Dynamic Independent Component/Vector Analysis: Time-Variant Linear Mixtures Separable by Time-Invariant Beamformers

In this paper, experiments on the application of the independent component analysis (ICA) technique to separate unknown source signals are reported. ICA is one of the fastest growing fields in signal processing with applications to speech recognition systems, telecommunications, and biomedical signal processing. It is a data-transformation technique that finds independent sources of activity from linear mixtures of unknown independent sources. The statistical method to measure independence is to find a linear representation of the non-Gaussian data so that the components are as independent as possible and the mutual information between them is minimum. Although extensive simulations have been performed to demonstrate the power of the learning algorithm for the problems of instantaneous mixing and un-mixing of sources, its application to the noise diagnosis and separation in an industrial setting has not been considered. Noise separation in machinery has a strong basis in the “cocktail problem” in which it is difficult to separate/isolate the voice of a person in a room filled with competing voices and noises. The experiments conducted consist of separating several artificially generated sources of noise. Our results demonstrate that ICA can be effectively employed for such kinds of applications. The underdetermined problem in which there are fewer sensors than sources in the ICA formulation is also examined by applying a time-invariant linear transformation of the acquired signals to identify a single source.

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Space Invariant Independent Component Analysis and ENose for Detection of Selective Chemicals in an Unknown Environment

Journal of Advanced Computational Intelligence and Intelligent Informatics ◽

10.20965/jaciii.2007.p1197 ◽

2007 ◽

Vol 11 (10) ◽

pp. 1197-1203

Author(s):

Tuan A. Duong ◽

◽

Margaret A. Ryan ◽

Vu A. Duong

Keyword(s):

Independent Component Analysis ◽

Gradient Descent ◽

Sensor Array ◽

Component Analysis ◽

Independent Component ◽

Sampled Data ◽

Natural Gradient ◽

Unknown Environment ◽

Entropy Information ◽

Time Invariant

In this paper, we present a space invariant architecture to enable the Independent Component Analysis (ICA) to solve chemical detection from two unknown mixing chemical sources. The two sets of unknown paired mixture sources are collected via JPL 16-ENose sensor array in the unknown environment with, at most, 12 samples data collected. Our space invariant architecture along with the maximum entropy information technique by Bell and Sejnowski and natural gradient descent by Amari has demonstrated that it is effective to separate the two mixing unknown chemical sources with unknown mixing levels to the array of two original sources under insufficient sampled data. From separated sources, they can be identified by projecting them on the 11 known chemical sources to find the best match for detection. We also present the results of our simulations. These simulations have shown that 100% correct detection could be achieved under the two cases: a) under-completed case where the number of input (mixtures) is larger than number of original chemical sources; and b) regular case where the number of input is as the same as the number of sources while the time invariant architecture approach may face the obstacles: overcomplete case, insufficient data and cumbersome architecture.

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A Constrained EM Algorithm for Independent Component Analysis

Neural Computation ◽

10.1162/089976601300014510 ◽

2001 ◽

Vol 13 (3) ◽

pp. 677-689 ◽

Cited By ~ 32

Author(s):

Max Welling ◽

Markus Weber

Keyword(s):

Factor Analysis ◽

Independent Component Analysis ◽

Em Algorithm ◽

Expectation Maximization ◽

Component Analysis ◽

Independent Component ◽

Independent Factor ◽

One Dimensional ◽

Linear Mixtures ◽

Independent Factor Analysis

We introduce a novel way of performing independent component analysis using a constrained version of the expectation-maximization (EM) algorithm. The source distributions are modeled as D one-dimensional mixtures of gaussians. The observed data are modeled as linear mixtures of the sources with additive, isotropic noise. This generative model is fit to the data using constrained EM. The simpler “soft-switching” approach is introduced, which uses only one parameter to decide on the sub- or supergaussian nature of the sources. We explain how our approach relates to independent factor analysis.

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ADVANCES IN BLIND SOURCE SEPARATION (BSS) AND INDEPENDENT COMPONENT ANALYSIS (ICA) FOR NONLINEAR MIXTURES

International Journal of Neural Systems ◽

10.1142/s012906570400208x ◽

2004 ◽

Vol 14 (05) ◽

pp. 267-292 ◽

Cited By ~ 86

Author(s):

CHRISTIAN JUTTEN ◽

JUHA KARHUNEN

Keyword(s):

Independent Component Analysis ◽

Blind Source Separation ◽

Source Separation ◽

Component Analysis ◽

Independent Component ◽

Structural Constraints ◽

Statistical Parameters ◽

Important Special Case ◽

Nonlinear Mixtures ◽

Linear Mixtures

In this paper, we review recent advances in blind source separation (BSS) and independent component analysis (ICA) for nonlinear mixing models. After a general introduction to BSS and ICA, we discuss in more detail uniqueness and separability issues, presenting some new results. A fundamental difficulty in the nonlinear BSS problem and even more so in the nonlinear ICA problem is that they provide non-unique solutions without extra constraints, which are often implemented by using a suitable regularization. In this paper, we explore two possible approaches. The first one is based on structural constraints. Especially, post-nonlinear mixtures are an important special case, where a nonlinearity is applied to linear mixtures. For such mixtures, the ambiguities are essentially the same as for the linear ICA or BSS problems. The second approach uses Bayesian inference methods for estimating the best statistical parameters, under almost unconstrained models in which priors can be easily added. In the later part of this paper, various separation techniques proposed for post-nonlinear mixtures and general nonlinear mixtures are reviewed.

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