How Many Separable Sources? Model Selection In Independent Components Analysis

Woods, Roger P.; Hansen, Lars Kai; Strother, Stephen C.

doi:10.1371/journal.pone.0118877

Cited by 7 publications

(11 citation statements)

References 46 publications

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“…Using a combination of component reproducibility and a measure of subsample-to-subsample fluctuations in reproducibility, we are clearly able to separate a complex mixture into sparse and Gaussian subspaces, as well as flag potentially spurious sources resulting from extraction of more sources than are actually present in the data. Even on data matrices with an extremely limited number of samples (150 for the Iris data), MIPReSt still obtains results consistent with other algorithms which are more heavily parameterized and much more computationally expensive [15]. In addition, MIPReSt’s use of FastICA allows it to recover both supergaussian and subgaussian sources without any need to specify the relative numbers of each.…”

Section: Discussionmentioning

confidence: 77%

“…Unfortunately, once Gaussian sources are mixed with nongaussian sources ICA encounters problems. The unmixing matrix loses uniqueness because of the rotational invariance of the Gaussian subspace; with only nongaussian sources uniqueness is preserved [ 15 ]. Once two or more Gaussian sources are present in the signal mixture ICA can no longer separate those sources, and ignoring these sources in the ICA model will result in spurious sparse sources.…”

Section: Introductionmentioning

confidence: 99%

“…Once two or more Gaussian sources are present in the signal mixture ICA can no longer separate those sources, and ignoring these sources in the ICA model will result in spurious sparse sources. This sphericity problem led Woods et al [ 15 ] to propose a model for mixed ICA/PCA. They maximize an explicit likelihood model that incorporates supergaussian, subgaussian, and Gaussian sources and use cross-validation to determine the appropriate number of components of each kind.…”

Section: Introductionmentioning

confidence: 99%

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An algorithm for separation of mixed sparse and Gaussian sources

Akkalkotkar

Brown

2017

PLoS ONE

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Independent component analysis (ICA) is a ubiquitous method for decomposing complex signal mixtures into a small set of statistically independent source signals. However, in cases in which the signal mixture consists of both nongaussian and Gaussian sources, the Gaussian sources will not be recoverable by ICA and will pollute estimates of the nongaussian sources. Therefore, it is desirable to have methods for mixed ICA/PCA which can separate mixtures of Gaussian and nongaussian sources. For mixtures of purely Gaussian sources, principal component analysis (PCA) can provide a basis for the Gaussian subspace. We introduce a new method for mixed ICA/PCA which we call Mixed ICA/PCA via Reproducibility Stability (MIPReSt). Our method uses a repeated estimations technique to rank sources by reproducibility, combined with decomposition of multiple subsamplings of the original data matrix. These multiple decompositions allow us to assess component stability as the size of the data matrix changes, which can be used to determinine the dimension of the nongaussian subspace in a mixture. We demonstrate the utility of MIPReSt for signal mixtures consisting of simulated sources and real-word (speech) sources, as well as mixture of unknown composition.

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Section: Discussionmentioning

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An algorithm for separation of mixed sparse and Gaussian sources

Akkalkotkar

Brown

2017

PLoS ONE

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“…The performance of MetICA was compared to other ICA algorithms (Table 1 ) using another non-targeted ICR/FT-MS-based metabolomics dataset (published data [ 57 ]). The data matrix counted initially 18591 signals measured in 51 urine samples from doped athletes, clean athletes and volunteers (non-athletes).…”

Section: Resultsmentioning

confidence: 99%

MetICA: independent component analysis for high-resolution mass-spectrometry based non-targeted metabolomics

et al. 2016

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BackgroundInterpreting non-targeted metabolomics data remains a challenging task. Signals from non-targeted metabolomics studies stem from a combination of biological causes, complex interactions between them and experimental bias/noise. The resulting data matrix usually contain huge number of variables and only few samples, and classical techniques using nonlinear mapping could result in computational complexity and overfitting. Independent Component Analysis (ICA) as a linear method could potentially bring more meaningful results than Principal Component Analysis (PCA). However, a major problem with most ICA algorithms is the output variations between different runs and the result of a single ICA run should be interpreted with reserve.ResultsICA was applied to simulated and experimental mass spectrometry (MS)-based non-targeted metabolomics data, under the hypothesis that underlying sources are mutually independent. Inspired from the Icasso algorithm, a new ICA method, MetICA was developed to handle the instability of ICA on complex datasets. Like the original Icasso algorithm, MetICA evaluated the algorithmic and statistical reliability of ICA runs. In addition, MetICA suggests two ways to select the optimal number of model components and gives an order of interpretation for the components obtained.ConclusionsCorrelating the components obtained with prior biological knowledge allows understanding how non-targeted metabolomics data reflect biological nature and technical phenomena. We could also extract mass signals related to this information. This novel approach provides meaningful components due to their independent nature. Furthermore, it provides an innovative concept on which to base model selection: that of optimizing the number of reliable components instead of trying to fit the data. The current version of MetICA is available at https://github.com/daniellyz/MetICA.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-016-0970-4) contains supplementary material, which is available to authorized users.

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“…Another research group has proposed to combine ICA with PCA. A new approach accommodated one or more Gaussian components in the ICA model and uses PCA to characterize contributions from this inseparable Gaussian subspace [73]. Successfully tested on the well-known Fisher's iris and Howells' craniometric data sets, mixed ICA/PCA was proven to be of potential interest in any chemical investigation, where the authenticity of blindly separated non-Gaussian sources might otherwise be questionable.…”

Section: Hybrid Approaches Based On Icamentioning

confidence: 99%

Independent components analysis (ICA) at the “cocktail-party” in analytical chemistry

Monakhova

Rutledge

2020

Talanta

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Independent components analysis (ICA) is a probabilistic method, whose goal is to extract underlying component signals, that are maximally independent and non-Gaussian, from mixed observed signals. Since the data acquired in many applications in analytical chemistry are mixtures of component signals, such a method is of great interest. In this article recent ICA applications for quantitative and qualitative analysis in analytical chemistry are reviewed. The following experimental techniques are covered: fluorescence, UV-VIS, NMR, vibrational spectroscopies as well as chromatographic profiles. Furthermore, we reviewed ICA as a preprocessing tool as well as existing hybrid ICA-based multivariate approaches. Finally, further research directions are proposed. Our review shows that ICA is starting to play an important role in analytical chemistry, and this will definitely increase in the future.

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How Many Separable Sources? Model Selection In Independent Components Analysis

Cited by 7 publications

References 46 publications

An algorithm for separation of mixed sparse and Gaussian sources

An algorithm for separation of mixed sparse and Gaussian sources

MetICA: independent component analysis for high-resolution mass-spectrometry based non-targeted metabolomics

Independent components analysis (ICA) at the “cocktail-party” in analytical chemistry

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