bicACO: An Ant Colony Inspired Biclustering Algorithm

A recent proposal developed to avoid some of the drawbacks presented by standard clustering algorithms is the so-called biclustering technique [1], which performs clustering of rows and columns of the data matrix simultaneously, allowing the extraction of additional information from the dataset. Since the biclustering problem is combinatorial, and ant-based systems present several advantages when dealing with this kind of problems [2], in this work we propose an antinspired algorithm for biclustering, which was named bicACO. In order to adapt ACO to the biclustering problem some modifications must be made. First of all, each ant will have a separate pheromone table, mainly because the biclustering is a multimodal problem and requires that several different solutions be provided at the same time. In this way, indirect communication on bicACO occurs only among ants related to the same bicluster, but in different iterations of the algorithm. Additionally, each one of the k ants (the desired number of biclusters) starts from the full matrix and decides upon which row/column to remove, according to the probabilistic equation given in [2]. Each ant will repeat this step while the residue of the bicluster (defined in [1]) is above a given threshold δ or the volume is above a minimum value. The pheromone table will represent the probability (probabilistic factor of the algorithm) of removing a row or column from the full data matrix of dimension n×m, so that the pheromone table will have a size of n+m. The heuristic term of the probabilistic equation is defined as the average residue of a given row/column. The probability of removing a given row/column will become higher if the corresponding average residue is high when compared to the average residue of other rows/columns. After each ant has built a unique bicluster, the pheromone table must be updated (iterative improvement step) proportionally to the obtained results (as in [3]) and, in order to avoid stagnation, the pheromone value of the rows/columns that remained on the bicluster is reduced until τij < Δτi (Eq. 1). Once this lower limit is reached, the pheromone will automatically start to increase, in order to favor the exploration of the search space. { τij = τij + ρ.(Δτi − τij) for all j ∈ Bi Δτi = V oli/ri i V oli/ri , (1)