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Tensor Decomposition of Microarray Data Jennifer Staigar1 Dr. Stanley Dunn2 1 Department of Mathematics, Rutgers University 2 Department of Biomedical Engineering, Rutgers University Many mathematical techniques are used to analyze DNA microarray data, with Singular Value Decomposition and Principal Components Analysis the most common used to elucidate gene regulatory networks. These techniques use data that has been pre-processed for fluorescence level; we consider the problem of modeling the expression data as a tensor with three factors: genes, fluorescence channels, and experimental conditions. We tested this model using S. cerevisiae cell cycle raw microarray data from two different experiments. A CP tensor decomposition of the data suggests that the factor which represents experimental conditions was more heavily weighted towards the first experimental condition (30 minutes into the cell cycle) versus the second experimental condition (40 minutes into the cell cycle). The factor that represents fluorescence channel indicated that on average, the gene expression for the two experiments is less than the baseline. We observed that within a functional group of genes, the results suggest that the tensor decomposition yields a rank ordering of gene expression which is independent of experimental conditions. The question as to whether genes can be clustered by these tensor factors is still open. The support of the Rutgers University DIMACS REU is gratefully acknowledged.