An Integrated QAP-Based Approach to Visualize Patterns of Gene Expression Similarity

This paper illustrates how the Quadratic Assignment Problem (QAP) is used as a mathematical model that helps to produce a visualization of microarray data, based on the relationships between the objects (genes or samples). The visualization method can also incorporate the result of a clustering algorithm to facilitate the process of data analysis. Specifically, we show the integration with a graph-based clustering algorithm that outperforms the results against other benchmarks, namely k−means and self-organizing maps. Even though the application uses gene expression data, the method is general and only requires a similarity function being defined between pairs of objects. The microarray dataset is based on the budding yeast (S. cerevisiae). It is composed of 79 samples taken from different experiments and 2,467 genes. The proposed method delivers an automatically generated visualization of the microarray dataset based on the integration of the relationships coming from similarity measures, a clustering result and a graph structure.