Dataset Information

How many separable sources? Model selection in independent components analysis.

ABSTRACT: Unlike mixtures consisting solely of non-Gaussian sources, mixtures including two or more Gaussian components cannot be separated using standard independent components analysis methods that are based on higher order statistics and independent observations. The mixed Independent Components Analysis/Principal Components Analysis (mixed ICA/PCA) model described here accommodates one or more Gaussian components in the independent components analysis model and uses principal components analysis to characterize contributions from this inseparable Gaussian subspace. Information theory can then be used to select from among potential model categories with differing numbers of Gaussian components. Based on simulation studies, the assumptions and approximations underlying the Akaike Information Criterion do not hold in this setting, even with a very large number of observations. Cross-validation is a suitable, though computationally intensive alternative for model selection. Application of the algorithm is illustrated using Fisher's iris data set and Howells' craniometric data set. Mixed ICA/PCA is of potential interest in any field of scientific investigation where the authenticity of blindly separated non-Gaussian sources might otherwise be questionable. Failure of the Akaike Information Criterion in model selection also has relevance in traditional independent components analysis where all sources are assumed non-Gaussian.

SUBMITTER: Woods RP

PROVIDER: S-EPMC4374758 | biostudies-literature | 2015

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

How many separable sources? Model selection in independent components analysis.

Woods Roger P RP Hansen Lars Kai LK Strother Stephen S

PloS one 20150326 3

Unlike mixtures consisting solely of non-Gaussian sources, mixtures including two or more Gaussian components cannot be separated using standard independent components analysis methods that are based on higher order statistics and independent observations. The mixed Independent Components Analysis/Principal Components Analysis (mixed ICA/PCA) model described here accommodates one or more Gaussian components in the independent components analysis model and uses principal components analysis to ch ...[more]

PMID: 25811988

Similar Datasets

Project description:BackgroundIndependent Component Analysis (ICA) is a method that models gene expression data as an action of a set of statistically independent hidden factors. The output of ICA depends on a fundamental parameter: the number of components (factors) to compute. The optimal choice of this parameter, related to determining the effective data dimension, remains an open question in the application of blind source separation techniques to transcriptomic data.ResultsHere we address the question of optimizing the number of statistically independent components in the analysis of transcriptomic data for reproducibility of the components in multiple runs of ICA (within the same or within varying effective dimensions) and in multiple independent datasets. To this end, we introduce ranking of independent components based on their stability in multiple ICA computation runs and define a distinguished number of components (Most Stable Transcriptome Dimension, MSTD) corresponding to the point of the qualitative change of the stability profile. Based on a large body of data, we demonstrate that a sufficient number of dimensions is required for biological interpretability of the ICA decomposition and that the most stable components with ranks below MSTD have more chances to be reproduced in independent studies compared to the less stable ones. At the same time, we show that a transcriptomics dataset can be reduced to a relatively high number of dimensions without losing the interpretability of ICA, even though higher dimensions give rise to components driven by small gene sets.ConclusionsWe suggest a protocol of ICA application to transcriptomics data with a possibility of prioritizing components with respect to their reproducibility that strengthens the biological interpretation. Computing too few components (much less than MSTD) is not optimal for interpretability of the results. The components ranked within MSTD range have more chances to be reproduced in independent studies.

Project description:BackgroundIndependent component analysis is an unsupervised machine learning algorithm that separates a set of mixed signals into a set of statistically independent source signals. Applied to high-quality gene expression datasets, independent component analysis effectively reveals both the source signals of the transcriptome as co-regulated gene sets, and the activity levels of the underlying regulators across diverse experimental conditions. Two major variables that affect the final gene sets are the diversity of the expression profiles contained in the underlying data, and the user-defined number of independent components, or dimensionality, to compute. Availability of high-quality transcriptomic datasets has grown exponentially as high-throughput technologies have advanced; however, optimal dimensionality selection remains an open question.MethodsWe computed independent components across a range of dimensionalities for four gene expression datasets with varying dimensions (both in terms of number of genes and number of samples). We computed the correlation between independent components across different dimensionalities to understand how the overall structure evolves as the number of user-defined components increases. We then measured how well the resulting gene clusters reflected known regulatory mechanisms, and developed a set of metrics to assess the accuracy of the decomposition at a given dimension.ResultsWe found that over-decomposition results in many independent components dominated by a single gene, whereas under-decomposition results in independent components that poorly capture the known regulatory structure. From these results, we developed a new method, called OptICA, for finding the optimal dimensionality that controls for both over- and under-decomposition. Specifically, OptICA selects the highest dimension that produces a low number of components that are dominated by a single gene. We show that OptICA outperforms two previously proposed methods for selecting the number of independent components across four transcriptomic databases of varying sizes.ConclusionsOptICA avoids both over-decomposition and under-decomposition of transcriptomic datasets resulting in the best representation of the organism's underlying transcriptional regulatory network.

Project description:BackgroundCultivated rice species (Oryza sativa L. and O. glaberrima Steud.) are generally considered among the crop species most sensitive to salt stress. A handful of lines are known to be tolerant, and a small number of these have been used extensively as donors in breeding programs. However, these donors use many of the same genes and physiological mechanisms to confer tolerance. Little information is available on the diversity of mechanisms used by these species to cope with salt stress, and there is a strong need to identify varieties displaying additional physiological and/or genetic mechanisms to confer higher tolerance.ResultsHere we present data on 103 accessions from O. sativa and 12 accessions from O. glaberrima, many of which are identified as salt tolerant for the first time, showing moderate to high tolerance of high salinity. The correlation of salinity-induced senescence (as judged by the Standard Evaluation System for Rice, or SES, score) with whole-plant and leaf blade Na+ concentrations was high across nearly all accessions, and was almost identical in both O. sativa and O. glaberrima. The association of leaf Na+ concentrations with cultivar-groups was very weak, but association with the OsHKT1;5 allele was generally strong. Seven major and three minor alleles of OsHKT1;5 were identified, and their comparisons with the leaf Na+ concentration showed that the Aromatic allele conferred the highest exclusion and the Japonica allele the least. A number of exceptions to this association with the Oryza HKT1;5 allele were identified; these probably indicate the existence of additional highly effective exclusion mechanisms. In addition, two landraces were identified, one from Thailand and the other from Senegal, that show high tissue tolerance.ConclusionsSignificant variation in salinity tolerance exists within both cultivated Oryza species, and this is the first report of significant tolerance in O. glaberrima. The majority of accessions display a strong quantitative relationship between tolerance and leaf blade Na+ concentration, and thus the major tolerance mechanisms found in these species are those contributing to limiting sodium uptake and accumulation in active leaves. However, there appears to be genetic variation for several mechanisms that affect leaf Na+ concentration, and rare cases of accessions displaying different mechanisms also occur. These mechanisms show great promise for improving salt tolerance in rice over that available from current donors.

Dataset Information

How many separable sources? Model selection in independent components analysis.

Publications

How many separable sources? Model selection in independent components analysis.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets