is not restricted to any dimensionality of the underlying space or discretization scheme thereof

BMICA-independent component analysis based on B-spline mutual information estimator

The information theoretic concept of mutual information provides a general framework to evaluate dependencies between variables. Its estimation however using B-Spline has not been used before in creating an approach for Independent Component Analysis. In this paper we present a B-Spline estimator for mutual information to find the independent components in mixed signals. Tested using electroencephalography (EEG) signals the resulting BMICA (B-Spline Mutual Information Independent Component Analysis) exhibits better performance than the standard Independent Component Analysis algorithms of FastICA, JADE, SOBI and EFICA in similar simulations. BMICA was found to be also more reliable than the 'renown' FastICA

Separating Reflections from Images Using Independent Components Analysis

The image of an object can vary dramatically depending on lighting, specularities/reflections and shadows. It is often advantageous to separate these incidental variations from the intrinsic aspects of an image. Along these lines this paper describes a method for photographing objects behind glass and digitally removing the reflections off the glass leaving the image of the objects behind the glass intact. We describe the details of this method which employs simple optical techniques and independent components analysis (ICA) and show its efficacy with several examples

Portfolio Value at Risk Based on Independent Components Analysis

Risk management technology applied to high dimensional portfolios needs simple and fast methods for calculation of Value-at-Risk (VaR). The multivariate normal framework provides a simple off-the-shelf methodology but lacks the heavy tailed distributional properties that are observed in data. A principle component based method (tied closely to the elliptical structure of the distribution) is therefore expected to be unsatisfactory. Here we propose and analyze a technology that is based on Independent Component Analysis (ICA). We study the proposed ICVaR methodology in an extensive simulation study and apply it to a high dimensional portfolio situation. Our analysis yields very accurate VaRs.independent component analysis, Value-at-Risk

The principal independent components of images

This paper proposes a new approach for the encoding of images by only a few important components. Classically, this is done by the Principal Component Analysis (PCA). Recently, the Independent Component Analysis (ICA) has found strong interest in the neural network community. Applied to images, we aim for the most important source patterns with the highest occurrence probability or highest information called principal independent components (PIC). For the example of a synthetic image composed by characters this idea selects the salient ones. For natural images it does not lead to an acceptable reproduction error since no a-priori probabilities can be computed. Combining the traditional principal component criteria of PCA with the independence property of ICA we obtain a better encoding. It turns out that this definition of PIC implements the classical demand of Shannon’s rate distortion theory