MOTIVATION: In consensus clustering, a clustering algorithm is used in combination with a subsampling procedure to detect stable clusters. Previous studies on both simulated and real data suggest that consensus clustering outperforms native algorithms. RESULTS: We extend here consensus clustering to allow for attribute weighting in the calculation of pairwise distances using existing regularized approaches. We propose a procedure for the calibration of the number of clusters (and regularization parameter) by maximizing the sharp score, a novel stability score calculated directly from consensus clustering outputs, making it extremely computationally competitive. Our simulation study shows better clustering performances of (i) approaches calibrated by maximizing the sharp score compared to existing calibration scores and (ii) weighted compared to unweighted approaches in the presence of features that do not contribute to cluster definition. Application on real gene expression data measured in lung tissue reveals clear clusters corresponding to different lung cancer subtypes. AVAILABILITY AND IMPLEMENTATION: The R package sharp (version ≥1.4.3) is available on CRAN at https://CRAN.R-project.org/package=sharp.

Most popular dimension reduction (DR) methods like t-SNE and UMAP are based on minimizing a cost between input and latent pairwise similarities. Though widely used, these approaches lack clear probabilistic foundations to enable a full understanding of their properties and limitations. To that extent, we introduce a unifying statistical framework based on the coupling of hidden graphs using cross entropy. These graphs induce a Markov random field dependency structure among the observations in both input and latent spaces. We show that existing pairwise similarity DR methods can be retrieved from our framework with particular choices of priors for the graphs. Moreover this reveals that these methods relying on shift-invariant kernels suffer from a statistical degeneracy that explains poor performances in conserving coarse-grain dependencies. New links are drawn with PCA which appears as a non-degenerate graph coupling model.

BACKGROUND: In unsupervised learning and clustering, data integration from different sources and types is a difficult question discussed in several research areas. For instance in omics analysis, dozen of clustering methods have been developed in the past decade. When a single source of data is at play, hierarchical clustering (HC) is extremely popular, as a tree structure is highly interpretable and arguably more informative than just a partition of the data. However, applying blindly HC to multiple sources of data raises computational and interpretation issues. RESULTS: We propose mergeTrees, a method that aggregates a set of trees with the same leaves to create a consensus tree. In our consensus tree, a cluster at height h contains the individuals that are in the same cluster for all the trees at height h. The method is exact and proven to be [Formula: see text], n being the individuals and q being the number of trees to aggregate. Our implementation is extremely effective on simulations, allowing us to process many large trees at a time. We also rely on mergeTrees to perform the cluster analysis of two real -omics data sets, introducing a spectral variant as an efficient and robust by-product. CONCLUSIONS: Our tree aggregation method can be used in conjunction with hierarchical clustering to perform efficient cluster analysis. This approach was found to be robust to the absence of clustering information in some of the data sets as well as an increased variability within true clusters. The method is implemented in R/C++ and available as an R package named mergeTrees, which makes it easy to integrate in existing or new pipelines in several research areas.

Networks provide a natural yet statistically grounded way to depict and understand how a set of entities interact. However, in many situations interactions are not directly observed and the network needs to be reconstructed based on observations collected for each entity. Our work focuses on the situation where these observations consist of counts. A typical example is the reconstruction of an ecological network based on abundance data. In this setting, the abundance of a set of species is collected in a series of samples and/or environments and we aim at inferring direct interactions between the species. The abundances at hand can be, for example, direct counts of individuals (ecology of macro-organisms) or read counts resulting from metagenomic sequencing (microbial ecology). Whatever the approach chosen to infer such a network, it has to account for the peculiaraties of the data at hand. The first, obvious one, is that the data are counts, i.e. non continuous. Also, the observed counts often vary over many orders of magnitude and are more dispersed than expected under a simple model, such as the Poisson distribution. The observed counts may also result from different sampling efforts in each sample and/or for each entity, which hampers direct comparison. Furthermore, because the network is supposed to reveal only direct interactions, it is highly desirable to account for covariates describing the environment to avoid spurious edges. Many methods of network reconstruction from count data have been proposed. In the context of microbial ecology, most methods (SparCC, REBACCA, SPIEC-EASI, gCODA, BanOCC) rely on a two-step strategy: transform the counts to pseudo Gaussian observations using simple transforms before moving back to the setting of Gaussian Graphical Models, for which state of the art methods exist to infer the network, but only in a Gaussian world. In this work, we consider instead a full-fledged probabilistic model with a latent layer where the counts follow Poisson distributions, conditional to latent (hidden) Gaussian correlated variables. In this model, known as Poisson log-normal (PLN), the dependency structure is completely captured by the latent layer and we model counts, rather than transformations thereof. To our knowledge, the PLN framework is quite new and has only been used by two other recent methods (Mint and plnDAG) to reconstruct networks from count data. In this work, we use the same mathematical framework but adopt a different optimization strategy which alleviates the whole optimization process. We also fully exploit the connection between the PLN framework and generalized linear models to account for the peculiarities of microbiological data sets. The network inference step is done as usual by adding sparsity inducing constraints on the inverse covariance matrix of the latent Gaussian vector to select only the most important interactions between species. Unlike the usual Gaussian setting, the penalized likelihood is generally not tractable in this framework. We resort instead to a variational approximation for parameter inference and solve the corresponding optimization problem by alternating a gradient descent on the variational parameters and a graphical-Lasso step on the covariance matrix. We also select the sparsity parameter using the resampling-based StARS procedure. We show that the sparse PLN approach has better performance than existing methods on simulated datasets and that it extracts relevant signal from microbial ecology datasets. We also show that the inference scales to datasets made up of hundred of species and samples, in line with other methods in the field. In short, our contributions to the field are the following: we extend the use of PLN distributions in network inference by (i) accounting for covariates and offset and thus removing some spurious edges induced by confounding factors, (ii) accounting for different sampling effort to integrate data sets from different sources and thus infer interactions between different types of organisms (e.g. bacteria - fungi), (iii) developing an inference procedure based on the iterative optimization of a well defined objective function. Our objective function is a provable lower bound of the observed likelihood and our procedure accounts for the uncertainty associated with the estimation of the latent variable, unlike the algorithm presented in Mint and plnDAG.

SUMMARY: The R package SIMoNe (Statistical Inference for MOdular NEtworks) enables inference of gene-regulatory networks based on partial correlation coefficients from microarray experiments. Modelling gene expression data with a Gaussian graphical model (hereafter GGM), the algorithm estimates non-zero entries of the concentration matrix, in a sparse and possibly high-dimensional setting. Its originality lies in the fact that it searches for a latent modular structure to drive the inference procedure through adaptive penalization of the concentration matrix. AVAILABILITY: Under the GNU General Public Licence at http://cran.r-project.org/web/packages/simone/