Multi-objective optimization for clustering 3-way gene expression data

The microarray technology allows to monitor the expression level of thousands of genes simultaneously. A typical experiment will for example compare gene expression between multiple biological samples such as tumor biopsies, or a single sample in response to a treatment over time. It is assumed that genes with similar function or sharing regulatory elements will display a common expression profile over a variety of biological conditions. Hence, classification methods are used to group genes according to their expression profile in a defined set of samples and/or to group samples based on the set of genes they express [1, 4]. Unsupervised classification methods or clustering are typically used when no a priori information is available on samples or genes [7, 2]. In biomedical research, you may want to study simultaneously different drugs in different experimental conditions (concentration, time point, . . . ) on a biological model, leading to the generation on 3-way data. To search for interesting genes, clustering can be performed separately for each drug. Doing in this way does not take into account the interaction between drugs and samples comparison conditions. In this paper, we used the Fuzzy C-Means method for clustering 3-way gene expression data via optimization of multiple objectives. A reformulation of the total criterion is used to obtain an expression which has less number of variables compared to the traditional FCM criterion. This transformation allows to use a global optimizer, the Genetic Algorithm, to partition genes into clusters of similar profile. Let T be the number of test drugs or data level and K the number of groups to get from the dataset containing N genes. The total criterion to minimize is given by the following equation: J(uki, ck) = T ∑