Abstract
BackgroundThe main limitations of most existing clustering methods used in genomic data analysis include heuristic or random algorithm initialization, the potential of finding poor local optima, the lack of cluster number detection, an inability to incorporate prior/expert knowledge, black-box and non-adaptive designs, in addition to the curse of dimensionality and the discernment of uninformative, uninteresting cluster structure associated with confounding variables.ResultsIn an effort to partially address these limitations, we develop the VIsual Statistical Data Analyzer (VISDA) for cluster modeling, visualization, and discovery in genomic data. VISDA performs progressive, coarse-to-fine (divisive) hierarchical clustering and visualization, supported by hierarchical mixture modeling, supervised/unsupervised informative gene selection, supervised/unsupervised data visualization, and user/prior knowledge guidance, to discover hidden clusters within complex, high-dimensional genomic data. The hierarchical visualization and clustering scheme of VISDA uses multiple local visualization subspaces (one at each node of the hierarchy) and consequent subspace data modeling to reveal both global and local cluster structures in a "divide and conquer" scenario. Multiple projection methods, each sensitive to a distinct type of clustering tendency, are used for data visualization, which increases the likelihood that cluster structures of interest are revealed. Initialization of the full dimensional model is based on first learning models with user/prior knowledge guidance on data projected into the low-dimensional visualization spaces. Model order selection for the high dimensional data is accomplished by Bayesian theoretic criteria and user justification applied via the hierarchy of low-dimensional visualization subspaces. Based on its complementary building blocks and flexible functionality, VISDA is generally applicable for gene clustering, sample clustering, and phenotype clustering (wherein phenotype labels for samples are known), albeit with minor algorithm modifications customized to each of these tasks.ConclusionVISDA achieved robust and superior clustering accuracy, compared with several benchmark clustering schemes. The model order selection scheme in VISDA was shown to be effective for high dimensional genomic data clustering. On muscular dystrophy data and muscle regeneration data, VISDA identified biologically relevant co-expressed gene clusters. VISDA also captured the pathological relationships among different phenotypes revealed at the molecular level, through phenotype clustering on muscular dystrophy data and multi-category cancer data.
Highlights
The main limitations of most existing clustering methods used in genomic data analysis include heuristic or random algorithm initialization, the potential of finding poor local optima, the lack of cluster number detection, an inability to incorporate prior/expert knowledge, black-box and non-adaptive designs, in addition to the curse of dimensionality and the discernment of uninformative, uninteresting cluster structure associated with confounding variables
VIsual Statistical Data Analyzer (VISDA)'s sample clustering requires dimensionality reduction via unsupervised informative gene selection, whereas the phenotype clustering algorithm exploits the knowledge of phenotype labels in performing supervised informative gene selection, supervised data visualization, and statistical modeling that preserves the unity of samples from the same phenotype, which fulfils that in phenotype clustering known phenotypes, i.e. groups of samples with the same phenotype label, are taken as data objects to be clustered
We show that VISDA gives stable and improved clustering accuracy compared to several benchmark clustering methods, i.e. conventional agglomerative
Summary
The main limitations of most existing clustering methods used in genomic data analysis include heuristic or random algorithm initialization, the potential of finding poor local optima, the lack of cluster number detection, an inability to incorporate prior/expert knowledge, black-box and non-adaptive designs, in addition to the curse of dimensionality and the discernment of uninformative, uninteresting cluster structure associated with confounding variables. (1) Clustering methods such as KMC and mixture model fitting are sensitive to the quality of model initialization and may converge to poor local optima of the objective function, which will yield inaccurate clustering outcomes, especially when applied to genomic datasets that have high dimensionality and small sample size [2125]. (7) Many clustering algorithms have a non-adaptive nature, without a mechanism for incorporating and taking advantage of results from other methods or user knowledge These algorithms may fail badly without a "backup plan" when the algorithm's underlying statistical or geometric cluster assumptions are violated. These algorithms may fail badly without a "backup plan" when the algorithm's underlying statistical or geometric cluster assumptions are violated. (For the benefit of readers, we expand on each of these limitations in section 1 of Additional file 1.)
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