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Determining the optimal number of independent components for reproducible transcriptomic data analysis.

ABSTRACT: Independent 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.Here 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.We 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.

SUBMITTER: Kairov U

PROVIDER: S-EPMC5594474 | biostudies-literature | 2017 Sep

REPOSITORIES: biostudies-literature

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Determining the optimal number of independent components for reproducible transcriptomic data analysis.

Kairov Ulykbek U Cantini Laura L Greco Alessandro A Molkenov Askhat A Czerwinska Urszula U Barillot Emmanuel E Zinovyev Andrei A

BMC genomics 20170911 1

<h4>Background</h4>Independent 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.<h4>Results</h4>Here we address the ...[more]

PMID: 28893186

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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:BACKGROUND:Analyzing the human transcriptome is crucial in advancing precision medicine, and the plethora of over half a million human microarray samples in the Gene Expression Omnibus (GEO) has enabled us to better characterize biological processes at the molecular level. However, transcriptomic analysis is challenging because the data is inherently noisy and high-dimensional. Gene set analysis is currently widely used to alleviate the issue of high dimensionality, but the user-defined choice of gene sets can introduce biasness in results. In this paper, we advocate the use of a fixed set of transcriptomic modules for such analysis. We apply independent component analysis to the large collection of microarray data in GEO in order to discover reproducible transcriptomic modules that can be used as features for machine learning. We evaluate the usability of these modules across six studies, and demonstrate (1) their usage as features for sample classification, and also their robustness in dealing with small training sets, (2) their regularization of data when clustering samples and (3) the biological relevancy of differentially expressed features. RESULTS:We identified 139 reproducible transcriptomic modules, which we term fundamental components (FCs). In studies with less than 50 samples, FC-space classification model outperformed their gene-space counterparts, with higher sensitivity (p <?0.01). The models also had higher accuracy and negative predictive value (p <?0.01) for small data sets (less than 30 samples). Additionally, we observed a reduction in batch effects when data is clustered in the FC-space. Finally, we found that differentially expressed FCs mapped to GO terms that were also identified via traditional gene-based approaches. CONCLUSIONS:The 139 FCs provide biologically-relevant summarization of transcriptomic data, and their performance in low sample settings suggest that they should be employed in such studies in order to harness the data efficiently.

Dataset Information

Determining the optimal number of independent components for reproducible transcriptomic data analysis.

Publications

Determining the optimal number of independent components for reproducible transcriptomic data analysis.

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