Regularization and grouping -omics data by GCA method: A transcriptomic case.

The paper presents the application of Grade Correspondence Analysis (GCA) and Grade Correspondence Cluster Analysis (GCCA) for ordering and grouping -omics datasets, using transcriptomic data as an example. Based on gene expression data describing 256 patients with Multiple Myeloma it was shown that the GCA method could be used to find regularities in the analyzed collections and to create characteristic gene expression profiles for individual groups of patients. GCA iteratively permutes rows and columns to maximize the tau-Kendall or rho-Spearman coefficients, which makes it possible to arrange rows and columns in such a way that the most similar ones remain in each other's neighbourhood. In this way, the GCA algorithm highlights regularities in the data matrix. The ranked data can then be grouped using the GCCA method, and after that aggregated in clusters, providing a representation that is easier to analyze-especially in the case of large sets of gene expression profiles. Regularization of transcriptomic data, which is presented in this manuscript, has enabled division of the data set into column clusters (representing genes) and row clusters (representing patients). Subsequently, rows were aggregated (based on medians) to visualise the gene expression profiles for patients with Multiple Myeloma in each collection. The presented analysis became the starting point for characterisation of differentiated genes and biochemical processes in which they are involved. GCA analysis may provide an alternative analytical method to support differentiation and analysis of gene expression profiles characterising individual groups of patients.