
Last edited by FishHead In 2014224 23:00 Editor
Many system can be viewed as an interacting network, where the nodes are the individuals we investigate and the edges represent the interaction between these nodes. If nodes are people, edges could be social connections. If nodes are genes, edges could be regulations. What we concern is the topology of this network, i.e. the distribution of these edges. Often, we face situations in which we donot know the network topology and what available is a set of insufficient data. In lab, it is time consuming and sometimes impossiple to do experiments with a sufficinet wide range of conditions. In social network, an observation covering a whole life span is also expensive. In such situations, we are hoping a full discription from incomplete
observations, which is an underdetermined problem in math. There is an interesting method called compressed sensing may achieve this goal.
math construction:
O=AX
O is a column vector of a set of observations from one node (e.g. a gene expression data in several conditoins). A is a matrix describing the specific kind of interaction this system holds. X is a column vector, of which every element represent the strength of edge between gene of vector O and other genes. Solving X is finding topology of this network, this is the job compressd sensing does.
Question are:
1. How to construct matrix A in such a way that it is handleable and a real reflection of biological system, i.e. reduce nonlinear interaction to a linear equation?
2. Is is roubust under noise?

