Entropy embedding and fluctuation analysis in genomic manifolds

The complexity of typically high-dimensional genomic data requires computational work prone to integrate different biological information sources through efficient model solutions. Usually, one step involves dimensionality reduction (DR), which requires projecting the input data onto a low dimensional subspace, and often leads to an embedding. Thus, DR should be able to filter out the uninformative dimensions and recover the original variables. This step is of crucial relevance for any reverse engineering and statistical inference attempt to reconstruct the dynamics underlying the biological systems under study, i.e. the interactions between its genes or proteins. DR has become almost a standard practice just following the pre-processing steps typically applied to the experimental measurements (mining, normalization, etc.). In this work, the data for the analysis reflect expression values of genes whose dynamics are affected by perturbation experiments. In particular, the aims are to monitor the response of genes involved in a certain pathway, and then to isolate their biological variability from any possible external influence. Last, it is of interest to control the stability of the system; with this regard, we look at dynamical aspects of data through embedding theory and entropy fluctuation analysis. We demonstrate that a redundant biological system can in principle be reduced to a minimal number of almost independent components. In particular, such structures detect the higher-order statistical dependencies in the training data in addition to the correlations. Two popular DR techniques are compared in relation to their ability to extract the most salient features, allow gene selection, and minimize the various interferences due to algorithmic approximation errors and variable noise covers.