Interactive knowledge discovery and data mining on genomic expression data with numeric formal concept analysis

Jose M González-Calabozo, Francisco J Valverde-Albacete, Carmen Peláez-Moreno

Gene Expression Data (GED) analysis poses a great challenge to the scientific community that can be framed into the Knowledge Discovery in Databases (KDD) and Data Mining (DM) paradigm. Biclustering has emerged as the machine learning method of choice to solve this task, but its unsupervised nature makes result assessment problematic. This is often addressed by means of Gene Set Enrichment Analysis (GSEA). We put forward a framework in which GED analysis is understood as an Exploratory Data Analysis (EDA) process where we provide support for continuous human interaction with data aiming at improving the step of hypothesis abduction and assessment. We focus on the adaptation to human cognition of data interpretation and visualization of the output of EDA. First, we give a proper theoretical background to bi-clustering using Lattice Theory and provide a set of analysis tools revolving around [Formula: see text]-Formal Concept Analysis ([Formula: see text]-FCA), a lattice-theoretic unsupervised learning technique for real-valued matrices. By using different kinds of cost structures to quantify expression we obtain different sequences of hierarchical bi-clusterings for gene under- and over-expression using thresholds. Consequently, we provide a method with interleaved analysis steps and visualization devices so that the sequences of lattices for a particular experiment summarize the researcher's vision of the data. This also allows us to define measures of persistence and robustness of biclusters to assess them. Second, the resulting biclusters are used to index external omics databases-for instance, Gene Ontology (GO)-thus offering a new way of accessing publicly available resources. This provides different flavors of gene set enrichment against which to assess the biclusters, by obtaining their p-values according to the terminology of those resources. We illustrate the exploration procedure on a real data example confirming results previously published. The GED analysis problem gets transformed into the exploration of a sequence of lattices enabling the visualization of the hierarchical structure of the biclusters with a certain degree of granularity. The ability of FCA-based bi-clustering methods to index external databases such as GO allows us to obtain a quality measure of the biclusters, to observe the evolution of a gene throughout the different biclusters it appears in, to look for relevant biclusters-by observing their genes and what their persistence is-to infer, for instance, hypotheses on their function.