is to speed up the computation of eigenvectors. Recently mathematicians have found that “random projections” can compress the information in a large matrix into a smaller matrix while essentially preserving the same eigenvectors. The compressed matrix can be used as a proxy for the original matrix, and SVD can then proceed with less computational cost.
One of Google’s biggest challenges is to guard the integrity of PageRanks against spammers. By building up artificial networks of links, spammers undercut the underlying assumption that a Web link represents a human judgment about the value of a Web page. While Google has refined the PageRank algorithm many times over to ferret out fake links, keeping ahead of the spammers is an ongoing mathematical science challenge.
2 / When the gene expressions for the C57BL/6J and A/J strains of mice are compared, it is possible to find gene networks using eigenvectors that are specific for brain regions, independent of genetic background. Image from S. de Jong, T.F. Fuller, E. Janson, E. Strengman, S. Horvath, M.J.H. Kas, and R.A. Ophoff, 2010, Gene expression profiling in C57BL/6J and A/J mouse inbred strains reveals gene networks specific for brain regions independent of genetic background, BMC Genomics 11:20. /