A survey of some tensor analysis techniques for biological systems

Background: Since biological systems are complex and often involve multiple types of genomic relationships, tensor analysis methods can be utilized to elucidate these hidden complex relationships. There is a pressing need for this, as the interpretation of the results of high-throughput experiments has advanced at a much slower pace than the accumulation of data. Results: In this review we provide an overview of some tensor analysis methods for biological systems. Conclusions: Tensors are natural and powerful generalizations of vectors and matrices to higher dimensions and play a fundamental role in physics, mathematics and many other areas. Tensor analysis methods can be used to provide the foundations of systematic approaches to distinguish significant higher order correlations among the elements of a complex systems via finding ensembles of a small number of reduced systems that provide a concise and representative summary of these correlations. [Figure not available: see fulltext.]