The software listed in this site is for non-commercial use only. It is provided as is, and it comes with no guaranttee. Neither current and former members of Glazebrook and Katagiri Labs nor Univ. of Minnesota are responsible for any damage caused by use of the software.

The Perl script for LEGG (locally linear embedding graph generator) can be downloaded here ("legg_v1p1.pl").

LEGG uses locally linear embedding (LLE; Roweis and Saul (2000)) to capture the relationships among the data points in local areas and represents the relationships as a directed graph. LLE is a non-linear dimensionality reduction procedure, in which a particular data point is best approximated by a linear combination of its neighboring data points. A neighbor data point that does not improve the approximation is removed as it represents information redundant with that represented by other (closer) neighbors. Using the LLE dimensionality reduction procedure, LEGG removes links that represent redundant information from a graph generated by connecting k-neighbors. In addition, the direction of each link represents information content relationships between two data points connected by the link. The mathematical principle of LEGG is the same as that of LCF (local context finder; Katagiri and Glazebrook (2003)). While LCF used an optimization algorithm to find the solution for LLE, LEGG's algorithm explicitly determines the solution. So, the solution is determined faster and more accurately in LEGG than LCF.

The script "legg_v1p1.pl"requires the Perl module "Math::MatrixReal". To visualize the relationship graph, "Pajek" is required. A tab-delimited text input file is required. LEGG explores the relationships among the columns using the rows as the parameters to describe each column. For example, if you want to compare the relationships among the samples in an expression profile data set, you need to have the samples as columns and the genes as rows in the input table.

.The script generates two output files:
(1) .txt file: This file is a record of various parameters determined by LEGG. For example, the fit of a LLE procedure for a particular data point, its neighbors used, and the coefficients in the linear combination for the neighbors.
(2) .net file: This file can be fed into Pajek to visualize the relationship graph.

Here is a more detailed description of the script.

This is a very minimal how to use Pajek to visualize the graph.