Most Tensor Problems Are NP-Hard
Journal of the ACM (JACM)
| Hi-index | 3.84 |
Motivation: Developmental transcriptional networks in plants and animals operate in both space and time. To understand these transcriptional networks it is essential to obtain whole-genome expression data at high spatiotemporal resolution. Substantial amounts of spatial and temporal microarray expression data previously have been obtained for the Arabidopsis root; however, these two dimensions of data have not been integrated thoroughly. Complicating this integration is the fact that these data are heterogeneous and incomplete, with observed expression levels representing complex spatial or temporal mixtures. Results: Given these partial observations, we present a novel method for reconstructing integrated high-resolution spatiotemporal data. Our method is based on a new iterative algorithm for finding approximate roots to systems of bilinear equations. Availability: Source code for solving bilinear equations is available at http://math.berkeley.edu/~dustin/bilinear/. Visualizations of reconstructed patterns on a schematic Arabidopsis root are available at http://www.arexdb.org/. Contact: dustin@math.berkeley.edu Supplementary information:Supplementary data are available at Bioinformatics online.