DNA analysis by microarrays is a powerful tool that allows replication of the RNA of hundreds of thousands of genes at the same time, generating a large amount of data in multidimensional space that must be analyzed using informatics tools. Various clustering techniques have been applied to analyze the microarrays, but they do not offer a systematic form of analysis. This paper proposes the use of Zinovyev's Elastic Net in an iterative way to find patterns of up-regulated genes. The new method proposed has been evaluated with up-regulated genes of the Escherichia Coli k12 bacterium and is compared with the Self-Organizing Maps (SOM) technique frequently used in this kind of analysis. The results show that the proposed method finds 87% of the up-regulated genes, compared to 65% of genes found by the SOM. A comparative analysis of Receiver Operating Characteristic with SOM shows that the proposed method is 12% more effective.